Team: Kerui Geng (Graduate student)

Project: Predicting consumers' following number of purchases based on their reviews and item characteristics

Github link: https://keruigeng.github.io (This link is a link to the github.io site); https://github.com/keruigeng/keruigeng.github.io/tree/master (This link is a link where you can find all the data, data are in the master branch)

Introduction¶

My plan is to use the combined dataset to predict consumers' future purchasing quantity based on their one-time purchase information. To achieve this, I take four main steps:

I combine product-level datasets from amazon with manufacturer datasets from People Data Lab.
I cleaned the previous combined data. To get the numerical aspect of the item characteristic, I subtract numerical information from string variables and split the category-subcategory variable into a set of categorical variables.
I analyze the data and find out the correlation between item characteristics and consumer's review rating with future purchasing quantiles. I also plot the consumer's future purchasing quantiles versus some item characteristics and consumer's review rating to explore their non-linear relationship.
I train a linear regression to explore whether consumer review can predict future purchasing quantiles. I also train a K-nearest neighborhood model and look at their test performance with consumer's review and without consumer's review indicators. To better predict the consumers' following number of purchases, I choose the random forest model as my prediction model and predict the future purchasing quantities bought.

In marketing, a good shopping experience here, measured based on a consumer's review rating, would boost consumers' trust in the seller, thus stimulating more purchases. In economics, some products are complementary, meaning consumers gain more utility if they consume several products together. Therefore, some item characteristics might predict the consumers' following purchasing quantity. In sum, my project mainly deals with those two questions:

(1): Do consumer's review ratings predict their following purchasing quantity?
(2): Can consumer's review rating and item characteristics predict consumers' following number of purchases well?

Hopefully, this project shield light on the importance of consumer review in predicting their future purchasing quantities. In addition, this project tries to create a system that can help online sellers predict consumers' future purchasing quantities. Understanding consumers' future purchasing quantities can help sellers adjust their goods in stock and change their marketing strategy. Those are important for the seller's total sales and potentially boost seller profits.

The following code will import the libraries that I will use throughout this project.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

##These two things can widen the notebook.
from IPython.core.display import display, HTML
display(HTML("<style>.container { width:95% !important; }</style>"))

Extraction, Transform, and Load (ETL)¶

Product Data:

The data is downloaded from data.world. This open and free platform provides rich data to the public. I download the Fashion products on Amazon.com from this platform (https://data.world/promptcloud/fashion-products-on-amazon-com). Fashion products on Amazon.com is a pre-crawled dataset, taken as a subset of a larger dataset (more than 7 million fashion products) created by extracting data from Amazon.

This dataset contains consumer-product level purchasing information. There are two sets of features. One set is the consumer's review rating, including the average review rating, the consumer's own review rating after purchasing, the gap between the consumer's own review rating and average review rating, and the number of reviews. The set of features is item characteristics, including the item price, category, manufacturer, number available in stock, etc. For labels, it tracks the consumers' other purchasing quantities after reviewing or buying this item. This data is beneficial for my project questions. It contains a rich set of product information for every purchase. Meanwhile, it tracks this consumer's other purchasing behavior after buying or viewing this product. This can help predict consumers' following purchasing behavior based on their current buying information.

###load the product level data
product_raw=pd.read_csv('./amazon_co_ecommerce_sample.csv')
product_raw

Manufacturer Data:

The manufacturer data is downloaded from People Data Lab. The data can be accessed here: https://pdl.ai/3Jh6dCb. This dataset contains manufacturer information for the global companies, including company country, industry, et al. This data can be merged with product-level data to obtain more manufacturer information, such as their location, year founded, and company size.

###load the manufacturer level data
manufacturer=pd.read_csv('https://pdl.ai/3Jh6dCb',compression='gzip', on_bad_lines='skip',lineterminator='\n',usecols=['country', 'founded','industry','locality','name','region','size'])
manufacturer

The next step is to combine the product data sets with manufacturer data. Since I am mainly interested in consumers' following purchasing quantities based on the item features, left join on product data is conducted here.

#manufacturer is the key variable to merge with company level data. drop the missing value of manufacturer
product_raw=product_raw.dropna(subset=['manufacturer'])
#merge the product data with manufacturer data
product_df=product_raw.merge(manufacturer,left_on='manufacturer',right_on='name',how='left')
product_df

Cleaning the product Data

Now the product data is ready. The next step is to clean the data. This includes getting numerical information from string variables, splitting the category-subcategory variable into a set of category variables, dropping the unnecessary variables, and dealing with missing data.

The first thing I should do is get numerical information from string variables. For example, string £9.99 can be extracted as a numerical value 9.99. Variables, "price", "number_available_in_stock", 'average_review_rating' and 'customer_review', are strings. I will get the numerical element of those variables. I create a new variable, customer review gap, which is the difference between customer_review and average_review_rating. For labels, I get the number of items bought after buying or viewing this product from two string labels.

product=product_df.copy()
#Iterm characteristics, "price", "number_available_in_stock" are string. I need the numerical element of those varibale.
product['price']=pd.to_numeric(product['price'].str.replace('£',''),errors='coerce')
product['number_available_in_stock']=product.number_available_in_stock.str.replace('new','')
product['number_available_in_stock']=product.number_available_in_stock.str.replace('used','')
product['number_available_in_stock']=pd.to_numeric(product['number_available_in_stock'].str.strip(),errors='coerce')

#Geting Consumer review rating numerical value from Consumer review string variables
product['average_review_rating']=pd.to_numeric(product.average_review_rating.str.replace('out of 5 stars','').str.strip())
product=product[-product['customer_reviews'].str.split('//').isna()]
product['customer_review']=0
a=product['customer_reviews'].str.split('//')
for i in range(len(a)):
  product['customer_review'][i]=a.iloc[i][1]
product['customer_review']=pd.to_numeric(product['customer_review'],errors='coerce') 
product['customer review gap']=product['customer_review']-product['average_review_rating']

#For labels, I get the quantity of items bought after buying or viewing this product from the followung two string labels.
product['Number of items bought after buying this item']=product.customers_who_bought_this_item_also_bought.str.count('http://www.amazon').fillna(0)
product['Number of items bought after viewing this item']=product.items_customers_buy_after_viewing_this_item.str.count('http://www.amazon').fillna(0)

The second thing I do is to split the category-subcategory variable into a set of category variables. "amazon_category_and_sub_category" is a string that denotes the categories and subcategories of items. There are multiple subcategories for one product. To model the impact of each subcategory, I transform this variable into a set of categorical variables.

product[['category','sub_category_1','sub_category_2','sub_category_3','sub_category_4']]=product.amazon_category_and_sub_category.str.split('>', expand=True)
product[['category','sub_category_1','sub_category_2','sub_category_3','sub_category_4']]

The third thing I do is to drop the unnecessary variables. Item 'uniq_id','product_name', 'sellers', 'amazon_category_and_sub_category', 'customers_who_bought_this_item_also_bought', 'description', 'product_information', 'product_description','items_customers_buy_after_viewing_this_item', 'customer_questions_and_answers','customer_reviews' are the information that is hard to quantify. I didn't need them to predict the consumer's following purchasing quantity. Therefore, I drop them here.

columns_to_drop=['uniq_id','product_name','sellers','amazon_category_and_sub_category','customers_who_bought_this_item_also_bought','description','product_information', 'product_description', 'items_customers_buy_after_viewing_this_item', 'customer_questions_and_answers','customer_reviews']
product=product.drop(columns_to_drop,axis=1)
product

The last thing I do is dealing with missing data. For quantitive variable, fill the missing value with variable mean. For qualatitive variable, fill the missing value with variable 0.

###For quantitive variable, fill the missing value with variable mean
product.fillna(product.mean(),inplace=True)
###For qualatitive variable, fill the missing value with variable 0
product.fillna(0,inplace=True)

/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:2: FutureWarning: Dropping of nuisance columns in DataFrame reductions (with 'numeric_only=None') is deprecated; in a future version this will raise TypeError.  Select only valid columns before calling the reduction.

###The data--product now is tidy, and suitful for analysis and prediction.
product.head()

Exploratory Data Analysis (EDA)¶

With the clean and tiny data, I can start to look at what it tells. This can be done in several steps. Firstly, I will look at the description of numerical variables, which gives us basic distribution information about my data. Then I look at the distribution of the following purchasing quantity. Next, I will examine the correlation between consumer review ratings and some important item characteristics with the following purchasing quantity. Lastly, I will use line plots of labels with respect to some features to show their non-linear relationship.

