Question

If the error sum of squares is 12 and the total sum of squares is 400, then the proportion of observed y variation explained by the simple linear regression model is___________:

a. 0.173
b. 0.970
c. 0.030
d. 0.985

Answer 1

The proportion of observed y variation explained by the simple linear regression model can be determined using the coefficient of determination, which is 1 - (error sum of squares / total sum of squares). In this case, it is b. 0.970.

Step-by-step explanation:

The proportion of observed y variation explained by the simple linear regression model can be determined using the coefficient of determination, denoted as r². The formula for calculating the coefficient of determination is 1 - (error sum of squares / total sum of squares).

In this case, the error sum of squares is 12 and the total sum of squares is 400. So, the proportion of observed y variation explained by the simple linear regression model is 1 - (12 / 400), which gives us 0.970.

Therefore, the correct answer is option b. 0.970.