Question: In addition to measuring the engagement of each of the sampled employees, the consultants also measured the amount of supervisor support that each of the sampled employees perceive they receive. The amount of supervisor support is measured by a SUP score on a scale of one to fifty. Using the ENG and SUP scores, the consultants performed the following simple linear regression analysis:

In the questions that follow, let the population regression line be denoted by \(E\left( y|x \right)={{\beta }_{0}}+{{\beta }_{1}}x\), where the response variable y is ENG and the predictor variable x is SUP. Recall that the simple linear regression model assumes constant variance, i.e., \(\operatorname{var}\left( y|x \right)={{\sigma }^{2}}\) .

What is the amount of variability in the ENG scores that is explained by taking the SUP scores into account through a linear relationship?