Firstly, check the distributions of numerical variables

##Look the basic information of numerical variable:range, mean and counts. Pay attention to extreme values. They might make no sense
product.describe()

Secondly, look at the distribution of the labels I am interested in. There are two labels I am interested in. One is number of items bought after buying this item. The other is number of items bought after viewing this item. I check the number of items for each purchasing quantity and use the histograms to show their distributions.

#check the number of items for each purchasing quantity
print(product['Number of items bought after buying this item'].value_counts())
print(product['Number of items bought after viewing this item'].value_counts())

6.0     7339
0.0     1068
1.0      424
5.0      361
2.0      321
4.0      239
3.0      235
12.0      15
10.0       1
Name: Number of items bought after buying this item, dtype: int64
4.0    5417
0.0    3063
1.0     608
2.0     507
3.0     408
Name: Number of items bought after viewing this item, dtype: int64

fig, (ax1,ax2) =plt.subplots(1,2,figsize=(13,7))
ax1.hist(product['Number of items bought after buying this item'])
ax1.set_xlabel('Number of items bought after buying this item')
ax2.hist(product['Number of items bought after viewing this item'])
ax2.set_xlabel('Number of items bought after viewing this item')

Text(0.5, 0, 'Number of items bought after viewing this item')

The majority of the number of items bought after buying this item is 6. Similarly, the majority of the number of items purchased after viewing this item is 4. There are just a few outliers. Even though not distributed symmetrically, they only have several values, and the range is small. So the skewness here doesn't affect my prediction.

Thirdly, look at the correlation between each variable and the following purchasing quantities. Some are positive, while others are negative. Therefore, I plot the correlation in an ascending order.

##check the correlation of outcome variable and item features to see their raw linear relationship
quantity_corr=product.corr()[['Number of items bought after buying this item','Number of items bought after viewing this item']].drop(['Number of items bought after buying this item','Number of items bought after viewing this item'])
quantity_corr['Number of items bought after buying this item'].sort_values().plot.bar(title ='Correlation for Number of items bought after buying this item',figsize=(9,5))
plt.show()
quantity_corr['Number of items bought after viewing this item'].sort_values().plot.bar(title ='Correlation for Number of items bought after viewing this item',figsize=(9,5))

<matplotlib.axes._subplots.AxesSubplot at 0x7f1242ca91d0>

The above figures show that the "number_available_in_stock" has a high and positive correlation with labels. The correlations of "price" with outcome variables are negative and small. The correlation of labels with 'Number_of_answered_questions' is nearly zero. However, those don't mean item characteristics have no power to predict consumers' following purchasing quantities. Category and subcategory may contribute to predicting but are not presented in the above figures.

For consumer review, 'average_review_rating' has a high and negative correlation with labels. 'number_of_reviews' and 'customer review gap' have positive but smaller correlations with labels. However, 'customer review' negatively correlates with labels, even though it is small. It is out of my guess. The correlation only shows the linear relationship. Therefore, I will show some non-linear relationships using some line plot in the ne

Lastly, use line plots of labels with respect to some features to show their non-linear relationship.

show the non-linear relationship of number available in stock with labels using line plots

#There are too many observations and highly non-linear relationshp. Therefore, I use the mean of labels for a certain range of number available in stock to smooth the line.
#The following three line codes calculate the average number of items bought for a 4 width interval.
product['number_available_in_stock_1']=round(product['number_available_in_stock']/3)*3
y_1=product.groupby('number_available_in_stock_1')['Number of items bought after buying this item'].mean()
y_2=product.groupby('number_available_in_stock_1')['Number of items bought after viewing this item'].mean()

product=product.drop('number_available_in_stock_1',axis=1)
x_1=pd.Series(y_1.index)
plt.rcParams["figure.figsize"] = (11,6)
plt.plot(x_1, y_1, 'r-')
plt.xlabel('Number available in stock')
plt.ylabel('Number of items bought')
plt.plot(x_1, y_2, 'g-')
plt.ylim(0,8)
plt.legend(["Number of items bought after buying this item", "Number of items bought after viewing this item"])

<matplotlib.legend.Legend at 0x7f1242c39350>

The above figures show that consumers bought more products after buying an item for the same number available in stock compared with that viewing an item. In addition, as "number_available_in_stock" increases, the number of items customers bought increases. But their relationship is not strictly linear. Therefore, the non-linear machine learning algorithm might work well in modeling their relationship.

show the non-linear relationship of "average_review_rating" and "customer review gap" with labels using line plots

#similar to the previous figure
product['average_review_rating_1']=round(product['average_review_rating']/3,2)*3
y_1=product.groupby('average_review_rating_1')['Number of items bought after buying this item'].mean()
y_2=product.groupby('average_review_rating_1')['Number of items bought after viewing this item'].mean()
product=product.drop('average_review_rating_1',axis=1)
x_1=pd.Series(y_1.index)
plt.rcParams["figure.figsize"] = (11,6)
plt.plot(x_1, y_1, 'r-')
plt.xlabel('Average review rating')
plt.ylabel('Number of items bought')
plt.plot(x_1, y_2, 'g-')
plt.ylim(0,10)
plt.legend(["Number of items bought after buying this item", "Number of items bought after viewing this item"])
plt.show()

product['customer review gap 1']=round(product['customer review gap']/3,1)*3
y_1=product.groupby('customer review gap 1')['Number of items bought after buying this item'].mean()
y_2=product.groupby('customer review gap 1')['Number of items bought after viewing this item'].mean()
product=product.drop('customer review gap 1',axis=1)
x_1=pd.Series(y_1.index)
plt.rcParams["figure.figsize"] = (11,6)
plt.plot(x_1, y_1, 'r-')
plt.xlabel('Customer review rating gap')
plt.ylabel('Number of items bought')
plt.plot(x_1, y_2, 'g-')
plt.ylim(0,8)
plt.legend(["Number of items bought after buying this item", "Number of items bought after viewing this item"])

<matplotlib.legend.Legend at 0x7f1242c06410>

The above figures show that for the same customer review rating, consumers bought more products after buying an item compared with that viewing an item. In addition, we can see as the average review rating exhibits a non-linearly relationship with the number of items bought, especially when the average review rating exceeds 3.5. The same is true for the customer review rating gap. Therefore, the non-linear machine learning algorithm might work well in modeling their relationship.

The relationship of term caegory has not be presented in the above analysis. In the following part, I will show the relationship of number of items bought with item catogories to see their non-linear relationship.

df_1 = product.groupby('category').mean().sort_values('Number of items bought after buying this item',ascending=False)
df_2=df_1[['Number of items bought after buying this item','Number of items bought after viewing this item']]
df_2.plot(kind = 'bar',figsize=(14,10))

<matplotlib.axes._subplots.AxesSubplot at 0x7f1242aaca50>

The above figure shows that there are significant differences in the following purchasing quantities among categories. For example, the average number of items bought after buying this item is 6 for office supplies. However, the average number for novelty jewelry is zero. Therefore, using a set of dummies to measure item categories is expected to have a strong predictive power for following purchasing quantities.

Model Fitting and Prediction¶

I will train different models to explore my two project questions in this part. To analyze the first question (Do consumer review ratings predict their following purchasing quantity?), I will take the next two steps. Firstly, I will train a linear regression to test whether consumers' review rating matters for predicting the following purchasing quantities. Secondly, I will train a K-nearest neighbor (KNN) model to see whether including the consumer's review rating will affect the prediction score.

Besides, I will explore the second question: Can consumer review ratings and item characteristics predict consumers' following number of purchases well? Firstly, I train a KNN model using and calculating its prediction performance. Next, I train a random forest regression model to calculate its prediction performance. Lastly, based on the performance of those two models, I choose one that achieves the best performance and plots the predicted labels versus actual labels.

