In a multiple regression model involving 50 observations, the following estimated regression equation was obtained: = 20 + 5x₁ - 4x₂ + 8x₃ + 8x₄ For this model, SSR = 700 and SSE = 100.At the 5% level, A) there is no evidence that the model is significant. B) it can be concluded that the model is significant. C) the conclusion is that the slope of x₁ is significant. D) there is evidence that the slope of x₂ is significant.

Question

Quizplus · Accepted Answer

To test if the model is significant, we perform an F-test with the null hypothesis being that all the regression coefficients in the model are zero. The F-statistic is calculated as (SSR/4)/(SSE/45) = 35. Since the p-value associated with this F-statistic is less than 0.05, we can conclude that the model is significant. Option B is correct. Option A is incorrect because the model is significant. Option C and D are incorrect because we cannot determine the significance of individual coefficients without performing t-tests or looking at the confidence intervals.

In a Multiple Regression Model Involving 50 Observations, the Following