Question

Exhibit 16-7

When a regression model was developed relating sales (Y) of a company to its product's price (X₁), the SSE was determined to be 495. A second regression model relating sales (Y) to product's price (X₁) and competitor's product price (X₂) resulted in an SSE of 396. The sample size for both models was 33.

Refer to Exhibit 16-7. The p-value for testing which model has significantly lower SSE is:

Group of answer choices

between 0.05 and 0.10

between 0.025 and 0.05

between 0.01 and 0.025

less than 0.01

I know there is no data, none was given and that is why I am confused

Answer 1

SSE for the first model when there is only one predictor X1 is 495

SSE for the second model when there are two predictors X1 and X2 is 396

So, the Regression sum of square after X2 is added = 495 - 396 = 99

And the second model has lower SSE of 396

The degree of freedom for SSR = 2-1 = 1

The degree of freedom for SSE = 33 - 2 = 31

So, F statistic is

F = (SSR / 1) / (SSE / 31) = (99) / (396 / 31) = 7.75

so p value is P(F > 7.75) = 0.009 which is less than 0.01