Use the value of the linear correlation coefficient to calcu

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r = 0.749 Calculate the coefficient of determination. (Round to three decimal places as needed.) What does this tell you about the explained variation of the data about the regression line? % of the variation can be explained by the regression line. (Round to one decimal place as needed.) About the unexplained variation? % of the variation is unexplained and is due to other factors or to sampling error. (Round to one decimal place as needed.)

Solution

we have r = 0.749

a) The coefficient of determinatoin is given by

r² = (0.749)² = 0.561

b) The coefficient of determination is r² = 0.561 that is 56.1 % of the variations can be explained by regression line.

c) 1 - r² = 1 - 0.561 = 0.439 that is 43.9 % oft the variation is unexplained and is due to other factors or to sampling error.