Question

Consider two variables and the least squares equation for their line y=.8565 + 0.40248 x. Regression analysis revealed the following: s = 0.517508 r = .9838 What percentage of the variation of y cannot be explained by the variation of x?

A. 96.8

B. 98.38

C. 3.2

D. 1.6
2

Answer 1

Given :

Least square regression equation is

y = 0.8565 + 0.40248x

Also,

S = 0.517508

r = 0.9838

Therefore ,

r^2 is defined as the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.

So

r^2 = r * r = 0.9838 * 0.9838 = 0.9679 = 96.8%

Data are variations explained.

Now we want to find variations not explained.

Therefore,

(1- r^2) = 1 - 0.9679 = 0.032 = 3.2%

answer : option "c" is correct.