The Enigma hotdogs (II)

Why did we include advertising expenses squared in the second model? Clearly, the quality of the model is determined by the behavior of the residuals, that is, the difference between observed and estimated values. Let’s construct a residual plot for the first model: price and advertising expenses are included in the first degree.

qt∼pt+at

All notations are given in the previous post. The results are shown in the figure below.

For convenience, a smoothed curve (green color) is provided. A visual examination reveals a dependence of the residuals on the fitted values (heteroskedasticity), and the Breusch-Pagan test confirms this conclusion:

Non-constant Variance Score Test

Variance formula: ∼ fitted.values

Chisquare = 5.230649, Df = 1, p = 0.022192

The behavior of the residuals confirms the assumption of using higher degrees in the model, so we will limit ourselves to the second degree for advertising expenses.

qt∼pt+at+I(at^2)

The residual plot for the second model is shown in the figure below.

The analysis of the residuals using the Breusch-Pagan test confirms their homogeneity (homoskedasticity).