Online shopping has dramatically increased during the last few years. Companies are always interested in studying customers' satisfaction of their goods and services. In a market study for a specific item, customers were asked to rate their online shopping experience. Each customer gave their subjective score on a integer scale, with 0 indicating not at all satisfied and 100 indicating totally satisfied for some specific aspects of a recent order. The collected dataset includes the following variables in a GenStat file: satisfaction: a score rating the overall satisfaction of the order; speed: a score rating the delivery speed of the order. A market researcher tries to investigate whether the delivery speed of an order can be used to predict the customer's overall satisfaction, using simple linear regression. I a) The market researcher decided to fit a simple linear regression model for satisfaction on speed. The following is the GenStat output from fitting this model, denoted by Model A. (One value has been deleted and replaced by *****.)
Online shopping has dramatically increased during the last few years. Companies are always interested in studying customers' satisfaction of their goods and services. In a market study for a specific item, customers were asked to rate their online shopping experience. Each customer gave their subjective score on a integer scale, with 0 indicating not at all satisfied and 100 indicating totally satisfied for some specific aspects of a recent order. The collected dataset includes the following variables in a GenStat file: satisfaction: a score rating the overall satisfaction of the order; speed: a score rating the delivery speed of the order. A market researcher tries to investigate whether the delivery speed of an order can be used to predict the customer's overall satisfaction, using simple linear regression. I a) The market researcher decided to fit a simple linear regression model for satisfaction on speed. The following is the GenStat output from fitting this model, denoted by Model A. (One value has been deleted and replaced by *****.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Transcribed Image Text:Q1
Online shopping has dramatically increased during the last few years.
Companies are always interested in studying customers' satisfaction of
their goods and services. In a market study for a specific item,
customers were asked to rate their online shopping experience. Each
customer gave their subjective score on a integer scale, with 0
indicating not at all satisfied and 100 indicating totally satisfied for
some specific aspects of a recent order. The collected dataset includes
the following variables in a GenStat file:
satisfaction:
speed:
A market researcher tries to investigate whether the delivery speed of
an order can be used to predict the customer's overall satisfaction,
using simple linear regression.
|
a score rating the overall satisfaction of the order;
a score rating the delivery speed of the order.
a) The market researcher decided to fit a simple linear regression
model for satisfaction on speed. The following is the GenStat
output from fitting this model, denoted by Model A. (One value
has been deleted and replaced by *****.)
Transcribed Image Text:Model A
Regression analysis
Response variate: satisfaction
Fitted terms: Constant, speed
Summary of analysis
Source
Regression
Residual
Total
d.f.
S.S.
m.s.
1
3670
3669.58
96
4152
43.25
97
7822
80.64
Percentage variance accounted for 46.4
Standard error of observations is estimated to be 6.58.
Message: the following units have large standardized residuals.
Response
Residual
32.00
-2.60
31.00
-2.68
Unit
1
93
Message: the following units have high leverage.
Response
Leverage
0.082
0.059
Unit
38
94
29.00
25.00
Estimates of parameters
Parameter estimate
Constant
speed
30.09
0.4611
s.e.
1.88
*****
v.r.
84.84
t(96)
16.00
9.21
F pr.
<.001
t pr.
<.001
<.001
(i) From the GenStat output above derive the sample size. (Do
not attempt to count the points in Figure 1!)
(ii) Calculate the estimated standard error of the parameter
associated with speed.
(iii) The output for Model A gives the required information to
test the hypothesis that the slope of the regression line is
zero. Give the value of the test statistic and report the results
of this test, stating your conclusion clearly.
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