large supe models with from area sensor system anticipate when shoppers ters, they open more che technology, and heckout time from four minutes to less than 30 seconds. Consider the data in the following table containing 32 observations. Suppose 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.) 50. 40 30 20 58 0 21 59 83 54 96 39 13 0 133 55 0 92 12 4 28 Shopping Time (minutes) . 23 18 25 28 40 45 33 25 12 53 21 13 37 15 12 17 20 40 60 80 Arrival Time (minutes before Shopping Time (minutes) 6:00 p.m.) 100 120 140 38 15 78 32 23 18 24 38 57 113 30 109 (a) Develop a scatter diagram for arrival time as the independent variable. 47 104 72 112 60 50 40 30 20 10 0 20 40 36 14 35 18 18 23 30 23 27 55 21 42 27 42 26 23 60 80 100 120 140 140 120 100 80 60 40 20 0 10 : 20 30 40 50 60 140 120 100 80 60 40 20 0 10 : 20 30 40 Shopping Time (Minutes) 50 60 koutlines 85 has allowed them to lower thell Activate Windows Go to Settings to activate Windo
large supe models with from area sensor system anticipate when shoppers ters, they open more che technology, and heckout time from four minutes to less than 30 seconds. Consider the data in the following table containing 32 observations. Suppose 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.) 50. 40 30 20 58 0 21 59 83 54 96 39 13 0 133 55 0 92 12 4 28 Shopping Time (minutes) . 23 18 25 28 40 45 33 25 12 53 21 13 37 15 12 17 20 40 60 80 Arrival Time (minutes before Shopping Time (minutes) 6:00 p.m.) 100 120 140 38 15 78 32 23 18 24 38 57 113 30 109 (a) Develop a scatter diagram for arrival time as the independent variable. 47 104 72 112 60 50 40 30 20 10 0 20 40 36 14 35 18 18 23 30 23 27 55 21 42 27 42 26 23 60 80 100 120 140 140 120 100 80 60 40 20 0 10 : 20 30 40 50 60 140 120 100 80 60 40 20 0 10 : 20 30 40 Shopping Time (Minutes) 50 60 koutlines 85 has allowed them to lower thell Activate Windows Go to Settings to activate Windo
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
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Transcribed Image Text:A large supermarket chain has invested heavily in data, technology, and analytics. Feeding predictive models with data from an infrared sensor system to anticipate when shoppers will reach the checkout counters, they are able to alert workers to open more checkout lines as needed. This has allowed them to lower their avera
checkout time from four minutes to less than 30 seconds. Consider the data in the following table containing 32 observations. Suppose each observation gives the arrival time (measured in minutes before p.m.) and the shopping time (measured in minutes).
O
Arrival Time
(minutes before
6:00 p.m.)
Shopping Time (Minutes)
58
21
59
83
54
96
39
13
0
133
55
0
92
12
4
28
Shopping Time
(minutes)
23
18
25
28
40
45
33
25
12
53
21
13
37
15
12
17
20
40 60 80 100 120
Arrival Time (Minutes Before 6:00 p.m.)
Arrival Time
(minutes before
6:00 p.m.)
140
38
AO
15
78
32
23
18
24
38
57
113
30
109
(a) Develop scatter diagram for arrival time as the independent variable.
47
104
72
112
Shopping Time
(minutes)
60
36
14
35
18
18
23
30
23
27
55
21
42
27
42
26
23
140
120
100
80
EL
60
40
20
0
0 20 40 60 80 100 120 140
Arrival Time (Minutes Before 6:00 p.m.)
10 20 30 40 50 60
Shopping Time (Minutes)
140
120
100
80
60
40
20
10
20 30 40
Shopping Time (Minutes)
50
60
Ⓡ
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Transcribed Image Text:(b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
The scatter diagram indicates a positive linear relationship between arrival time and shopping time.
O The scatter diagram indicates no apparent relationship between arrival time and shopping time.
O The scatter diagram indicates a negative linear relationship between arrival time and shopping time.
O The scatter diagram indicates a nonlinear relationship between arrival time and shopping time.
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) =
112.23
Explain. (Select all that apply.)
✔The point is an outlier or influential observation because it does not fit the trend shown by the remaining data.
The point is an outlier or influential observation because it has high leverage.
The point is an outlier or influential observation because if it were dropped from the data set, the intercept of the estimated regression line would change
sign.
The point is an outlier or influential observation because if it were dropped from the data set, the slope of the estimated regression line would change sign.
There are no outliers or influential observations.
(c) 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.)
ŷ =
ŷ =
X
(d) 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.)
(38, 36)
(113, 55)
(112, 23)
(54,40)
(e) 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. (If there are no influential observations, enter your estimated regression equation
from part (c).)
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.
Yes, because the value of the slope of the fitted line changed after removing the influential observation.
O No, because the value of the slope of the fitted line did not change after removing the influential observation.
O There are no outliers or influential observations.
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