Please follow the instructions on the syllabus indicating how to complete and turn in this assignment.

$1.(2$ points$)$ Suppose a university institutes a new student retention initiative designed to increase the percentage of freshman who return for their sophomore year. The initiative is undertaken and they see the retention rate increase from $75\%$ to $78\%.$ Administration hails the success and rewards the retention staff with substantial raises. Is the observed increase in retention rates compelling evidence to warrant the raises? What are the weaknesses of this evidence and how could regression analysis help address them?

$2.(2$ points$)$ Suppose you run a regression with quantity as your dependent variable and advertising as one of your independent variables. The p$-$value on advertising is $\mathrm{.}08.$ The marketing team is arguing that their advertising efforts are impacting sales, but the finance$/$economics department is arguing that there isn$$t evidence that the advertising is impacting sales. What side would you take and why? Note that this question squarely hits the idea that stats is part science$/$part art...

$4.(6$ points$)$ Propose a GENERAL $($do not put in numbers for coefficients$)$ regression equation you would like to estimate. Write out the equation $($again without specific numbers for coefficients$)$ and define the dependent and independent variables, and indicate how you would measure them. What type of data would you use and, as a result, what is an observation in your dataset? Finally, why would you want to estimate this regression $$ what would be the purpose$/$insight$?$ Keep in mind that this question is worth $60\%$ of this problem set!