#get the features and transform the categorical vaariables into a set of dummies.
X_selected=product.drop(['Number of items bought after buying this item','Number of items bought after viewing this item'],axis=1)
###Transform the categorical variable into dummies.
X=pd.get_dummies(X_selected)
print(X.shape)
X

(10003, 3118)

#Get labels from product data
y1=product['Number of items bought after buying this item']
y2=product['Number of items bought after viewing this item']

Split the sample into train datasets and test datasets. This helps us train the model on train datasets and test model's performance on test datasets.

from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestRegressor
X1_train,X1_test,y1_train,y1_test=train_test_split(X,y1,test_size=0.2,random_state=42)
X2_train,X2_test,y2_train,y2_test=train_test_split(X,y2,test_size=0.2,random_state=42)

Question 1. Explore the first question:Do consumer's review ratings predict their following purchasing quantity? Firstly, I will train a linear regression to test whether consumer's review rating mattters for predicting following purchasing quantities.

from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
from scipy import stats
#the following code estimate the linear relationship between number of items bought after buying this item and features
X2 = sm.add_constant(X1_train)
est = sm.OLS(y1_train, X2)
est2 = est.fit()
est2.summary()

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
  x = pd.concat(x[::order], 1)

#the following code estimate the linear relationship between number of items bought after viewing this item and features
X2 = sm.add_constant(X2_train)
est = sm.OLS(y2_train, X2)
est2 = est.fit()
est2.summary()

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
  x = pd.concat(x[::order], 1)

The previous results show that none of the review indicators(number_of_reviews,average_review_rating,customer_review, customer review gap) can significantly predict the purchasing quantities. It indicates that consumer reviews don't affect customers' future purchasing quantities.

Secondly, I will train a K-nearest neighbor model to see whether including the consumer's review rating or not will affect the prediction score. In the following cell, I will train a KNN model using all product features but excluding consumer review indicators.

from sklearn.neighbors import KNeighborsRegressor
from sklearn.metrics import mean_squared_error
#get the features without consumer review and transform the categorical vaariables into a set of dummies.
X_selected_drop_review=product.drop(['Number of items bought after buying this item','Number of items bought after viewing this item','number_of_reviews','average_review_rating','customer_review', 'customer review gap'],axis=1)
#Transform the categorical variable into dummies.
X_drop_review=pd.get_dummies(X_selected_drop_review)
X1_train_drop_review,X1_test_drop_review,y1_train_drop_review,y1_test_drop_review=train_test_split(X_drop_review,y1,test_size=0.2,random_state=42)
X2_train_drop_review,X2_test_drop_review,y2_train_drop_review,y2_test_drop_review=train_test_split(X_drop_review,y2,test_size=0.2,random_state=42)


#Since I only want to test the importance of consumer's review, the key point is to see the model's prediction performace with consumer's review and without consumer's review.
#Therefore,  I set k=10 here
knn_reg=KNeighborsRegressor(n_neighbors=10)
knn_reg.fit(X1_train_drop_review,y1_train_drop_review)
y1_test_pred=knn_reg.predict(X1_test_drop_review)
mse=mean_squared_error(y1_test_drop_review,y1_test_pred)
rmse=np.sqrt(mse)
print(f'The mse of knn model without consumer review for number of items bought after buying this item is {rmse}')
knn_reg.fit(X2_train_drop_review,y2_train_drop_review)
y2_test_pred=knn_reg.predict(X2_test_drop_review)
mse=mean_squared_error(y2_test_drop_review,y2_test_pred)
rmse=np.sqrt(mse)
print(f'The mse of knn model without consumer review for number of items bought after viewing this item is {rmse}')

The mse of knn model without consumer review for number of items bought after buying this item is 2.06581248166316
The mse of knn model without consumer review for number of items bought after viewing this item is 1.7568527923912503

#g cell, I will train a KNN model using all pruduct features, including consumer review indicators.
knn_reg.fit(X1_train,y1_train)
y1_test_pred=knn_reg.predict(X1_test)
mse=mean_squared_error(y1_test,y1_test_pred)
rmse=np.sqrt(mse)
print(f'The mse of knn model with consumer review for number of items bought after buying this item is {rmse}')
knn_reg.fit(X2_train,y2_train)
y2_test_pred=knn_reg.predict(X2_test)
mse=mean_squared_error(y2_test,y2_test_pred)
rmse=np.sqrt(mse)
print(f'The mse of knn model with consumer review for number of items bought after viewing this item is {rmse}')

The mse of knn model with consumer review for number of items bought after buying this item is 1.9517275372884646
The mse of knn model with consumer review for number of items bought after viewing this item is 1.697886507015309

The above results indicate that adding a consumer's review indeed decreases the test root mean squared error(rmse). Adding consumer reviews decreases the rmse of the number of items bought after buying this item by 5.52%. Adding consumer reviews decreases the rmse of the number of items bought after viewing this item by 3.36%. Even though the review coefficients are not significant in the linear model, the KNN model that can capture the non-linear relationships indicates that a consumer's review can contribute to predicting the consumer's following purchasing quantities.

Question 2. I will explore the second question: Can consumer review ratings and item characteristics predict consumers' following number of purchases well? Firstly, I train a KNN model using and calculating its prediction performance.

from sklearn.neighbors import KNeighborsRegressor
from sklearn.metrics import mean_squared_error
from sklearn.model_selection import cross_val_score
RMSE_knn=[]
for k in range(1,100,5):
  knn_reg=KNeighborsRegressor(n_neighbors=k)
  score1=cross_val_score(knn_reg,X1_train,y1_train,cv=3,scoring='neg_mean_squared_error',n_jobs=-1).mean()
  score2=cross_val_score(knn_reg,X2_train,y2_train,cv=3,scoring='neg_mean_squared_error',n_jobs=-1).mean()
  RMSE_knn.append([k,np.sqrt(-score1),np.sqrt(-score2)])

RMSE_knn_df=pd.DataFrame(RMSE_knn,columns=['number of neighbors','cross validation rmse for number of items bought after buying','cross validation rmse for number of items bought after viewing'])
print(f'The smallest root mean squared error of knn model for number of items bought after buying this item is {RMSE_knn_df.iloc[:,1].min()}')
print(f'The smallest root mean squared error of knn model for number of items bought after viewing this item is {RMSE_knn_df.iloc[:,2].min()}')
RMSE_knn_df

The smallest root mean squared error of knn model for number of items bought after buying this item is 1.9408344489769884
The smallest root mean squared error of knn model for number of items bought after viewing this item is 1.676003325882236

Based on previous results, k=51 returns the smallest cross-validation rmse. Therefore, for the following cell, set k=51 and train the KNN model on the whole training dataset. Then calculate the test rmse for the test datasets.

index_min_rmse=RMSE_knn_df.iloc[:,1].argmin()
k=RMSE_knn_df.iloc[index_min_rmse,0]
knn_reg=KNeighborsRegressor(n_neighbors=k)
knn_reg.fit(X1_train,y1_train)
y1_test_pred=knn_reg.predict(X1_test)
rmse=np.sqrt(mean_squared_error(y1_test,y1_test_pred))
print(f'The test rmse of knn model with consumer review for number of items bought after buying this item is {rmse}')
knn_reg.fit(X2_train,y2_train)
y2_test_pred=knn_reg.predict(X2_test)
rmse=np.sqrt(mean_squared_error(y2_test,y2_test_pred))
print(f'The test rmse of knn model with consumer review for number of items bought after viewing this item is {rmse}')

The test mse of knn model with consumer review for number of items bought after buying this item is 1.8973387681505385
The test mse of knn model with consumer review for number of items bought after viewing this item is 1.664352490838144

Next, I train a random forest regression model to calculate its cross-validation performance.

RMSE_tree=[]
n_estimators=[5,10,20,50,100]
max_depths=[1,5,10,50,100]
for n in n_estimators:
  for d in max_depths:
    rnd_reg=RandomForestRegressor(n_estimators=n,max_depth=d,random_state=42,n_jobs=-1)
    score1=cross_val_score(rnd_reg,X1_train,y1_train,cv=3,scoring='neg_mean_squared_error').mean()
    score2=cross_val_score(rnd_reg,X2_train,y2_train,cv=3,scoring='neg_mean_squared_error').mean()
    RMSE_tree.append([n,d,np.sqrt(-score1),np.sqrt(-score2)])

RMSE_tree_df=pd.DataFrame(RMSE_tree,columns=['number of estimators','maximum depths','cross validation rmse for number of items bought after buying this item','cross validation rmse for number of items bought after viewing this item'])
print(f'The smallest root mean squared error of random forest model for number of items bought after buying this item is {RMSE_tree_df.iloc[:,2].min()}')
print(f'The smallest root mean squared error of random forest for number of items bought after viewing this item is {RMSE_tree_df.iloc[:,3].min()}')
RMSE_tree_df

The smallest root mean squared error of random forest model for number of items bought after buying this item is 1.8586859283405264
The smallest root mean squared error of random forest for number of items bought after viewing this item is 1.573818887148256

