If the slope of the regression line is negative and the correlation coefficient is -.5, coefficient of determination is:
- It would be -0.25.
Correlation coefficient = r and coefficient of determination = r^2. Then, coefficient of determination would be (-0.50)^2 = 0.25, but because slope is negative, the coefficient of determination would be also negative.
Can you check my answer if it is right or not?
Yes, your answer is correct. The coefficient of determination, denoted as r^2, represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). Since the correlation coefficient (r) is -0.5, squaring it gives an r^2 value of 0.25.
However, it's important to note that the coefficient of determination can never be negative, as it represents the proportion of explained variance. So while the squared correlation coefficient is 0.25, the coefficient of determination will be positive regardless of the sign of the slope of the regression line. Thus, the correct answer would be 0.25, not -0.25.