Question

Coefficient of determination measures 

(A) Correlation between the dependent and independent variables. 
(B) The residual sum of squares as a proportion of the total sum of squares. 
(C) The explained sum of squares as a proportion of the total sum of squares. 
(D) How well the sample regression fits the data. 
Choose the correct answer from the options given below:
 

• A. (A), (B) and (D) only
• B. (A), (C) and (D) only
• C. (A), (B), (C) and (D)
• D. (C) and (D) only

Hint:

The coefficient of determination (\( R^2 \)) measures the proportion of variance explained by the regression model. Higher \( R^2 \) values indicate better model fit.

Answer 1

The Correct Option is B

Step 1: Understand the coefficient of determination.
The coefficient of determination, denoted \( R^2 \), measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It provides a key indication of how well a regression model explains the data.

Step 2: Analysis of options.
- (A) Correlation between the dependent and independent variables: This is partially correct. The coefficient of determination is related to the square of the correlation coefficient, but it is not simply the correlation itself.
- (B) The residual sum of squares as a proportion of the total sum of squares: This is incorrect. The coefficient of determination is related to the proportion of the explained sum of squares, not the residual sum of squares.
- (C) The explained sum of squares as a proportion of the total sum of squares: This is correct. The coefficient of determination is defined as the ratio of the explained variation to the total variation in the dependent variable.
- (D) How well the sample regression fits the data: This is correct. \( R^2 \) is a measure of how well the regression model fits the observed data.

Step 3: Conclusion.
The correct answer is (A), (C), and (D) only, as they accurately describe the coefficient of determination.