Question 11.31

11.31 Predicting retail sales.

Daily sales at a secondhand shop are recorded over a 25-day period.8 The daily gross sales and total number of items sold are broken down into items paid by check, cash, and credit card. The owners expect that the daily numbers of cash items, check items, and credit card items sold will accurately predict gross sales.

retail

  1. Describe the distribution of each of these four variables using both graphical and numerical summaries. Briefly summarize what you find and note any unusual observations.
  2. Use plots and correlations to describe the relationships between each pair of variables. Summarize your results.
  3. Run a multiple regression and give the least-squares equation.
  4. Analyze the residuals from this multiple regression. Are there any patterns of interest?
  5. One of the owners is troubled by the equation because the intercept is not zero (that is, no items sold should result in $0 gross sales). Explain to this owner why this isn’t a problem.

11.31

(a) All four variables are somewhat right-skewed. There is a potential outlier for gross sales. (b) All three explanatory variables look linearly related with gross sales but each scatterplot has a few semi-outlying observations that could be potentially influential. From the correlation matrix, we can see that both cash items and check items have quite strong linear relationships with gross sales, but they also have some correlation between them. (c) . (d) The Normal quantile plot shows a roughly Normal distribution with no outliers. The three residual plots all look pretty good (random) but show a couple semi-outlying observations we identified earlier. (e) The intercept is not significantly different from 0; .