A magazine collected the ratings for food, decor, service and the cost per person for a sample of 30 restaurants. They combined the ratings to create a summated rating and used that to predict the cost of a restaurant meal. The data are modeled by $\hat{Y}_i = -13.7871 + 0.9467X_i$, where $X_i$ is the summated ratings and $\hat{Y}_i$ is meal cost. Perform a residual analysis for these data. Evaluate whether the assumptions of regression have been seriously violated.
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Which of the assumptions of regression, if any, have been seriously violated? Select all that apply.
A. The assumption of linearity has been violated because the data are clearly curvilinear.
B. The assumption of independence of errors has been violated because the errors are not independent of one another.
C. The assumption of equal variance has been violated because the variability of the residuals is not constant for all values of X.
D. The assumption of normality has been violated because the normal probability plot does not appear to be a straight line.
E. The assumptions of linearity, independence, normality, and equal variance do not appear to have been seriously violated.
