Question

A statistics practitioner in a large university is investigating the factors that affect the salary of professors. He wondered if evaluations by students are related to salaries. To this end, he collected 100 observations on: y = Annual salary (in dollars) x = Mean score on teaching evaluation To accomplish his goal, he assumes the following relationship: y = β(0) + β(1)x + ε Then, using Excel’s Data Analysis, he obtained the following result. R2=0.23 Coefficient Standard Error Intercept 25675.5 11393 x 5321 2119

The estimated regression model is given by y hat= b0+b1x = 25675.5 + 5321* x. What is the interpretation of b1?
a. When the mean score on teaching evaluation increases by 1, the average annual salary increases by 25675.5 dollars.
b. When the mean score on teaching evaluation increases by 1, the average annual salary increases by 5321 dollars.
c. When annual salary increases by a dollar, the mean score on teaching evaluation increases by 5321.
d. When annual salary increases by a dollar, the mean score on teaching evaluation increases by 25675.5.

Answer 1

b. When the mean score on teaching evaluation increases by 1, the average annual salary increases by 5321 dollars.

Explanation:

The parameter b1 is the slope of the linear regression model. It has a value of 5,321 in this model.

It also represents the rate of variation of the salaries (predicted y, the dependendant or response variable) to a variation of one unit in the evaluation score (x, the independente variable).

Then, for each unit that the evaluation score (x) increases, the annual salary is predicted to increase in $5,321.

The answer is:

b. When the mean score on teaching evaluation increases by 1, the average annual salary increases by 5321 dollars.