If the slope of the regression line is negative and the correlation coefficient is -0.5, coefficient of determination is:
r = -0.5 r2 = 0.25 but because slope of regression line is negative, then coefficient of determination would be also negative. r2 = -0.25
The coefficient of determination is always positive.
The coefficient of determination (r^2) is always a positive value between 0 and 1, regardless of the slope of the regression line. The coefficient of determination represents the proportion of the variation in the dependent variable that can be explained by the independent variable(s). Therefore, it cannot be negative.
Given that the correlation coefficient (r) is -0.5, the coefficient of determination (r^2) can be calculated by squaring the value of r:
r^2 = (-0.5)^2 = 0.25
So, the coefficient of determination is 0.25, and not -0.25.
The coefficient of determination is a measure of how well the regression line fits the data points. It represents the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).
To calculate the coefficient of determination, you need to square the correlation coefficient (r). In this case, the correlation coefficient is -0.5. When you square -0.5, you get 0.25.
However, the coefficient of determination is always positive and represents the proportion of variance that can be explained by the regression line. Therefore, even if the slope of the regression line is negative, the coefficient of determination will still be positive.
In this case, since the calculated r^2 value is 0.25, the coefficient of determination is 0.25. It indicates that 25% of the variance in the dependent variable can be explained by the independent variable.