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Answer: 59% of the total variation in the dependent variable is explained by the independent variables
The coefficient of determination (R-squared) measures the proportion of variance in the dependent variable that is explained by the independent variables in a regression model. In this case, with R-squared = 0.59, it means that 59% of the total variation in the dependent variable is explained by the three independent variables. **Key points:** - R-squared ranges from 0 to 1, where 0 indicates no explanatory power and 1 indicates perfect explanation - In multiple regression, R-squared represents the combined explanatory power of all independent variables - Option A is incorrect because the dependent variable doesn't explain variation - it's what's being explained - Option B is incorrect because the correlation coefficient would be the square root of R-squared (√0.59 ≈ 0.77), not equal to it - Option C is incorrect because high correlation between independent variables (multicollinearity) would be indicated by other diagnostics, not by R-squared value
Author: Nikitesh Somanthe
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In a problem involving three independent variables and one dependent variable, assume that the computed coefficient of determination is 0.59. This result means that:
A
59% of the total variation is explained by the dependent variable
B
The correlation coefficient is 0.59 as well
C
At least two of the three independent variables are highly correlated
D
59% of the total variation in the dependent variable is explained by the independent variables