Fit and interpret a linear model using the Teams table in the publicly available Lahman baseball database. You can follow the link and download the $.$csv files; once you download the zipped folder, you can find the file by following:

baseballdatabank $$ core $$ Teams.csv$.$ If you are using R$,$ it might be more convenient to install the Lahman package and load the teams dataframe:

install.packages$("$Lahman$")$

library$($Lahman$)$

teams $=$ Teams

We are going to model how run differential impacts the number of games a team will win in a single season. Start by creating a new variable for run differential, which is the number of runs scored minus the number of runs allowed:

R$\_$diff $=$ R $-$ RA$.$ Next, fit a simple linear model where the dependent variable is wins $($W$)$ and the independent variable is run differential. Only use data from seasons after $1970.$ You may take any additional steps you deem appropriate to

clean the data. Please answer the following questions and share any code or output you used to formulate your responses.

According to your model fit, how many extra runs are needed to obtain $1$ extra win?