Asked by Sydni Redding on Jul 22, 2024
Verified
In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. = 45+ 19x1 + 63x2 + 80x3
For this model, SSR = 800 and SSE = 200.The multiple coefficient of determination for the above model is
A) .667.
B) .800.
C) .336.
D) .200.
SSR
Sum of Squared due to Regression, indicates the proportion of variance in the dependent variable that is predictable from the independent variable(s).
SSE
Sum of Squared Errors, a measure used in statistics to quantify the difference between observed and predicted values.
- Explain the significance of the multiple coefficient of determination in relation to how well a model aligns with observed data.
Verified Answer
JS
Jackie SiebertJul 25, 2024
Final Answer :
B
Explanation :
The formula for the multiple coefficient of determination is:
R squared = SSR / SST
where SST is the total sum of squares, which is equal to the sum of squared residuals (SSE) plus the sum of squared regression (SSR):
SST = SSE + SSR
Plugging in the given values, we get:
SST = SSE + SSR = 200 + 800 = 1000
R squared = SSR / SST = 800 / 1000 = 0.8
Therefore, the multiple coefficient of determination for the above model is 0.8 or 80%. The closest choice is B.
R squared = SSR / SST
where SST is the total sum of squares, which is equal to the sum of squared residuals (SSE) plus the sum of squared regression (SSR):
SST = SSE + SSR
Plugging in the given values, we get:
SST = SSE + SSR = 200 + 800 = 1000
R squared = SSR / SST = 800 / 1000 = 0.8
Therefore, the multiple coefficient of determination for the above model is 0.8 or 80%. The closest choice is B.
Learning Objectives
- Explain the significance of the multiple coefficient of determination in relation to how well a model aligns with observed data.
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