A researcher studies the relationship between SAT scores,the test-taker's family income,and his or her grade point average (GPA).Data are collected from 24 students.He estimates the following model:SAT = β₀ + β₁ GPA + β₂ Income + ε.The following table summarizes a portion of the regression results. Which of the following is the value of the test statistic for testing the joint significance of the linear regression model? A) 6.40 B) 134.45 C) 67.23 D) 45.13

Question

Quizplus · Accepted Answer

The test statistic for testing the joint significance of the linear regression model is given by F = (SSR/K)/SSE/(n-K-1), where SSR is the sum of squared residuals of the full model (including all parameters), SSE is the sum of squared residuals of the restricted model (excluding the predictor in question), K is the number of predictors in the full model, and n is the sample size.

From the table, we can see that SSR = 1001.58, SSE = 2150.62, K = 3, and n = 24. Plugging these values into the formula, we get F = (1001.58/3)/(2150.62/(24-3-1)) = 67.23.

Therefore, the answer is C, 67.23.

A Researcher Studies the Relationship Between SAT Scores,the Test-Taker's Family