Based on previous results, n_estimators=100 and max_depth=10 return the smallest cross-validation rmse. Therefore, for the following cell, set n_estimators=100 and max_depth=10 and train the random forest model on the whole training dataset. Then calculate the test rmse for the test datasets.

index_min_rmse=RMSE_tree_df.iloc[:,2].argmin()
n=RMSE_tree_df.iloc[index_min_rmse,0]
d=RMSE_tree_df.iloc[index_min_rmse,1]
rnd_reg=RandomForestRegressor(n_estimators=n,max_depth=d,random_state=42,n_jobs=-1)
rnd_reg.fit(X1_train,y1_train)
y1_test_pred=rnd_reg.predict(X1_test)
rmse=np.sqrt(mean_squared_error(y1_test,y1_test_pred))
print(f'The test rmse of random forest model with consumer review for number of items bought after buying this item is {rmse}')
rnd_reg.fit(X2_train,y2_train)
y2_test_pred=rnd_reg.predict(X2_test)
rmse=np.sqrt(mean_squared_error(y2_test,y2_test_pred))
print(f'The test rmse of random forest model with consumer review for number of items bought after viewing this item is {rmse}')

The test rmse of random forest model with consumer review for number of items bought after buying this item is 1.7924393033729449
The test rmse of random forest model with consumer review for number of items bought after viewing this item is 1.5625982325557126

Lastly, based on the performance of those two models, the test rmse of the random forest model is smaller. Therefore, I chose the random forest model as the training and prediction model and plotted the predicted labels versus actual labels.

data_new=pd.DataFrame(X1_test,columns=X1_test.columns,index=y1_test.index)
data_new['y1_test']=y1_test
data_new['y1_test_pred']=pd.Series(y1_test_pred)
data_new['y2_test']=y2_test
data_new['y2_test_pred']=pd.Series(y2_test_pred)

data_new['number_available_in_stock_1']=round(data_new['number_available_in_stock']/3)*3
y_1=data_new.groupby('number_available_in_stock_1')['y1_test'].mean()
y_2=data_new.groupby('number_available_in_stock_1')['y1_test_pred'].mean()
y_3=data_new.groupby('number_available_in_stock_1')['y2_test'].mean()
y_4=data_new.groupby('number_available_in_stock_1')['y2_test_pred'].mean()

x_1=pd.Series(y_1.index)
plt.rcParams["figure.figsize"] = (11,6)
plt.plot(x_1, y_1, 'r-')
plt.plot(x_1, y_2, 'g-')
plt.plot(x_1, y_3, 'y-')
plt.plot(x_1, y_4, 'b-')
plt.xlabel('Number available in stock')
plt.ylabel('Number of items bought')
plt.ylim(0,10)
plt.legend(["True Number of items bought after buying this product", "Predicted Number of items bought after buying this product","True Number of items bought after viewing this product", "Predicted Number of items bought after viewing this product"])

<matplotlib.legend.Legend at 0x7f122eb56e10>

The above figure plots the true number of items bought versus the predicted amounts of the item bought. Red and green lines represent the number of items bought after purchasing this product. Yellow and blue lines represent the number of items bought after viewing this product. The average root means squared errors are 1.79 and 1.56, respectively. The predictions are ok when the number available is smaller than 30. However, the results could be better when the number available is larger than 35. One possible reason is the consumer's future purchasing behaviors are so complex. Future economic conditions and preferences may influence it, and many factors that my model needs to capture. More indicators, especially consumer characteristics, can be collected to achieve better prediction.

Conlusions¶

This project mainly deals with two questions for consumers' future purchasing behaviors.

The first one is: Do consumers' review ratings predict their following purchasing quantity? Based on the linear regression model, no significant coefficients are found. However, the linear regression model can only capture the linear relationship of features with labels. To capture the non-linear relationship, I train a K-nearest neighborhood model and look at their test performance with the consumer's review and without the consumer's review indicators. Adding consumer review indicators decreases test rooted mean squared error for the number of items bought after buying this product by 5.52%. It reduces test rooted mean squared error for the number of items purchased after viewing this product by 3.36%. This indicates that consumer review indeed can contribute to predicting their following purchasing quantities.

The second one is: Can consumer review ratings and item characteristics predict consumers' following number of purchases well? To better predict the consumers' following number of purchases, I use the cross-validation method to choose the best parameters of the K-nearest neighborhood model and random forest model. After getting the best parameter, I calculate each model's prediction rooted mean squared errors. The rooted mean squared error for the K-nearest neighborhood model is 1.8973387681505385 for the number of items bought after buying this product and 1.664352490838144 for the number of items purchased after viewing this product. The rooted mean squared error for the random forest model is 1.7924393033729449 for the number of items bought after buying this product and 1.5625982325557126 for the number of items purchased after viewing this product. Generally, the rooted mean squared errors for the random forest model are smaller than the K-nearest neighborhood model. Therefore, I choose the random forest model as my prediction model and predict the future purchasing quantities bought. The prediction results are ok but could be better. One possible reason is the consumer's future purchasing behaviors are so complex. Future economic conditions and preferences may influence it, and many factors that my model needs to capture. More indicators, especially consumer characteristics, can be collected to achieve better prediction.

Here are some links that are related to this project. Amazon fashion data are an important dataset in product recommendation. The first link tries to predict outfit compatibility and retrieve complementary items from the set dataset I use. The second is to develop a system to recommend product size fits {Small, Fit, Large} to customers. I hope this tutorial is helpful for understanding consumer behaviors.

Link 1: https://www.amazon.science/publications/outfit-transformer-outfit-representations-for-fashion-recommendation

Link 2: https://www.amazon.science/publications/recommending-product-sizes-to-customers

from google.colab import drive
drive.mount('/content/drive')
!git pull

Mounted at /content/drive
fatal: not a git repository (or any of the parent directories): .git

%%shell
jupyter nbconvert --to html 'DS project Final.ipynb'

[NbConvertApp] WARNING | pattern 'DS project Final.ipynb' matched no files
This application is used to convert notebook files (*.ipynb)
        to various other formats.

        WARNING: THE COMMANDLINE INTERFACE MAY CHANGE IN FUTURE RELEASES.

Options
=======
The options below are convenience aliases to configurable class-options,
as listed in the "Equivalent to" description-line of the aliases.
To see all configurable class-options for some <cmd>, use:
    <cmd> --help-all

