Question

When we estimate a linear multiple regression model (including a linear simple regression model), it appears that the calculation of the coefficient of determination, R2, for this model can be accomplished by using the squared sample correlation coefficient between the original values and the predicted values of the dependent variable of this model.

Is this statement true? If yes, why? If not, why not? Please use either matrix algebra or algebra to support your reasoning.

Answer 1

this statement is completely false because the calculation of the coefficient of determination, R2, for this model can be accomplished by using the squared sample correlation coefficient between the independent and dependent variable of this model.

there is perfect correlation between the original values and the predicted values so this is not possible to sya that the square of it is coefficient of determination.

let us consider

(x)	(Y)
9	98
12	186
16	203
18	159
35	263

the correlation coefficient is 0.8448

coefficient of determination is 0.7136

whereas

(x)	(Y)	estimated value
9	98	585.117
12	186	1028.766
16	203	1114.471
18	159	892.6463
35	263	1416.958

the correlation coefficient is 1

coefficient of determination is 1 which is not possible