$4.$

Using the college.csv dataset

Perform a Simple Linear Regression of Top$10$perc as the independent variable to graduation rate as the dependent variable $-$ show all code to answer the following questions.

Create a data frame called X that drops Grad.Rate $($since this is the dependent variable$).$ Alternatively, you can create a new X dataframe that is only comprised of the dependent variable Top$10$perc. Whichever way you go$,$ you will only be using the single independent variable.

Create a Series called y that is the Grad.rate feature.

Perform an $80/20$ test train split resulting in X$\_$train X$\_$test, y$\_$train and y$\_$test

Train and test the model.

Show the coefficient and intercept

Show R$^2$ and RMSE $-$ interpret these.

Show a line chart with datapoints and the regression line. Title and label accordingly.

$7.$

Leveraging the X and y defined in Question $4,$ perform a multiple linear regression.

Perform label encoding for any categorical features. You will need to drop any categorical features after this step since linear regression operates on numerical data.

Perform an $80/20$ test train split resulting in X$\_$train X$\_$test, y$\_$train and y$\_$test

Use all features perform the regression

Train and test the model.

Provide R$^2$

P$-$values

F$-$Statistic

Coefficients and intercept

Interpret results.