Retail chain Kroger has more than locations and is the largest supermarket in the United States based on revenue. Kroger has invested heavily in data, technology, and analytics. Feeding predictive models with data from an infrared sensor system called QueVision to anticipate when shoppers will reach the checkout counters, Kroger is able to alert workers to open more checkout lines as needed. This has allowed Kroger to lower its average checkout time from four minutes to less than seconds (Retail Touchpoints). Consider the data in the file Checkout. The file contains observations. Each observation gives the arrival time (measured in minutes before p. m.) and the shopping time (measured in minutes). Arrival Time (Minutes Shopping
Before 6:00 p. m.) Time (Minutes)
59 24
22 19
58 25
84 29
53 40
97 45
38 32
12 25
0 11
132 54
55 21
0 14
91 36
11 15
3 11
27 16
39 37
15 13
77 35
31 17
24 17
19 24
23 30
39 24
58 26
114 56
30 22
108 41
48 26
103 41
71 27
111 24
A. Develop a scatter diagram for arrival time as the independent variable.
B. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
C. Does there appear to be an outlier or influential observation?
D. Using the entire data set, develop the estimated regression equation that can be used to predict the shopping time given the arrival time. (Let x = arrival time (in minutes before 6:00 p. m.), and let y = shopping time (in minutes).
E. Use residual analysis to determine whether any outliers or influential observations are present. Which of the following points have a standardized residual greater than 2 or less than −2?
a. (39, 37).
b. (114, 56).
c. (53, 40).
d. (111, 24).
F. After looking at the scatter diagram in part (a), suppose you were able to visually identify what appears to be an influential observation. Drop this observation from the data set and fit an estimated regression equation to the remaining data.
Compare the estimated slope for the new estimated regression equation to the estimated slope obtained in part (c). Does this approach confirm the conclusion you reached in part (d)? Explain.