In a simple linear regression problem,suppose that $\sum e _ { i } ^ { 2 } = 12.48 \text { and } \sum \left( Y _ { i } - Y \right) ^ { 2 } = 124.8$
.Then the percentage of variation explained $R ^ { 2 }$
must be 0.90.

Question

In a simple linear regression problem,suppose that $\sum e _ { i } ^ { 2 } = 12.48 \text { and } \sum \left( Y _ { i } - Y \right) ^ { 2 } = 124.8$ 
.Then the percentage of variation explained $R ^ { 2 }$ 
must be 0.90.

Quizplus · Accepted Answer

The coefficient of determination $R^2$ is calculated as $1 - \frac{\sum e_i^2}{\sum (Y_i - \bar{Y})^2}$. Substituting the given values, $R^2 = 1 - \frac{12.48}{124.8} = 0.90$.

In a Simple Linear Regression Problem,suppose That ∑ei2=12.48 and ∑(Yi−Y)2=124.8\sum e _ { i } ^ { 2 } = 12.48 \text { and } \sum \left( Y _ { i } - Y \right) ^ { 2 } = 124.8∑ei2​=12.48 and ∑(Yi​−Y)2=124.8

In a Simple Linear Regression Problem,suppose That $\sum e _ { i } ^ { 2 } = 12.48 \text { and } \sum \left( Y _ { i } - Y \right) ^ { 2 } = 124.8$