Final answer:
To calculate MSR and MSE for the given regression data, use the formulas MSR = SSR / degrees of freedom for regression and MSE = SSE / degrees of freedom for error. After calculating SSE (SST - SSR), we find MSR = 6213.375 and MSE = 65.094. The F statistic is then calculated as F = MSR / MSE, which can be used to perform an F-test at α = 0.05 to determine if the regression model is significant.
Step-by-step explanation:
To calculate the Mean Square Regression (MSR) and the Mean Square Error (MSE), you use the following formulas:
- MSR = SSR / degrees of freedom for regression
- MSE = SSE / degrees of freedom for error
Given that SSR = 6213.375 and SST (which is the sum of SSR and SSE) = 6734.125, we can calculate SSE as SST - SSR = 6734.125 - 6213.375 = 520.750.
With 10 observations and 2 predictors, degrees of freedom for regression is 2 - 1 = 1 and degrees of freedom for error is 10 - 2 = 8. Therefore:
- MSR = 6213.375 / 1 = 6213.375
- MSE = 520.750 / 8 = 65.094
For the F-test, you calculate the F statistic using MSR and MSE, which is F = MSR / MSE. Then, using an F distribution table or software, you compare the calculated F to the critical F value at α = 0.05 to determine if the regression model is statistically significant.
The calculated F statistic is:
F = 6213.375 / 65.094 ≈ 95.401
If the calculated F is greater than the critical F value from the F distribution table at α = 0.05, we reject the null hypothesis that the model is not significant.