10.10 Complete check of the residuals. In Example 10.12 (page 574), we checked model assumptions using a scatterplot (Figure 10.9). Let’s consider assessing the model assumptions using the residuals.

  1. (a) Fit the (EDUC, INC) data using least-squares regression and obtain the residuals. Write down the least-squares regression line.

  2. (b) Generate a plot of the residuals versus EDUC and comment on the pattern. Does a linear fit appear reasonable? Does there appear to be constant variance? Are there any unusual observations? Explain your answers.

  3. (c) Construct a histogram and a Normal quantile plot of the residuals. Do the residuals appear Normal? Explain your answer.

  4. (d) Analysis of the residuals is typically done because patterns in the residuals are easier to see. Do you think the plots in parts (b) and (c) magnify the violations of assumptions better than the scatterplot in Figure 10.9? Write a short paragraph comparing the scatterplot with the residual plots.