--debug
    set log level to logging.DEBUG (maximize logging output)
    Equivalent to: [--Application.log_level=10]
--show-config
    Show the application's configuration (human-readable format)
    Equivalent to: [--Application.show_config=True]
--show-config-json
    Show the application's configuration (json format)
    Equivalent to: [--Application.show_config_json=True]
--generate-config
    generate default config file
    Equivalent to: [--JupyterApp.generate_config=True]
-y
    Answer yes to any questions instead of prompting.
    Equivalent to: [--JupyterApp.answer_yes=True]
--execute
    Execute the notebook prior to export.
    Equivalent to: [--ExecutePreprocessor.enabled=True]
--allow-errors
    Continue notebook execution even if one of the cells throws an error and include the error message in the cell output (the default behaviour is to abort conversion). This flag is only relevant if '--execute' was specified, too.
    Equivalent to: [--ExecutePreprocessor.allow_errors=True]
--stdin
    read a single notebook file from stdin. Write the resulting notebook with default basename 'notebook.*'
    Equivalent to: [--NbConvertApp.from_stdin=True]
--stdout
    Write notebook output to stdout instead of files.
    Equivalent to: [--NbConvertApp.writer_class=StdoutWriter]
--inplace
    Run nbconvert in place, overwriting the existing notebook (only 
            relevant when converting to notebook format)
    Equivalent to: [--NbConvertApp.use_output_suffix=False --NbConvertApp.export_format=notebook --FilesWriter.build_directory=]
--clear-output
    Clear output of current file and save in place, 
            overwriting the existing notebook.
    Equivalent to: [--NbConvertApp.use_output_suffix=False --NbConvertApp.export_format=notebook --FilesWriter.build_directory= --ClearOutputPreprocessor.enabled=True]
--no-prompt
    Exclude input and output prompts from converted document.
    Equivalent to: [--TemplateExporter.exclude_input_prompt=True --TemplateExporter.exclude_output_prompt=True]
--no-input
    Exclude input cells and output prompts from converted document. 
            This mode is ideal for generating code-free reports.
    Equivalent to: [--TemplateExporter.exclude_output_prompt=True --TemplateExporter.exclude_input=True]
--log-level=<Enum>
    Set the log level by value or name.
    Choices: any of [0, 10, 20, 30, 40, 50, 'DEBUG', 'INFO', 'WARN', 'ERROR', 'CRITICAL']
    Default: 30
    Equivalent to: [--Application.log_level]
--config=<Unicode>
    Full path of a config file.
    Default: ''
    Equivalent to: [--JupyterApp.config_file]
--to=<Unicode>
    The export format to be used, either one of the built-in formats
            ['asciidoc', 'custom', 'html', 'latex', 'markdown', 'notebook', 'pdf', 'python', 'rst', 'script', 'slides']
            or a dotted object name that represents the import path for an
            `Exporter` class
    Default: 'html'
    Equivalent to: [--NbConvertApp.export_format]
--template=<Unicode>
    Name of the template file to use
    Default: ''
    Equivalent to: [--TemplateExporter.template_file]
--writer=<DottedObjectName>
    Writer class used to write the 
                                        results of the conversion
    Default: 'FilesWriter'
    Equivalent to: [--NbConvertApp.writer_class]
--post=<DottedOrNone>
    PostProcessor class used to write the
                                        results of the conversion
    Default: ''
    Equivalent to: [--NbConvertApp.postprocessor_class]
--output=<Unicode>
    overwrite base name use for output files.
                can only be used when converting one notebook at a time.
    Default: ''
    Equivalent to: [--NbConvertApp.output_base]
--output-dir=<Unicode>
    Directory to write output(s) to. Defaults
                                  to output to the directory of each notebook. To recover
                                  previous default behaviour (outputting to the current 
                                  working directory) use . as the flag value.
    Default: ''
    Equivalent to: [--FilesWriter.build_directory]
--reveal-prefix=<Unicode>
    The URL prefix for reveal.js (version 3.x).
            This defaults to the reveal CDN, but can be any url pointing to a copy 
            of reveal.js. 
            For speaker notes to work, this must be a relative path to a local 
            copy of reveal.js: e.g., "reveal.js".
            If a relative path is given, it must be a subdirectory of the
            current directory (from which the server is run).
            See the usage documentation
            (https://nbconvert.readthedocs.io/en/latest/usage.html#reveal-js-html-slideshow)
            for more details.
    Default: ''
    Equivalent to: [--SlidesExporter.reveal_url_prefix]
--nbformat=<Enum>
    The nbformat version to write.
            Use this to downgrade notebooks.
    Choices: any of [1, 2, 3, 4]
    Default: 4
    Equivalent to: [--NotebookExporter.nbformat_version]

Examples
--------

    The simplest way to use nbconvert is

            > jupyter nbconvert mynotebook.ipynb

            which will convert mynotebook.ipynb to the default format (probably HTML).

            You can specify the export format with `--to`.
            Options include ['asciidoc', 'custom', 'html', 'latex', 'markdown', 'notebook', 'pdf', 'python', 'rst', 'script', 'slides'].

            > jupyter nbconvert --to latex mynotebook.ipynb

            Both HTML and LaTeX support multiple output templates. LaTeX includes
            'base', 'article' and 'report'.  HTML includes 'basic' and 'full'. You
            can specify the flavor of the format used.

            > jupyter nbconvert --to html --template basic mynotebook.ipynb

            You can also pipe the output to stdout, rather than a file

            > jupyter nbconvert mynotebook.ipynb --stdout

            PDF is generated via latex

            > jupyter nbconvert mynotebook.ipynb --to pdf

            You can get (and serve) a Reveal.js-powered slideshow

            > jupyter nbconvert myslides.ipynb --to slides --post serve

            Multiple notebooks can be given at the command line in a couple of 
            different ways:

            > jupyter nbconvert notebook*.ipynb
            > jupyter nbconvert notebook1.ipynb notebook2.ipynb

            or you can specify the notebooks list in a config file, containing::

                c.NbConvertApp.notebooks = ["my_notebook.ipynb"]

            > jupyter nbconvert --config mycfg.py

To see all available configurables, use `--help-all`.

---------------------------------------------------------------------------
CalledProcessError                        Traceback (most recent call last)
<ipython-input-67-acf04a781971> in <module>
----> 1 get_ipython().run_cell_magic('shell', '', "jupyter nbconvert --to html 'DS project Final.ipynb'\n")

/usr/local/lib/python3.7/dist-packages/IPython/core/interactiveshell.py in run_cell_magic(self, magic_name, line, cell)
   2357             with self.builtin_trap:
   2358                 args = (magic_arg_s, cell)
-> 2359                 result = fn(*args, **kwargs)
   2360             return result
   2361 

/usr/local/lib/python3.7/dist-packages/google/colab/_system_commands.py in _shell_cell_magic(args, cmd)
    107   result = _run_command(cmd, clear_streamed_output=False)
    108   if not parsed_args.ignore_errors:
--> 109     result.check_returncode()
    110   return result
    111 

/usr/local/lib/python3.7/dist-packages/google/colab/_system_commands.py in check_returncode(self)
    133     if self.returncode:
    134       raise subprocess.CalledProcessError(
--> 135           returncode=self.returncode, cmd=self.args, output=self.output)
    136 
    137   def _repr_pretty_(self, p, cycle):  # pylint:disable=unused-argument

CalledProcessError: Command 'jupyter nbconvert --to html 'DS project Final.ipynb'
' returned non-zero exit status 255.

