The following ANOVA table was obtained when estimating a multiple regression mod

Question

The following ANOVA table was obtained when estimating a multiple regression model. a. Calculate the standard error of the estimate. (Round your answer to 2 decimal places.) b. Calculate the coefficient of determination. (Round your answer to 4 decimal places.) Interpret the coefficient of determination. The proportion of the variation in y that is explained by the regression model. The proportion of the variation in x that is explained by the regression model. c. Calculate adjusted R^2. (Round your answer to 4 decimal places.)

Explanation / Answer

a) The Root Mean Square Error (also known as the standard error of the estimate) is the square root of the Residual Mean Square. It estimates the common within-group standard deviation.

sqrt(2273.21) = 47.68

b) Coefficient of Determination = r2 = 1 - SS(Residual) / SS(Total)

r2 = 1 - 45464.27/234251.27 = 0.8059167 = 0.8059

c) The proportion of the variation in y that is explained by the regression model.

d) n = 23, k = 3
R2adj = R2 - (1-R2 )*(k-1)/(n-k) = 0.8059167 - 0.1940833*2/20 = 0.7865

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