The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + .7x₁ + 3x₂ Also provided are SST = 1200 and SSE = 384.At the 5% level, the model A) is significant. B) is not significant. C) would be significant if the sample size was larger than 30. D) has significant individual parameters.

Question

Quizplus · Accepted Answer

To test the overall significance of the model, we use the F-test. The formula for calculating the F statistic is:

F = (SSR / k) / (SSE / (n - k - 1))

Where SSR is the regression sum of squares, k is the number of predictors in the model, SSE is the error sum of squares, and n is the sample size.

Using the given information, we can calculate that SSR = SST - SSE = 1200 - 384 = 816, k = 2, and n = 30. Substituting into the F formula, we get:

F = (816 / 2) / (384 / 27) = 11.25

To find the critical value for F at the 5% level, we look up the F distribution with 2 and 27 degrees of freedom in a table or use a calculator. The critical value is approximately 3.35.

Since our calculated F value (11.25) is greater than the critical value (3.35), we reject the null hypothesis that all the coefficients in the model are zero. Therefore, we conclude that the model is significant at the 5% level.

The Following Estimated Regression Equation Was Developed Relating Yearly Income