University of California Distributions of Variables Statistics Worksheet

Q1. Summarize the distributions of both variables based on what you observe in the plots.

Q2. Include the correlations as part of your summary.

a)Summarize the joint relationship between math and reading scores based on the scatterplot in the in the first plot (black and white plot).

b)Summarize the additional information about the joint relationship between math and reading scores, by lunch type, that you observe in the second plot relative to the first plot.

c)Summarize additional information you glean about the joint relationship between math and reading scores, by test prep type, that you observe in the third plot relative to the first and second plots.

Q3.Regression of Reading on Math

a)Fit a linear regression for reading on math [do not use any log transformations] and show the regression summary.

b)In the HW3 template, we provide code to create a scatterplot of reading on math. You need to complete the geom_abline(intercept=, slope=) part of the code, filling in the values for the estimated intercept and slope, to create a scatterplot that shows the regression line. Interpret the scatterplot.

c)Interpret the coefficient of determination in the context of the problem.

Q4.Model Diagnostics

a) In the HW3 template we provide the code to create a residual plot for the original regression of reading on math. Do you see any patterns in this plot that indicate a violation of any of our regression assumptions? Use the residual plot to comment on the assumptions related to linearity, constant variance, and the presence of outliers.

b) In the HW3 template we provide the code to create a histogram and normal probability plot of the residuals for the regression, putting both plots in one figure. Do you think the residuals are approximately normally distributed? Explain.

c)Do you think that math scores are a useful variable for predicting the reading scores? Explain.

5. a) Write out the two regression lines, one for each test prep type [round parameter estimates to two decimal places]. No other interpretations needed.

b) In the HW3 template we provide the code using ggplot to create a scatterplot has all points color coded by test prep status. We also provide code to add three regression lines to the plot (original regression and two lines when taking test prep status into account). Of the two regression models (test prep not included in model (blue line) or test prep included in model (cyan and salmon lines)), which model do you recommend using for predicting math scores from reading scores? Explain.