Use the dataset cars, which records various measurements some different cars; README.

Use mpgCity as your numeric response variable. Pick 1 categorical and 1 numerical explanatory variable to use throughout.

  1. Means by levels of the categorical explanatory variable.

    1. Make transparent box plots with your response variable on the y-axis and the categorical variable on the x-axis.

    2. Write a complete English sentence about the plot in the context of the data.

  2. Simple Linear Regression.

    1. Make a scatter plot of your two numerical variables, and put a line through the data using geom_smooth(...).

    2. Write a complete English sentence about the plot in the context of the data.

  3. Unique intercepts by levels of the categorical explanatory variable.

    1. Fit a multiple linear regression model with unique intercepts by levels of the categorical explanatory variable.

    2. Make a scatter plot with lines through the data matching your model.

    3. Write a complete English sentence about the plot/modelin the context of the data.

  4. Unique slopes by levels of the categorical explanatory variable.

    1. Fit a multiple linear regression model with unique slopes by levels of the categorical explanatory variable, and one intercept for all slopes.

    2. Interpret the intercept in context of the data. If the interpretation does not make sense, explain why.

    3. Interpret a slope in context of the data.

    4. Choose a value within the range of your numerical explanatory variable along the x-axis, call it xnew. Create bootstrap confidence intervals for predictions at xnew for two different levels of the categorical explanatory variable.

    5. Interpret your two confidence intervals in context of the data.

    6. Make an informative conclusion about your confidence intervals.

    7. Choose a value outside the range of your numerical explanatory variable along the x-axis, call it xnew_ex. What do we call this, when we predict outside the range of our data?

    8. Make a prediction at xnew_ex and interpret it context of the data. Does your prediction make sense? Why or why not?

  5. Unique intercepts and slopes by levels of the categorical explanatory variable.

    1. Fit a multiple linear regression model with unique slopes and intercepts by levels of the categorical explanatory variable.

    2. Which level has the smallest (in absolute value) slope (not slope offset)? You’ll have to do some math to calculate all the appropriate slopes.

    3. What does the smallest slope indicate about that level? Interpret largest slope in context of the data.