- #1
maverick280857
- 1,789
- 4
Hello,
In simple linear regression (or even in multiple linear regression) how does one prove that the coefficient of determination, given by
[tex]R^2 = \frac{SS_{Reg}}{SS_{Total}} = 1-\frac{SS_{Res}}{SS_{Total}}= 1-\frac{\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}{\sum_{i=1}^{n}(y_i-\overline{y})^2}[/tex]
is strictly less than 1, if there are repeat points? That is, if there are multiple values of the response [itex]y_i[/itex] at one value of the regressor [itex]x_i[/itex]?
Thanks in advance.
In simple linear regression (or even in multiple linear regression) how does one prove that the coefficient of determination, given by
[tex]R^2 = \frac{SS_{Reg}}{SS_{Total}} = 1-\frac{SS_{Res}}{SS_{Total}}= 1-\frac{\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}{\sum_{i=1}^{n}(y_i-\overline{y})^2}[/tex]
is strictly less than 1, if there are repeat points? That is, if there are multiple values of the response [itex]y_i[/itex] at one value of the regressor [itex]x_i[/itex]?
Thanks in advance.