## Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and the slope estimates for the model

### economics

##### Description

Here are a few exercises, the first of which involves doing a regression by hand. It doesn't take too long to see how boring this is, and how much more tedious it would be if the number of observations (or explanatory variables, as we will see) were large. For this reason, we will soon turn these tasks over to the computer. For now, though, it is useful to do things by hand to get a feel for what the machine is doing. Show all of your work.

1. Do this one by hand, just for the (unpleasant) experience. The following table contains ACT scores and GPA (grade point average) scores for 8 college students. (The ACT is an SAT-type test, popular at Midwestern schools. Instead of ranging from 200 – 800, the ACT ranges from 20 – 30.) Grade point average is based on a 4-point scale and has been rounded to one digit after the decimal.

(i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and the slope estimates for the model

Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score increases by 5 points?