Asked by Sumaya Hassan on Jul 22, 2024
Verified
A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165
SSE = 60
The multiple coefficient of determination is
A) .3636.
B) .7333.
C) .275.
D) .5.
Sum Of Squares
In statistics, the sum of squares is a measure used to quantify the variation or dispersion of a set of numbers.
Independent Variables
Variables in an experiment or model that are manipulated or classified by the researcher to observe their effect on the dependent variable.
- Understand the concept of the coefficient of determination in multiple regression analysis.
Verified Answer
BM
Basheer MaflahiJul 25, 2024
Final Answer :
B
Explanation :
The total sum of squares (SST) can be calculated as the sum of SSR and SSE: SST = SSR + SSE = 165 + 60 = 225.
The multiple coefficient of determination, R-squared, is the proportion of the total variation in the dependent variable (y) that is explained by the independent variables (x1, x2, x3, x4).
R-squared = SSR/SST = 165/225 = 0.7333
Therefore, the best choice is B, which corresponds to R-squared = 0.7333.
The multiple coefficient of determination, R-squared, is the proportion of the total variation in the dependent variable (y) that is explained by the independent variables (x1, x2, x3, x4).
R-squared = SSR/SST = 165/225 = 0.7333
Therefore, the best choice is B, which corresponds to R-squared = 0.7333.
Learning Objectives
- Understand the concept of the coefficient of determination in multiple regression analysis.
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