Question

You are given the total variation, the unexplained variation(SS), and the least squares point estimate b₁ below.

Total variation =13.459; SSE= 2.806; b₁= 2.6652

Find explained variation, the simple correlation of determination (r²) and the simple correlation coefficient (r). interpret r₂.

Answer 1

The explained variation is 10.653, the simple correlation of determination (r²) is 7.08606004, and the simple correlation coefficient (r) is approximately 2.66. Approximately 70.86% of the total variation can be explained by the regression line.

Step-by-step explanation:

The explained variation can be found by subtracting the unexplained variation (SSE) from the total variation. So, explained variation = total variation - SSE. In this case, explained variation = 13.459 - 2.806 = 10.653.

The simple correlation of determination (r²) is the square of the simple correlation coefficient (r). So, r² = b₁² = 2.6652² = 7.08606004.

The simple correlation coefficient (r) can be found by taking the square root of the simple correlation of determination (r²). So, r = √r² = √7.08606004 ≈ 2.66. The interpretation of r² is that approximately 70.86% of the total variation can be explained by the regression line.