A researcher is investigating possible explanations for deaths in traffic accidents.He examined data from 1991 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of his investigation he ran the multiple regression model, Deaths = $\beta$₀ + $\beta$₁(Children)+ $\beta$₂(Income)+ $\varepsilon$_i, Where the deviations $\varepsilon$_i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of $\sigma$.This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose we wish to test the hypotheses H₀: $\beta$₁ = $\beta$₂ = 0 versus H_a: at least one of the $\beta$_j is not 0 using the ANOVA F test.What is the value of the F statistic? A)0.94 B)15.9 C)24 D)381.5

Question

Quizplus · Accepted Answer

The ANOVA F test is used to test the hypothesis that at least one of the regression coefficients is non-zero. The test statistic is calculated as the ratio of the mean square regression to the mean square error. In this case, the mean square regression is the sum of squares due to regression (SSR) divided by the degrees of freedom for regression (k-1), and the mean square error is the sum of squares due to error (SSE) divided by the degrees of freedom for error (n-k). From the output given, SSR = 14207.14, SSE = 57112.86, k = 3, and n-k = 48. Thus, the F statistic is:

F = (SSR / (k-1)) / (SSE / (n-k)) = (14207.14 / 2) / (57112.86 / 48) = 381.5

Therefore, the answer is D.

A Researcher Is Investigating Possible Explanations for Deaths in Traffic β\betaβ

A Researcher Is Investigating Possible Explanations for Deaths in Traffic $\beta$