	uniq_id	product_name	manufacturer	price	number_available_in_stock	number_of_reviews	number_of_answered_questions	average_review_rating	amazon_category_and_sub_category	customers_who_bought_this_item_also_bought	description	product_information	product_description	items_customers_buy_after_viewing_this_item	customer_questions_and_answers	customer_reviews	sellers
0	eac7efa5dbd3d667f26eb3d3ab504464	Hornby 2014 Catalogue	Hornby	£3.42	5 new	15.0	1.0	4.9 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Hornby-R8150-Catalogue...	Product Description Hornby 2014 Catalogue Box ...	Technical Details Item Weight640 g Product Dim...	Product Description Hornby 2014 Catalogue Box ...	http://www.amazon.co.uk/Hornby-R8150-Catalogue...	Does this catalogue detail all the previous Ho...	Worth Buying For The Pictures Alone (As Ever) ...	{"seller"=>[{"Seller_name_1"=>"Amazon.co.uk", ...
1	b17540ef7e86e461d37f3ae58b7b72ac	FunkyBuys® Large Christmas Holiday Express Fes...	FunkyBuys	£16.99	NaN	2.0	1.0	4.5 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Christmas-Holiday-Expr...	Size Name:Large FunkyBuys® Large Christmas Hol...	Technical Details Manufacturer recommended age...	Size Name:Large FunkyBuys® Large Christmas Hol...	http://www.amazon.co.uk/Christmas-Holiday-Expr...	can you turn off sounds // hi no you cant turn...	Four Stars // 4.0 // 18 Dec. 2015 // By\n \...	{"seller"=>{"Seller_name_1"=>"UHD WHOLESALE", ...
2	348f344247b0c1a935b1223072ef9d8a	CLASSIC TOY TRAIN SET TRACK CARRIAGES LIGHT EN...	ccf	£9.99	2 new	17.0	2.0	3.9 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Classic-Train-Lights-B...	BIG CLASSIC TOY TRAIN SET TRACK CARRIAGE LIGHT...	Technical Details Manufacturer recommended age...	BIG CLASSIC TOY TRAIN SET TRACK CARRIAGE LIGHT...	http://www.amazon.co.uk/Train-With-Tracks-Batt...	What is the gauge of the track // Hi Paul.Trut...	Highly Recommended! // 5.0 // 26 May 2015 ...	{"seller"=>[{"Seller_name_1"=>"DEAL-BOX", "Sel...
3	e12b92dbb8eaee78b22965d2a9bbbd9f	HORNBY Coach R4410A BR Hawksworth Corridor 3rd	Hornby	£39.99	NaN	1.0	2.0	5.0 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	NaN	Hornby 00 Gauge BR Hawksworth 3rd Class W 2107...	Technical Details Item Weight259 g Product Dim...	Hornby 00 Gauge BR Hawksworth 3rd Class W 2107...	NaN	NaN	I love it // 5.0 // 22 July 2013 // By\n \n...	NaN
4	e33a9adeed5f36840ccc227db4682a36	Hornby 00 Gauge 0-4-0 Gildenlow Salt Co. Steam...	Hornby	£32.19	NaN	3.0	2.0	4.7 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Hornby-R6367-RailRoad-...	Product Description Hornby RailRoad 0-4-0 Gild...	Technical Details Item Weight159 g Product Dim...	Product Description Hornby RailRoad 0-4-0 Gild...	http://www.amazon.co.uk/Hornby-R2672-RailRoad-...	NaN	Birthday present // 5.0 // 14 April 2014 // By...	NaN
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
9995	44d6967f083825a5de36ad4865a65bcd	Batman 1966 TV Series Action Figures - The Rid...	Mattel	£22.95	5 new	3.0	3.0	5.0 out of 5 stars	Hobbies > Collectible Figures & Memorabilia > ...	http://www.amazon.co.uk/Batman-1966-Series-Act...	DC 66 Batman Classic TV Series 6 Inch Riddler ...	Technical Details Item Weight136 g Product Dim...	DC 66 Batman Classic TV Series 6 Inch Riddler ...	NaN	NaN	Realistic // 5.0 // 31 Mar. 2014 // By\n \n...	{"seller"=>[{"Seller_name_1"=>"Star Action Fig...
9996	08f0747b6fc6687215ffb994c3a6fb32	Star Wars Costume, Kids Stormtrooper Costume S...	Star Wars	£39.99	NaN	1.0	3.0	4.0 out of 5 stars	Characters & Brands > Star Wars > Toys	http://www.amazon.co.uk/Storm-Trooper-Costume-...	NaN	Technical Details Additional Information AS...	NaN	http://www.amazon.co.uk/Storm-Trooper-Costume-...	NaN	... what I see my grandson us going to have fu...	NaN
9997	bf6cc073f8f24e6e338190fa16f6ee9d	Defiance Lawkeeper Metal Badge Prop Replica	Olde Scotland Yard Ltd.	£43.99	3 new	1.0	3.0	5.0 out of 5 stars	Novelty & Special Use > Novelty > Accessories ...	NaN	Includes 1x Badge with holder and chain High...	Technical Details Item Weight159 g Product Dim...	Includes 1x Badge with holder and chain High...	http://www.amazon.co.uk/Olde-Scotland-Yard-Ltd...	NaN	Five Stars // 5.0 // 18 Dec. 2015 // By\n \...	{"seller"=>[{"Seller_name_1"=>"YUK", "Seller_p...
9998	cd783d0b8b44e631b9788b203eaaefae	Justice League of America Series 3 Green Lante...	DC Comics	£49.81	3 new	1.0	3.0	5.0 out of 5 stars	Hobbies > Collectible Figures & Memorabilia > ...	NaN	Designed by Ed BenesIt's here - the third seri...	Technical Details Item Weight181 g Product Dim...	Designed by Ed BenesIt's here - the third seri...	NaN	NaN	The best sculpt in a while // 5.0 // 13 May 20...	{"seller"=>[{"Seller_name_1"=>"Smaller World F...
9999	94d18e86e504bee1e392df7e5738b18a	Star Wars 1/72 Y-Wing Starfighter	Bandai	£21.20	31 new	11.0	3.0	4.5 out of 5 stars	Characters & Brands > Star Wars > Toys	http://www.amazon.co.uk/Bandai-Star-Wars-Fight...	NaN	Technical Details Item Weight299 g Product Dim...	NaN	NaN	NaN	Gold leader // 5.0 // 31 Aug. 2015 // By\n ...	NaN

	country	founded	industry	locality	name	region	size
0	united states	NaN	construction	NaN	kimball construction services inc.	NaN	1-10
1	united states	NaN	financial services	sag harbor	breakwater yacht club	new york	1-10
2	united kingdom	1963.0	construction	sidcup	knapman & sons (builders) ltd	greater london	11-50
3	NaN	2001.0	staffing and recruiting	NaN	marketingselection	NaN	1-10
4	czechia	1901.0	consumer goods	NaN	lux czech s.r.o.	praha	11-50
...	...	...	...	...	...	...	...
11705924	finland	2006.0	management consulting	helsinki	stratebility oy	uusimaa	1-10
11705925	NaN	NaN	media production	NaN	filmati milanesi	NaN	1-10
11705926	united states	1993.0	construction	mount sinai	certified chimney service inc	new york	1-10
11705927	brazil	1975.0	automotive	NaN	jedal redentor	NaN	51-200
11705928	finland	2019.0	computer games	espoo	uuvana studios	uusimaa	1-10

	uniq_id	product_name	manufacturer	price	number_available_in_stock	number_of_reviews	number_of_answered_questions	average_review_rating	amazon_category_and_sub_category	customers_who_bought_this_item_also_bought	...	customer_questions_and_answers	customer_reviews	sellers	country	founded	industry	locality	name	region	size
0	eac7efa5dbd3d667f26eb3d3ab504464	Hornby 2014 Catalogue	Hornby	£3.42	5 new	15.0	1.0	4.9 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Hornby-R8150-Catalogue...	...	Does this catalogue detail all the previous Ho...	Worth Buying For The Pictures Alone (As Ever) ...	{"seller"=>[{"Seller_name_1"=>"Amazon.co.uk", ...	NaN	NaN	NaN	NaN	NaN	NaN	NaN
1	b17540ef7e86e461d37f3ae58b7b72ac	FunkyBuys® Large Christmas Holiday Express Fes...	FunkyBuys	£16.99	NaN	2.0	1.0	4.5 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Christmas-Holiday-Expr...	...	can you turn off sounds // hi no you cant turn...	Four Stars // 4.0 // 18 Dec. 2015 // By\n \...	{"seller"=>{"Seller_name_1"=>"UHD WHOLESALE", ...	NaN	NaN	NaN	NaN	NaN	NaN	NaN
2	348f344247b0c1a935b1223072ef9d8a	CLASSIC TOY TRAIN SET TRACK CARRIAGES LIGHT EN...	ccf	£9.99	2 new	17.0	2.0	3.9 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Classic-Train-Lights-B...	...	What is the gauge of the track // Hi Paul.Trut...	Highly Recommended! // 5.0 // 26 May 2015 ...	{"seller"=>[{"Seller_name_1"=>"DEAL-BOX", "Sel...	united kingdom	1978.0	building materials	NaN	ccf	manchester	501-1000
3	348f344247b0c1a935b1223072ef9d8a	CLASSIC TOY TRAIN SET TRACK CARRIAGES LIGHT EN...	ccf	£9.99	2 new	17.0	2.0	3.9 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Classic-Train-Lights-B...	...	What is the gauge of the track // Hi Paul.Trut...	Highly Recommended! // 5.0 // 26 May 2015 ...	{"seller"=>[{"Seller_name_1"=>"DEAL-BOX", "Sel...	NaN	NaN	NaN	NaN	ccf	NaN	201-500
4	348f344247b0c1a935b1223072ef9d8a	CLASSIC TOY TRAIN SET TRACK CARRIAGES LIGHT EN...	ccf	£9.99	2 new	17.0	2.0	3.9 out of 5 stars	Hobbies > Model Trains & Railway Sets > Rail V...	http://www.amazon.co.uk/Classic-Train-Lights-B...	...	What is the gauge of the track // Hi Paul.Trut...	Highly Recommended! // 5.0 // 26 May 2015 ...	{"seller"=>[{"Seller_name_1"=>"DEAL-BOX", "Sel...	france	1973.0	business supplies and equipment	nanterre	ccf	ile-de-france	51-200
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
10019	44d6967f083825a5de36ad4865a65bcd	Batman 1966 TV Series Action Figures - The Rid...	Mattel	£22.95	5 new	3.0	3.0	5.0 out of 5 stars	Hobbies > Collectible Figures & Memorabilia > ...	http://www.amazon.co.uk/Batman-1966-Series-Act...	...	NaN	Realistic // 5.0 // 31 Mar. 2014 // By\n \n...	{"seller"=>[{"Seller_name_1"=>"Star Action Fig...	NaN	NaN	NaN	NaN	NaN	NaN	NaN
10020	08f0747b6fc6687215ffb994c3a6fb32	Star Wars Costume, Kids Stormtrooper Costume S...	Star Wars	£39.99	NaN	1.0	3.0	4.0 out of 5 stars	Characters & Brands > Star Wars > Toys	http://www.amazon.co.uk/Storm-Trooper-Costume-...	...	NaN	... what I see my grandson us going to have fu...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
10021	bf6cc073f8f24e6e338190fa16f6ee9d	Defiance Lawkeeper Metal Badge Prop Replica	Olde Scotland Yard Ltd.	£43.99	3 new	1.0	3.0	5.0 out of 5 stars	Novelty & Special Use > Novelty > Accessories ...	NaN	...	NaN	Five Stars // 5.0 // 18 Dec. 2015 // By\n \...	{"seller"=>[{"Seller_name_1"=>"YUK", "Seller_p...	NaN	NaN	NaN	NaN	NaN	NaN	NaN
10022	cd783d0b8b44e631b9788b203eaaefae	Justice League of America Series 3 Green Lante...	DC Comics	£49.81	3 new	1.0	3.0	5.0 out of 5 stars	Hobbies > Collectible Figures & Memorabilia > ...	NaN	...	NaN	The best sculpt in a while // 5.0 // 13 May 20...	{"seller"=>[{"Seller_name_1"=>"Smaller World F...	NaN	NaN	NaN	NaN	NaN	NaN	NaN
10023	94d18e86e504bee1e392df7e5738b18a	Star Wars 1/72 Y-Wing Starfighter	Bandai	£21.20	31 new	11.0	3.0	4.5 out of 5 stars	Characters & Brands > Star Wars > Toys	http://www.amazon.co.uk/Bandai-Star-Wars-Fight...	...	NaN	Gold leader // 5.0 // 31 Aug. 2015 // By\n ...	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

