In a regression model involving 30 observations, the following estimated regression equation was obtained:

For this model SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

Question

In a regression model involving 30 observations, the following estimated regression equation was obtained:

For this model SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is

BlackTom AI · Accepted Answer

Step into the setup of an F-test for overall regression significance. The F statistic compares the model’s explained variability to the unexplained variability using the Mean Square due to Regression (MSR) and the Mean Square due to Error (MSE).

Option 1: 43.75. This value comes from the standard formula F = (SSR/df_model) / (SSE/df_error). With SSR = 700 and SSE = 100, and assuming there are 4 predictors (excluding the intercept), the degrees of freedom are df_model = 4 and df_error = n - p - 1 = 30 - 4 - 1 = 25. Thus MSR = 700/4 = 175 and MSE = 100/25 = 4. Therefore F = 175 / 4 = 43.75, which matches this option.

Option 2: 0.875. This would imply a very small MSR relative to MSE, which would occur if either the SSR or df_model were small or if the df_error were large. Given SSR = 700 and df_model = 4, the computed F is far from 0.875, so this is incorrect.

Option 3: 50.19. This would require a different combination of SSR, SSE, or degrees of freedom than provided. Using the given SSR and SSE with df_model = 4 and df_error = 25 yields 43.75, not 50.19, so this option miscalculates the ratio.

Option 4: 7.00. An F-statistic of 7.00 would correspond to a much smaller MSR relative to MSE (e.g., MSR around 28 and MSE around 4). With the actual MSR = 175 and MSE = 4, the ratio is far larger, so this option is not correct.

In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. The computed F statistic for testing the significance of the above model is单项选择题

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