Car Price Prediction:

The project covers the following:

1. exploratory data analysis
2. regression model
3. ANOVA Analysis
4. Model Diagnosis
   • Check Constant Variance
   • Check Influence Point (Delete Influence Point)
   • Check Nomality
   • Check Variance Inflation Factor
5. Model Selection (Step BIC)

Dataset:

https://www.kaggle.com/datasets/hellbuoy/car-price-prediction

EDA (Exploratory Data Analysis):

• Percentage distribution in each predictor:
• Correlation Matrix:

Regression Model:

model = smf.ols("price~symboling+fueltype+aspiration+doornumber+carbody+drivewheel+enginelocation+wheelbase+carlength+carwidth+carheight+curbweight+enginetype+cylindernumber+enginesize+fuelsystem+boreratio+stroke+compressionratio+horsepower+peakrpm+citympg+highwaympg", data=train_data).fit()

ANOVA Analysis:

• ANOVA Typ1 table shows additional significant predictors: [aspiration, carlength, doornumber, drivewheel, fuelsystem, horsepower, symboling, wheelbase],
• ANOVA Typ3 will have the same result as ANOVA Typ2 Both table show that [carbody, carwidth, curbweight, cylindernumber, enginelocation, enginesize, enginetype, fueltype, peakrpm, stroke] are the significant predictors of the fitted model.

Model Diagnosis:

1. Check Constant Variance

Model: $e^2_i = \gamma_0 + \gamma_1 x_{i,1} + ... + \gamma_{p-1} x_{i, p-1} + \xi_i$
$H_0: \gamma_1+\gamma_2+\gamma_3+...+\gamma_{p-1}=0$
$H_1:$ at least one $\gamma_k \neq 0$
$p_value=0.02646033548618978$
As $p_value \lt \alpha$, indicates significant heteroscendasticity problem

2. Check Influence Point & Check Nomality

• With Influence Point:
  

• Delete Influence Point and Fit the Model Again:
  

3. Check Variance Inflation Factor:

Summary for VIF process, the predictors without violating the multicollinearity issue:
['aspiration', 'doornumber', 'drivewheel', 'enginelocation', 'wheelbase', 'carlength', 'carwidth', 'carheight', 'enginesize', 'boreratio', 'stroke', 'compressionratio', 'horsepower', 'peakrpm', 'highwaympg']

4. Model Selection (Step BIC)

Summary:

After removing the influence point, we fix the normality issue and keep the model away from heteroscedasticity.
We use Step-BIC to find the best model using the updated dataset.
Final Selected Model:
price ~ enginesize + cylindernumber + enginetype + horsepower + carwidth + stroke + compressionratio + enginelocation + curbweight + peakrpm + carlength + doornumber