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

For this model SSR = 700 and SSE = 100. The critical F value at 95% confidence 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 critical F value at 95% confidence is

BlackTom AI · Accepted Answer

First, let's identify the components needed to compute the F critical value.
The model has 30 observations and, from the equation image, includes an intercept and four predictors, so the number of regressors is 4. Therefore:
- Degrees of freedom for regression (df_reg) = 4
- Degrees of freedom for error (df_res) = n - (p + 1) = 30 - 5 = 25
Next, the mean squares are computed from the given sums of squares:
- MSR = SSR / df_reg = 700 / 4 = 175
- MSE = SSE / df_res = 100 / 25 = 4
Thus, the F statistic for the overall regression is:
- F = MSR / MSE = 175 / 4 = 43.75
Now, regarding the critical F value at 95% confidence, it depends on the degrees of freedom (df1 = 4 and df2 = 25) and the alpha level of 0.05. For df1 = 4 and df2 = 25 at the 0.05 level, the generally tabulated critical value is approximately 2.76. This reflects the threshold beyond which the null hypothesis (that all slopes are zero) would be rejected at that significance level.
- Option 2.53: This value is lower than the typical 0.05-level critical value for these dfs, so it would not be the correct Fcritical for df1 = 4, df2 = 25 at 0.05. It's more characteristic of a scenario with different dfs or a less stringent alpha.
- Option 2.69: Similar issue; it is not the standard critical value for df1 = 4 and df2 = 25 at 0.05, though it is in the same neighborhood. The exact df and alpha matter, and 2.69 is not the conventional 0.05 critical for these dfs.
- Option 2.76: This is the commonly cited 95% (alpha = 0.05) critical value for df1 = 4 and df2 = 25, matching the standard F-distribution table for these degrees of freedom.
- Option 2.99: This would correspond to a higher threshold and is not the standard 95% critical value for these dfs; it would be closer to a more stringent cutoff or different df configuration.
In summary, given df1 = 4 and df2 = 25 at the 0.05 significance level, the appropriate critical F value is about 2.76, while the other options do not match these degrees of freedom and the usual 0.05 threshold.

MSIS 212 P 1 05 Mngrl Decision Makng Spring 2025 HW5.Reg.2

In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. The critical F value at 95% confidence is

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