https://classroom.github.com/a/DBmUsRom

Due: 2020-04-27 by 11:59pm

Use the dataset elmhurst, which measures the amount of money students at Elmhurst College recieved in aid, as a gift, and the student’s family income, to fit a simple linear regression model.

  1. Use the variable family_income as the explanatory variable and gift_aid as the response variable to make the following.

    1. A scatter plot, with explanatory and response variables on the apppropriate axes. Use stat_smooth() to draw a linear regression line through the data.

    2. Fit linear regression to the variables in your plot.

    3. Predict family income, \(\hat{y}\) using all the observtions in the elmhurst dataframe.

    4. Calculate the residuals, \(y - \hat{y}\), and make a density plot of these. What approximate shape do they take on?

    5. Interpret the estimated intercept in context of the data. Don’t forget the appropriate units. You should look these up on the elmhurst README.

    6. Interpret the estimated slope in context of the data. Don’t forget the appropriate units.

    7. Provide a bootstrap confidence interval for the slope. Interpret it in context of the data with the standard phrase used for confidence intervals.

    8. Provide a bootstrap confidence interval for the predicted gift aid, when family income is equal to $50,000. Careful with your units. Interpret it in context of the data with the standard phrase used for confidence intervals.