1. Two-way categorical analysis. Using two categorical variables with two to five levels each, specify a hypothesis test for homogeneity of proportions associated with your research questions.
    • (1 p) Specify the hypotheses in words and notation.
    • (1 p) State the conclusion of the test in the context of the problem.
    • (1 p) Plot a mosaic plot of the data and Pearson residuals.
    • (1 p) Interpret the mosaic plot with reference to the Pearson residuals.
  2. Simple linear regression. Select two numerical variables.
    • (1 p) Plot the data and, if required, transform the variables so a roughly linear relationship is observed. All interpretations will be done on this scale of the variables.
    • (0 p) Fit the simple linear regression model.
    • (1 p) Assess the residuals for lack of fit (interpret plots of residuals vs fitted and \(x\)-value).
    • (1 p) Assess the residuals for normality (interpret QQ-plot and histogram).
    • (1 p) Assess the relative influence of points.
    • (1 p) Test whether the slope is different from zero, \(H_A: \beta_1 \ne 0\).
    • (1 p) Interpret the \(R^2\) value.

Turn in your master HW file with these sections appended to the bottom.