$1.(35$ points$)$ The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. Using the data in SMOKE, we estimate a linear probability model for smokes: Using data we estimate the following OLS regression. dsmokes $=\mathrm{.}656$

$(\mathrm{.}855)[\mathrm{.}856]\mathrm{.}069(\mathrm{.}204)[\mathrm{.}207]$ log$($cigprice$)+\mathrm{.}012(.\mathrm{.}026)[\mathrm{.}026]$ log$($income$)\mathrm{.}029(\mathrm{.}006)[\mathrm{.}006]$ educ $+\mathrm{.}020(\mathrm{.}006)[\mathrm{.}005]$ age $\mathrm{.}00026(\mathrm{.}00006)[\mathrm{.}00006]$ age$2\mathrm{.}101$

$(\mathrm{.}039)[\mathrm{.}038]$ restaurn $\mathrm{.}026(\mathrm{.}052)[\mathrm{.}050]$ white

n $=807,$ R$2=0\mathrm{.}062$

where

cigprice $=$ the per pack price of cigarettes $($in cents$).$

white $=$ equals one if the respondent is white, and zero otherwise.

income $=$ annual income.

educ $=$ years of schooling.

age $=$ age measured in years.

restaurn $=$ a binary indicator equal to unity if the person resides in a state with restaurant smoking restrictions.

Both the usual and heteroskedasticity$-$robust standard errors are reported.

$($a$)$ Are there any important differences between the two sets of standard errors?

$($b$)$ Holding other factors fixed, if a person resides in a state with restaurant smoking restrictions how

does this affect the probability of them smoking?

$($c$)$ Person number $206$ in the data set has the following characteristics: cigpric $=67\mathrm{.}44,$ income $=6,500,$

educ $=12,$ age $=77,$ restaurn $=0,$ white $=0,$ and smokes $=0.$ Compute the predicted probability of smoking for this person and comment on the result.

$2.(15$ points$)$ Consider a linear model to explain GPA:

GP A $=$ $0+$ $1$study $+$ $2$sleep $+$ $3$work $+$ u

E$($u$|$study$,$ sleep, work$)=0$

E$($var$|$study$,$ sleep, work$)=$ $2$ study$2$

Write the transformed equation that has a homoskedastic error term.

$($These following questions are computer questions and are to be answered in RStudios coding$)$

Use the data in PNTSPRD for this exercise.

$($a$)$ The variable sprdcvr is a binary variable equal to one if the Las Vegas point spread for a college basketball game was covered. The expected value of sprdcvr$,$ say $,$ is the probability that the spread is covered in a randomly selected game.

Test H$0$ : $=\mathrm{.}5$ against H$1$ : $=\mathrm{.}5$ at the $10\%$ significance level and discuss your findings. $($Hint: This is easily done using a t test by regressing sprdcvr on an

intercept only.$)$

$($b$)$ How many games in the sample of $553$ were played on a neutral court?

$($c$)$ Estimate the linear probability model

sprdcvr $=$ $0+$ $1$f avhome $+$ $2$neutral $+$ $3$f av$25+$ $4$und$25+$ u

and report the results in the usual form. $($Report the usual OLS standard errors and the heteroskedasticity$-$ robust standard errors.$)$ Which variable is most significant, both practically and statistically?

$2.$ Use the data in KIELMC for this exercise. Reference the functions I uploaded for this

assignment for an example.

$($a$)$ Provide a table with summary statistics for this data set. Use sumtable function. If your code does not output, comment out the code. This should still work when you knit to an html file.

$($b$)$ Using ggplot, create a scatter plot with log price on the vertical axis and log distance on the horizontal axis. On your scatter plot, make the observations that are from $1981$ a different color than those from $1978.$