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 determine if the model is significant, we need to conduct a hypothesis test on the overall model using an F-test. The null hypothesis is that all the regression coefficients (excluding the intercept) are equal to zero, meaning the model is not significant. The alternative hypothesis is that at least one regression coefficient is not equal to zero, meaning the model is significant.

The F-statistic can be calculated as (MSR/MSE), where MSR is the mean sum of squares for regression and MSE is the mean sum of squares for error.

MSR = (SST - SSE)/k = (1200 - 384)/2 = 408
MSE = SSE/(n-k-1) = 384/(30-2-1) = 13.71

F = MSR/MSE = 408/13.71 = 29.76

Using an F-table or calculator with 2 degrees of freedom for the numerator and 27 degrees of freedom for the denominator (since there are 30 observations and 2 independent variables), we find that the critical value for a 5% level of significance is 3.38. Since our calculated F-value of 29.76 is greater than the critical value of 3.38, we reject the null hypothesis and conclude that the model is significant at the 5% level. Therefore, the answer is A.

The Following Estimated Regression Equation Was Developed Relating Yearly Income