camillelib / linear_regression_project

Applying linear regression to predict the price of a lego set

Applying Linear Regression to a Lego dataset

Overview

Using a linear regression model, can we help predict the price of a lego set based on specific variables?

Process followed

Librairies used

• pandas
• statsmodels
• scipy.stats
• matplotlib.pyplot

Steps

1. Data collection

Dataset imported from : https://github.com/seankross/lego/tree/master/data-tidy

2. Data cleaning:

• Deleting 8 columns

• Deleting ~2000 empty rows

• Reducing the number of themes

• Replacing "Year" by "Age" to avoid time series

• Creating dummies for non-numerical columns

• Checking if the dataset has duplicates - does not have any

• Convert numerical columns to be normally distributed using the boxcox method:

Distribution in the dataset:

Both are lognormally distributed.

Distribution after using the boxcox method with a lambda 0:

• Identifying outliers:

Solution: creating 2 new columns identifying outliers

3. Regression analysis: Dropping 9 more variables with the first analysis based on high pvalues

4. Checking the 5 assumptions for linear regression

1. Multicollinearity

Dropping 5 more columns, we checked the assumption.

2. Linearity

The assumption is verified

3. Autocorrelation

The Durbin-Watson test shows a positive autocorrelation with a coefficient of 1.11

4. Homoscedasticity

The assumption is potentially not verified.

5. Exogeneity of residuals

The assumption is not verified as the residuals don't follow a normal law according to the Anderson-Darling test (pvalue < 0.05)

Results

The final linear regression model has a high R², however the 5 assumptions are not verified.

Result of the OLS model:

The model equation: ln(y)= -0.21+1.8xOutliers_pieces+ β1xThemes+β2xPackagings+β3xAvailability+0.68xNumber_pieces

Plotting the model :

Conclusion

The model can be used to explain the current prices of these lego sets however is not yet usable for predictions as all assumptions are not checked.