Retail chain Kroger has more than 2,700 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 30 seconds.† Consider the data in the file Checkout. The file contains 32 observations. Each observation gives the arrival time (measured in minutes before 6 p. m.) and the shopping time (measured in minutes). Arrival Time (Minutes Before 6:00 p. m.)Shopping Time (Minutes)
5924
2219
5825
8429
5340
9745
3832
1225
011
13254
5521
014
9136
1115
311
2716
3937
1513
7735
3117
2417
1924
2330
3924
5826
11456
3022
10841
4826
10341
7127
11124

(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? (Enter your answer as an ordered pair in the form x, y. If there is no answer, enter NONE.)

(x, y) =

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). Round your numerical values to four decimal places.)

Å· =

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? (Select all that apply.)

(39, 37) ; (114, 56 ) ; (53, 40) l (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.