Question

The coefficient of determination, R2 : Is always negative May be negative or positive Ranges from -1 to +1 Ranges from zero to one Is the ratio of unexplained variation to explained variation Is the ratio of explained variation to unexplained variation has the same sign as the slope of the regression line

Answer 1

Solution: There are two terms R and R². R denotes the correlation coefficient and R² denotes the coefficient of determination.The correlation coefficient R measures the strength and the direction of a linear relationship between two variables. The value of R may be negative or positive and it ranges from -1 to +1. The Correlation coefficient R has the same sign as the slope of the regression line.

The coefficient of Determination R² measures the proportion of the variance of the dependent variable that is predictable from the explanatory variables. The Coefficient of Determination R² is the square of Correlation Coefficient R.The coefficient of determination, R² is always positive and it ranges from zero to one. It is the ratio of the explained variation to the total variation. The sign of the coefficient of determination is not always the same as the sign of the slope of the regression line.