Answer :
To answer the questions related to the ANOVA table, we need to use the provided information. Here are the calculations:
a-1. The standard error of estimate (SE) can be calculated using the mean square error (MSE) from the ANOVA table. It is the square root of MSE.
SE = √(MSE) = √(52.80) ≈ 7.27
a-2. About 95% of the residuals will be within ±2 standard errors of estimate.
The range of residuals will be between ±2 * SE, which is ±2 * 7.27 = ±14.54.
b-1. The coefficient of multiple determination (R-squared) can be found by dividing the regression sum of squares (SSR) by the total sum of squares (SST).
R-squared = SSR / SST = 3,918.73 / 6,664.41 ≈ 0.588
b-2. The percentage variation for the independent variables is calculated by multiplying R-squared by 100.
Percentage variation = R-squared * 100 ≈ 0.588 * 100 ≈ 58.8%
c. The coefficient of multiple determination, adjusted for the degrees of freedom, can be calculated using the formula:
Adjusted R-squared = 1 - [(1 - R-squared) * (n - 1) / (n - p - 1)]
where n is the total number of observations and p is the number of independent variables (regressors).
Since the degrees of freedom are not provided in the ANOVA table, we cannot calculate the adjusted R-squared without that information.
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