Question

if the r-value, or correlation coefficient, of a data set is 0.854, what is the coefficient of determination to three decimal places?

Answer 1

To find the coefficient of determination, square the correlation coefficient:
(0.854)² = 0.729316.  To three decimal places, this would be 0.729.

Answer 2

Answer with explanation:

Coefficient of determination(r²), is defined as, how well the data values are associated with each other when Regression line is drawn. In regression analysis, the coefficient of determination  measures , how well the regression predictions approximate the real data points, means it measures the closeness between two variables.The Value of r², lies between  0 to 1. If value of r²=1, it shows ,regression line that is data values are Perfectly associated with each other.

If ,r²=0, it means there is no variation between two variables.There is 0% variation between two variables.

→Coefficient of Variation=[Correlation coefficient]²

                                         =r²

                                        =(0.854)²

                                        =0.854 × 0.854

                                         =0.729316

                                          =0.730(Approx)