**Due:** At the start of class on Thursday, Feb. 3. Please turn in a hard copy.

**Textbook Questions** 2.5, 2.6, 2.10, 2.11, 2.12, 2.13, 2.14. For the TRUE or FALSE questions, make sure to provide an explanation.

**Extra Question**

For this question, we will use data from Project Star. To access this data, please install the `Ecdat`

package and run the following code: `data(Star, package="Ecdat")`

. To view a description of the data, you can run the following code: `?Ecdat::Star`

.

Project Star is a very well-known experiment in Tennessee in the 1980s where students were randomly assigned to be in a small class, a regular class, or in a class with a teaching aid. The study was focused on whether or not reducing class sizes improved student’s test scores.

For this problem, we will be interested in the \(ATT\) of being in a small class relative to a regular class for boys on their math test scores (that is, I’d like for you to use a subset of the data that only includes boys and only includes students who were assigned to a small class or regular class).

Exploiting that the treatment is randomly assigned, calculate an estimate of the \(ATT\) by comparing the mean of

`tmathssk`

for boys in small class sizes relative to boys in regular classes.Now, use a regression to calculate the same \(ATT\) as we were interested in from part (a). [For this part, you can compare your answer to results that use

`lm`

, but I’d like for you to use matrix algebra for your main result.] How do the results compare to the ones from part (a)?Now, run a regression that additionally includes the teacher’s experience (

`totexpk`

) and free lunch status (`freelunk`

) as additional regressors. [As before, you can compare your answer to the ones from`lm`

, but please report your final answer using matrix algebra.] How do these results compare to the ones from parts (a) and (b)?