It is never possible for $\sum(\hat{y}-\bar{y})^{2}$ to exceed $\sum(y-\bar{y})^{2}$.

Question

Quizplus · Accepted Answer

The expression $\sum(\hat{y}-\bar{y})^{2}$ represents the sum of squared deviations of the predicted values ($\hat{y}$) from the mean of the observed values ($\bar{y}$), which is a part of the total variance explained by the model. The expression $\sum(y-\bar{y})^{2}$ represents the total variance in the observed data. Since the model cannot explain more variance than is present in the data, the sum of squared deviations of the predicted values from the mean cannot exceed the total variance in the observed data.

It Is Never Possible For ∑(y^−yˉ)2\sum(\hat{y}-\bar{y})^{2}∑(y^​−yˉ​)2 To Exceed ∑(y−yˉ)2\sum(y-\bar{y})^{2}∑(y−yˉ​)2

It Is Never Possible For $\sum(\hat{y}-\bar{y})^{2}$ To Exceed $\sum(y-\bar{y})^{2}$