	category	sub_category_1	sub_category_2	sub_category_3	sub_category_4
0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
1	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
2	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
3	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
4	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
...	...	...	...	...	...
10019	Hobbies	Collectible Figures & Memorabilia	Collectible Props & Memorabilia	None	None
10020	Characters & Brands	Star Wars	Toys	None	None
10021	Novelty & Special Use	Novelty	Accessories	Buttons & Pins	None
10022	Hobbies	Collectible Figures & Memorabilia	Collectible Props & Memorabilia	None	None
10023	Characters & Brands	Star Wars	Toys	None	None

	manufacturer	price	number_available_in_stock	number_of_reviews	number_of_answered_questions	average_review_rating	country	founded	industry	locality	...	size	customer_review	customer review gap	Number of items bought after buying this item	Number of items bought after viewing this item	category	sub_category_1	sub_category_2	sub_category_3	sub_category_4
0	Hornby	3.42	5.0	15.0	1.0	4.9	NaN	NaN	NaN	NaN	...	NaN	4.0	-0.9	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
1	FunkyBuys	16.99	NaN	2.0	1.0	4.5	NaN	NaN	NaN	NaN	...	NaN	4.0	-0.5	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
2	ccf	9.99	2.0	17.0	2.0	3.9	united kingdom	1978.0	building materials	NaN	...	501-1000	5.0	1.1	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
3	ccf	9.99	2.0	17.0	2.0	3.9	NaN	NaN	NaN	NaN	...	201-500	5.0	1.1	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
4	ccf	9.99	2.0	17.0	2.0	3.9	france	1973.0	business supplies and equipment	nanterre	...	51-200	5.0	1.1	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains	None
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
10019	Mattel	22.95	5.0	3.0	3.0	5.0	NaN	NaN	NaN	NaN	...	NaN	0.0	-5.0	6.0	0.0	Hobbies	Collectible Figures & Memorabilia	Collectible Props & Memorabilia	None	None
10020	Star Wars	39.99	NaN	1.0	3.0	4.0	NaN	NaN	NaN	NaN	...	NaN	0.0	-4.0	6.0	4.0	Characters & Brands	Star Wars	Toys	None	None
10021	Olde Scotland Yard Ltd.	43.99	3.0	1.0	3.0	5.0	NaN	NaN	NaN	NaN	...	NaN	0.0	-5.0	0.0	1.0	Novelty & Special Use	Novelty	Accessories	Buttons & Pins	None
10022	DC Comics	49.81	3.0	1.0	3.0	5.0	NaN	NaN	NaN	NaN	...	NaN	0.0	-5.0	0.0	0.0	Hobbies	Collectible Figures & Memorabilia	Collectible Props & Memorabilia	None	None
10023	Bandai	21.20	31.0	11.0	3.0	4.5	NaN	NaN	NaN	NaN	...	NaN	0.0	-4.5	6.0	0.0	Characters & Brands	Star Wars	Toys	None	None

	manufacturer	price	number_available_in_stock	number_of_reviews	number_of_answered_questions	average_review_rating	country	founded	industry	locality	...	size	customer_review	customer review gap	Number of items bought after buying this item	Number of items bought after viewing this item	category	sub_category_1	sub_category_2	sub_category_3
0	Hornby	3.42	5.000000	15.0	1.0	4.9	0	2005.821429	0	0	...	0	4.0	-0.9	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains
1	FunkyBuys	16.99	7.914095	2.0	1.0	4.5	0	2005.821429	0	0	...	0	4.0	-0.5	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains
2	ccf	9.99	2.000000	17.0	2.0	3.9	united kingdom	1978.000000	building materials	0	...	501-1000	5.0	1.1	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains
3	ccf	9.99	2.000000	17.0	2.0	3.9	0	2005.821429	0	0	...	201-500	5.0	1.1	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains
4	ccf	9.99	2.000000	17.0	2.0	3.9	france	1973.000000	business supplies and equipment	nanterre	...	51-200	5.0	1.1	6.0	4.0	Hobbies	Model Trains & Railway Sets	Rail Vehicles	Trains

	price	number_available_in_stock	number_of_reviews	number_of_answered_questions	average_review_rating	founded	customer_review	customer review gap	Number of items bought after buying this item	Number of items bought after viewing this item
count	10003.000000	10003.000000	10003.000000	10003.000000	10003.000000	10003.000000	10003.000000	10003.000000	10003.000000	10003.000000
mean	19.948474	7.914095	9.110767	1.833442	4.707648	2005.821429	4.647271	-0.060348	4.874138	2.450665
std	35.307812	7.606340	33.639905	2.418367	0.372248	0.525695	0.738815	0.824338	2.132685	1.813776
min	0.010000	1.000000	1.000000	1.000000	2.300000	1973.000000	0.000000	-5.000000	0.000000	0.000000
25%	5.950000	3.000000	1.000000	1.000000	4.500000	2005.821429	4.000000	0.000000	5.000000	0.000000
50%	12.990000	7.000000	2.000000	1.000000	5.000000	2005.821429	5.000000	0.000000	6.000000	4.000000
75%	19.948474	7.914095	6.000000	2.000000	5.000000	2005.821429	5.000000	0.400000	6.000000	4.000000
max	995.110000	92.000000	1399.000000	39.000000	5.000000	2019.000000	5.000000	2.700000	12.000000	4.000000

Dep. Variable:	Number of items bought after buying this item	R-squared:	0.517
Model:	OLS	Adj. R-squared:	0.294
Method:	Least Squares	F-statistic:	2.319
Date:	Tue, 13 Dec 2022	Prob (F-statistic):	4.80e-146
Time:	18:13:29	Log-Likelihood:	-14528.
No. Observations:	8002	AIC:	3.412e+04
Df Residuals:	5471	BIC:	5.180e+04
Df Model:	2530
Covariance Type:	nonrobust

Omnibus:	1486.135	Durbin-Watson:	2.014
Prob(Omnibus):	0.000	Jarque-Bera (JB):	3610.303
Skew:	-1.037	Prob(JB):	0.00
Kurtosis:	5.555	Cond. No.	5.62e+21

Omnibus:	160.785	Durbin-Watson:	2.000
Prob(Omnibus):	0.000	Jarque-Bera (JB):	170.137
Skew:	-0.352	Prob(JB):	1.14e-37
Kurtosis:	3.115	Cond. No.	5.62e+21

	number of neighbors	cross validation rmse for number of items bought after buying	cross validation rmse for number of items bought after viewing
0	1	2.620864	2.245743
1	6	2.030041	1.724016
2	11	1.980025	1.692788
3	16	1.966941	1.683139
4	21	1.956641	1.676098
5	26	1.951605	1.676003
6	31	1.947791	1.676182
7	36	1.945609	1.676419
8	41	1.943214	1.676207
9	46	1.943080	1.676556
10	51	1.940834	1.676821
11	56	1.941867	1.676084
12	61	1.942896	1.677170
13	66	1.942697	1.678522
14	71	1.944429	1.679600
15	76	1.946953	1.681408
16	81	1.947928	1.681781
17	86	1.948680	1.682160
18	91	1.950075	1.683856
19	96	1.952045	1.684951

	number of estimators	maximum depths	cross validation rmse for number of items bought after buying this item	cross validation rmse for number of items bought after viewing this item
0	5	1	1.961887	1.690989
1	5	5	1.877692	1.616078
2	5	10	1.884838	1.611063
3	5	50	2.021582	1.706025
4	5	100	2.049856	1.720523
5	10	1	1.961686	1.690813
6	10	5	1.873247	1.609704
7	10	10	1.870263	1.591478
8	10	50	1.983212	1.651405
9	10	100	2.008818	1.665355
10	20	1	1.960646	1.691009
11	20	5	1.871827	1.605079
12	20	10	1.866740	1.583181
13	20	50	1.962978	1.624367
14	20	100	1.988037	1.634918
15	50	1	1.959849	1.690548
16	50	5	1.870955	1.602865
17	50	10	1.860800	1.577872
18	50	50	1.940269	1.611716
19	50	100	1.965879	1.621264
20	100	1	1.959811	1.690691
21	100	5	1.869788	1.602060
22	100	10	1.858686	1.573819
23	100	50	1.938411	1.604537
24	100	100	1.962044	1.613706

