Asked by Alejandra Veloz on Jul 13, 2024
Verified
For a multiple regression model, SSR = 600 and SSE = 200.The multiple coefficient of determination is
A) .333.
B) .275.
C) .30.
D) .75.
Determination
Generally refers to the process of firm decision-making or the resolving of a problem; in statistics, it may refer to the coefficient of determination.
SSR
Sum of Squared Residuals; a measure of the discrepancy between the data and an estimation model.
- Understanding how to compute and interpret the multiple coefficient of determination.
Verified Answer
AL
Austin LutherJul 16, 2024
Final Answer :
D
Explanation :
The multiple coefficient of determination, denoted as R-squared (R²), is defined as the proportion of variation in the dependent variable (y) that is explained by the independent variables (x's) in the multiple regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data.
R² is calculated as:
R² = SSR / SST
where SST (total sum of squares) is the sum of the squared differences between the observed y values and the mean of y. In other words, SST measures the total variation in y.
Since the model has k independent variables and n observations, we can write:
SST = SSR + SSE
where SSE (error sum of squares) is the sum of the squared differences between the observed y values and the predicted y values from the model. In other words, SSE measures the unexplained variation in y.
Substituting the given values, we get:
SST = 600 + 200 = 800
R² = SSR / SST = 600 / 800 = 0.75
Therefore, the multiple coefficient of determination is 0.75, which means that 75% of the variation in the dependent variable is explained by the independent variables in the model. The best choice is D.
R² is calculated as:
R² = SSR / SST
where SST (total sum of squares) is the sum of the squared differences between the observed y values and the mean of y. In other words, SST measures the total variation in y.
Since the model has k independent variables and n observations, we can write:
SST = SSR + SSE
where SSE (error sum of squares) is the sum of the squared differences between the observed y values and the predicted y values from the model. In other words, SSE measures the unexplained variation in y.
Substituting the given values, we get:
SST = 600 + 200 = 800
R² = SSR / SST = 600 / 800 = 0.75
Therefore, the multiple coefficient of determination is 0.75, which means that 75% of the variation in the dependent variable is explained by the independent variables in the model. The best choice is D.
Learning Objectives
- Understanding how to compute and interpret the multiple coefficient of determination.
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