Question 11.49

11.49 Checking the model assumptions.

CASE 11.2 Statistical inference requires us to make some assumptions about our data. These should always be checked prior to drawing conclusions. For brevity, we did not discuss this assessment for the movie revenue data of Section 11.2, so let’s do it here.

movies

  1. Obtain the residuals for the multiple regression in Example 11.13 (pages 552–553), and construct a histogram and Normal quantile plot. Do the residuals appear approximately Normal? Explain your answer.
  2. Plot the residuals versus the opening-weekend revenue. Comment on anything unusual in the plot.
  3. Repeat part (b) using the explanatory variable Budget on the x axis.
  4. Repeat part (b) using the predicted value on the x axis.
  5. Summarize your overall findings from these summaries. Are the model assumptions reasonably satisfied? Explain your answer.

11.49

(a) The residuals are right-skewed and not Normally distributed. (b) There are two outliers in the residual plot for Opening—one with a very high residual, one with a very large Opening value. (c) The residual plot for Budget again shows the observation with a very high residual; otherwise, it looks fairly good (random). (d) The residual plot against the predicted values shows a megaphone effect suggesting non-constant variance. (e) The model assumptions are not reasonably satisfied; the residuals are right-skewed, and there are several outliers in the dataset that are potentially influencing the regression analysis.