Assignment 7

## Backward Elimination Method 
## ---------------------------
## 
## Candidate Terms: 
## 
## 1. Store 
## 2. Holiday_Flag 
## 3. Temperature 
## 4. Fuel_Price 
## 5. CPI 
## 6. Unemployment 
## 
## 
## Step   => 0 
## Model  => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment 
## R2     => 0.918 
## 
## Initiating stepwise selection... 
## 
## 
## No more variables to be removed.

## Backward Elimination Method 
## ---------------------------
## 
## Candidate Terms: 
## 
## 1. Store 
## 2. Holiday_Flag 
## 3. Temperature 
## 4. Fuel_Price 
## 5. CPI 
## 6. Unemployment 
## 7. Store:Holiday_Flag 
## 8. Store:Temperature 
## 9. Store:Fuel_Price 
## 10. Store:CPI 
## 11. Store:Unemployment 
## 12. Holiday_Flag:Temperature 
## 13. Holiday_Flag:Fuel_Price 
## 14. Holiday_Flag:CPI 
## 15. Holiday_Flag:Unemployment 
## 16. Temperature:Fuel_Price 
## 17. Temperature:CPI 
## 18. Temperature:Unemployment 
## 19. Fuel_Price:CPI 
## 20. Fuel_Price:Unemployment 
## 21. CPI:Unemployment 
## 
## 
## Step   => 0 
## Model  => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Unemployment + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment 
## R2     => 0.93 
## 
## Initiating stepwise selection... 
## 
## Step     => 1 
## Removed  => Unemployment 
## Model    => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:CPI + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment 
## R2       => 0.93027 
## 
## Step     => 2 
## Removed  => Holiday_Flag:CPI 
## Model    => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + Fuel_Price:Unemployment + CPI:Unemployment 
## R2       => 0.93027 
## 
## Step     => 3 
## Removed  => Fuel_Price:Unemployment 
## Model    => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI + CPI:Unemployment 
## R2       => 0.93027 
## 
## Step     => 4 
## Removed  => CPI:Unemployment 
## Model    => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:Fuel_Price + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI 
## R2       => 0.93026 
## 
## Step     => 5 
## Removed  => Store:Fuel_Price 
## Model    => Weekly_Sales ~ Store + Holiday_Flag + Temperature + Fuel_Price + CPI + Store:Holiday_Flag + Store:Temperature + Store:CPI + Store:Unemployment + Holiday_Flag:Temperature + Holiday_Flag:Fuel_Price + Holiday_Flag:Unemployment + Temperature:Fuel_Price + Temperature:CPI + Temperature:Unemployment + Fuel_Price:CPI 
## R2       => 0.92952 
## 
## 
## No more variables to be removed.
## 
## Variables Removed: 
## 
## => Unemployment 
## => Holiday_Flag:CPI 
## => Fuel_Price:Unemployment 
## => CPI:Unemployment 
## => Store:Fuel_Price

The model, using the training data, has an R^2 of 0.9328. The model, using the validation data on R^2 of 0.917

Interpret 3 predictors

Fuel Price: When fuel prices go up, sales go down

Holiday_Flag: Sales increase during holidays

CPI: as the CPI goes up, so do sales