Asked by Morgan Rivers on Jun 24, 2024
Verified
For a multiple regression model the following statistics are given: Total SS = 400, SSR = 350, k = 4, and n = 20. The coefficient of determination adjusted for degrees of freedom is:
A) 87.5%
B) 15.83%
C) 12.5%
D) 84.17%
E) 16.54%
Coefficient Of Determination
A statistical measure that determines the proportion of variance in the dependent variable predictable from the independent variable(s).
Total SS
The total sum of squares in statistical analysis, representing the overall variation within a data set.
SSR
Sum of Squared Residuals; it represents the sum of the squared differences between the observed and predicted values in statistical analysis.
- Acquire knowledge on the concept and mathematical calculation of the adjusted multiple determination coefficient.
Verified Answer
So, R-squared = SSR/Total SS = 350/400 = 0.875
The adjusted R-squared formula takes into account the number of predictors and the sample size:
Adjusted R-squared = 1 - [(1 - R-squared)(n - 1)/(n - k - 1)]
Plugging in the numbers:
Adjusted R-squared = 1 - [(1 - 0.875)(20 - 1)/(20 - 4 - 1)] = 0.8417 or 84.17%
Therefore, the answer is D.
Learning Objectives
- Acquire knowledge on the concept and mathematical calculation of the adjusted multiple determination coefficient.
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