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	-0.0008	0.025	-0.034	0.973	-0.050	0.048
price	-0.0020	0.001	-2.493	0.013	-0.004	-0.000
number_available_in_stock	0.1530	0.032	4.815	0.000	0.091	0.215
number_of_reviews	0.0025	0.001	3.171	0.002	0.001	0.004
number_of_answered_questions	0.0108	0.011	0.984	0.325	-0.011	0.032
average_review_rating	0.9975	6.208	0.161	0.872	-11.173	13.168
founded	0.0024	0.001	4.639	0.000	0.001	0.003
customer_review	-1.3984	6.209	-0.225	0.822	-13.570	10.773
customer review gap	1.3513	6.209	0.218	0.828	-10.820	13.523
number_available_in_stock_1	-0.1319	0.031	-4.199	0.000	-0.193	-0.070
manufacturer_101	0.4940	1.826	0.271	0.787	-3.086	4.074
manufacturer_13	1.8806	1.900	0.990	0.322	-1.844	5.605
manufacturer_16th Birthday 16th Foil Banner - 9ft	-2.9679	1.820	-1.630	0.103	-6.536	0.601
manufacturer_1st birthday	1.0110	1.820	0.556	0.579	-2.556	4.578
manufacturer_2-in-1 Chess & Draughts	-0.2041	1.855	-0.110	0.912	-3.841	3.433
manufacturer_24 Game	0.6188	1.826	0.339	0.735	-2.960	4.198
manufacturer_4 Pocket Pro Binder Black	0.2933	2.003	0.146	0.884	-3.634	4.220
manufacturer_45" Sunset Glow Pool	1.5734	1.850	0.850	0.395	-2.054	5.200
manufacturer_4M	0.8691	1.083	0.802	0.422	-1.254	2.993
manufacturer_4M Crafty Kids	1.6023	1.325	1.209	0.227	-0.996	4.200
manufacturer_50Fifty	2.0373	1.299	1.568	0.117	-0.510	4.585
manufacturer_50th Birthday	1.2975	1.884	0.689	0.491	-2.396	4.991
manufacturer_60°	-0.0549	2.294	-0.024	0.981	-4.553	4.443
manufacturer_8	0.5141	1.825	0.282	0.778	-3.065	4.093
manufacturer_80s Material Girl	1.0179	1.874	0.543	0.587	-2.657	4.693
manufacturer_A B Gee	0.0443	1.067	0.042	0.967	-2.047	2.135
manufacturer_A Kent & Cleal game	0.2843	0.700	0.406	0.685	-1.088	1.657
manufacturer_A Nightmare On Elm Street	-0.2127	1.855	-0.115	0.909	-3.849	3.424
manufacturer_A Plus	1.5024	1.804	0.833	0.405	-2.035	5.040
manufacturer_A to Z	0.7977	1.825	0.437	0.662	-2.779	4.375
manufacturer_A-szcxtop	1.9088	1.855	1.029	0.303	-1.727	5.545
manufacturer_A.S.PUPPETS	1.7757	0.480	3.697	0.000	0.834	2.717
manufacturer_AAA	-5.2161	1.831	-2.849	0.004	-8.806	-1.627
manufacturer_AB Gee	1.0608	1.863	0.569	0.569	-2.591	4.713
manufacturer_ABC	1.9321	1.054	1.833	0.067	-0.134	3.998
manufacturer_AC.Crafts	-2.3067	1.837	-1.256	0.209	-5.908	1.295
manufacturer_ACROBAT & BUFFOONERY LTD	1.5305	1.819	0.841	0.400	-2.035	5.096
manufacturer_AFUNTA	2.5498	1.860	1.371	0.170	-1.096	6.195
manufacturer_AFV Club	-1.3284	0.881	-1.507	0.132	-3.056	0.399

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	0.0071	0.022	0.332	0.740	-0.035	0.049
price	-0.0023	0.001	-3.265	0.001	-0.004	-0.001
number_available_in_stock	0.1109	0.028	4.027	0.000	0.057	0.165
number_of_reviews	0.0005	0.001	0.760	0.447	-0.001	0.002
number_of_answered_questions	0.0068	0.009	0.722	0.470	-0.012	0.025
average_review_rating	1.2433	5.381	0.231	0.817	-9.306	11.793
founded	0.0014	0.000	3.103	0.002	0.001	0.002
customer_review	-1.4972	5.381	-0.278	0.781	-12.047	9.053
customer review gap	1.4780	5.381	0.275	0.784	-9.072	12.028
number_available_in_stock_1	-0.0950	0.027	-3.490	0.000	-0.148	-0.042
manufacturer_101	0.8612	1.583	0.544	0.586	-2.242	3.964
manufacturer_13	2.7930	1.647	1.696	0.090	-0.435	6.021
manufacturer_16th Birthday 16th Foil Banner - 9ft	-0.1086	1.578	-0.069	0.945	-3.202	2.984
manufacturer_1st birthday	-2.1221	1.577	-1.345	0.179	-5.214	0.970
manufacturer_2-in-1 Chess & Draughts	0.3681	1.608	0.229	0.819	-2.784	3.520
manufacturer_24 Game	0.8737	1.582	0.552	0.581	-2.228	3.976
manufacturer_4 Pocket Pro Binder Black	0.8639	1.736	0.498	0.619	-2.540	4.268
manufacturer_45" Sunset Glow Pool	1.1346	1.604	0.708	0.479	-2.009	4.278
manufacturer_4M	1.6326	0.939	1.739	0.082	-0.208	3.473
manufacturer_4M Crafty Kids	2.9207	1.149	2.543	0.011	0.669	5.173
manufacturer_50Fifty	0.3283	1.126	0.291	0.771	-1.880	2.536
manufacturer_50th Birthday	2.1281	1.633	1.303	0.193	-1.073	5.330
manufacturer_60°	0.6726	1.989	0.338	0.735	-3.226	4.571
manufacturer_8	-2.7107	1.582	-1.713	0.087	-5.813	0.391
manufacturer_80s Material Girl	1.0526	1.625	0.648	0.517	-2.132	4.238
manufacturer_A B Gee	-1.3805	0.924	-1.493	0.135	-3.193	0.432
manufacturer_A Kent & Cleal game	0.7372	0.607	1.215	0.224	-0.452	1.927
manufacturer_A Nightmare On Elm Street	1.2479	1.608	0.776	0.438	-1.904	4.400
manufacturer_A Plus	-2.1568	1.564	-1.379	0.168	-5.223	0.909
manufacturer_A to Z	-2.5727	1.582	-1.627	0.104	-5.673	0.528
manufacturer_A-szcxtop	-2.1868	1.608	-1.360	0.174	-5.338	0.965
manufacturer_A.S.PUPPETS	0.7274	0.416	1.747	0.081	-0.089	1.544
manufacturer_AAA	-2.8840	1.587	-1.817	0.069	-5.995	0.227
manufacturer_AB Gee	1.3167	1.615	0.816	0.415	-1.849	4.482
manufacturer_ABC	1.2976	0.914	1.420	0.156	-0.493	3.089
manufacturer_AC.Crafts	-0.9939	1.592	-0.624	0.533	-4.116	2.128
manufacturer_ACROBAT & BUFFOONERY LTD	1.0830	1.577	0.687	0.492	-2.008	4.174
manufacturer_AFUNTA	2.7363	1.612	1.698	0.090	-0.423	5.896
manufacturer_AFV Club	-2.0420	0.764	-2.674	0.008	-3.539	-0.545