A multiple regression has a sample of 16 with 3 independent variables. Given SSE = 180 and SSR = 90 what is the value of the F test statistic used to test the significance of the overall multiple regression model.
Question
A multiple regression has a sample of 16 with 3 independent variables. Given SSE = 180 and SSR = 90 what is the value of the F test statistic used to test the significance of the overall multiple regression model.
Solution
To calculate the F test statistic for a multiple regression model, we need to know the sum of squares due to regression (SSR), the sum of squares due to error (SSE), the number of predictors (p), and the total sample size (n).
Here are the steps to calculate the F statistic:
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Calculate the degrees of freedom for the regression (df1) and the error (df2). The degrees of freedom for the regression is equal to the number of predictors, which is 3 in this case. The degrees of freedom for the error is equal to the total sample size minus the number of predictors minus 1, which is 16 - 3 - 1 = 12.
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Calculate the mean square due to regression (MSR) and the mean square due to error (MSE). The MSR is equal to the SSR divided by df1, which is 90 / 3 = 30. The MSE is equal to the SSE divided by df2, which is 180 / 12 = 15.
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Calculate the F statistic. The F statistic is equal to the MSR divided by the MSE, which is 30 / 15 = 2.
So, the F test statistic used to test the significance of the overall multiple regression model is 2.
Similar Questions
A sample of 12 observations collected in a multiple regression study on two independent variables (X1 and X2) shows the following partial results. SST = 12321 and SSE = 3516. If SSR(X1) = 4496 and SSR(X2) = 5378, what would be the value of the partial F test statistic used to test the null hypothesis that variable X1 does not significantly improve the model after variable X2 has been included? Round your final answer to two decimal places.
Suppose that in a multiple regression the F test statistic is significant, but none of the t test statistics are significant. This means that ________. a. multicollinearity may be present b. autocorrelation may be present c. collinearity may be present d. (a) and (c).
A sample of 12 observations collected in a multiple regression study on two independent variables (X1 and X2) shows the following partial results. SST = 12321 and SSE = 3516. If SSR(X1) = 4496 and SSR(X2) = 5378, and you would like to test the null hypothesis that variable X1 does not significantly improve the model after variable X2 has been included, what would be the critical value of F at the 5% level of significance?
The overall regression F-statistic tests the null hypothesis that: a. all slope coefficients and the intercept are zero. b. all slope coefficients are zero. c. the slope coefficient of the variable of interest is zero, but that the other slope coefficients are not. d. the intercept in the regression and at least one, but not all, of the slope coefficients is zero.
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