if the independent variable in a regression model explains none of the variation in the dependent variable. then the predicted value of rthe regression model, Y hat, is the average value of the dependent variable Y bar. I do not get the underlying logic, why Y hat = Y bar in the above condition.
So look at the ANOVA table Variable******DOF******Sum Of Squares Regression****1********0 So YHat-Ybar = 0… or YHat=YBar
but why sum of squares is zero
if the independent variable in a regression model explains none of the variation in the dependent variable
that is what I am asking, why if the independent variable in a regression model explains none of the variation in the dependent variable then sum of squares is 0 cpk123 Wrote: ------------------------------------------------------- > if the independent variable in a regression model > explains none of the variation in the dependent > variable
> I do not get the underlying logic, why Y hat = Y bar in the above condition. Yhat does not equal to Ybar. What the statement you refer to is saying, is that when the regression equation does not explain any of the variation, the coefficient of determination is zero, and the correlation is also zero. Ybar is a single point on the vertical axis which cuts in a straight horizontal through the middle of the Yhat line. What do you think the correlation between Ybar and this line? It’s zero, because Ybar basically divides the Yhat line into two symmetrical halves. There is no relationship (i.e., zero correlation) between points on Ybar (a single value) and points on Yhat, e.g., you will find that when (say) Yhat=5, Ybar=20, when Yhat= - 5, Ybar=20, and when Yhat=0, Ybar=20.