A survey of employees at a large financial organisation was conducted to determine the overall sentiment towards various aspects of how the company operates. 30 randomly selected departments in the organisation participated in the study. Every employee in these 30 randomly selected departments filled in a questionnaire, and the data were aggregated to calculate the following two variables of interest: Rating The percentage of favourable responses (in each department) to the overall running of the company. ComplaintsThe percentage of favourable responses (in each department) to how the company handles employee complaints

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A survey of employees at a large financial organisation was conducted to determine the overall sentiment
towards various aspects of how the company operates. 30 randomly selected departments in the
organisation participated in the study. Every employee in these 30 randomly selected departments filled
in a questionnaire, and the data were aggregated to calculate the following two variables of interest:
Rating The percentage of favourable
responses (in each department)
to the overall running of the
company.
ComplaintsThe percentage of favourable
responses (in each
department) to how the company
handles employee complaints
Source: Chatterjee, S. and Price, B. (1977) Regression Analysis by Example. New York: Wiley. (Section
3.7, p.68ff of 2nd ed. (1991).)
A simple linear regression was conducted. A scatter plot of Rating versus Complaints is shown in
Figure 1 and the results of the regression analysis are shown in Table 1.
Rating
80
70
60
50
40
40
Model
1
Figure 1: Rating versus Complaints.
50
14.376
.755
Unstandardized Coefficients
B
Std. Error
(Constant)
Complaints
a. Dependent Variable: Rating
Table 1: Regression output.
Rating versus Complaints
6.620
.098
60
Complaints
Coefficients
Standardized
Coefficients
Beta
.825
70
t
2.172
7.737
Sig.
.039
.000
80
90
95.0% Confidence Interval for B
Lower Bound Upper Bound
27.937
.954
.816
.555
Transcribed Image Text:A survey of employees at a large financial organisation was conducted to determine the overall sentiment towards various aspects of how the company operates. 30 randomly selected departments in the organisation participated in the study. Every employee in these 30 randomly selected departments filled in a questionnaire, and the data were aggregated to calculate the following two variables of interest: Rating The percentage of favourable responses (in each department) to the overall running of the company. ComplaintsThe percentage of favourable responses (in each department) to how the company handles employee complaints Source: Chatterjee, S. and Price, B. (1977) Regression Analysis by Example. New York: Wiley. (Section 3.7, p.68ff of 2nd ed. (1991).) A simple linear regression was conducted. A scatter plot of Rating versus Complaints is shown in Figure 1 and the results of the regression analysis are shown in Table 1. Rating 80 70 60 50 40 40 Model 1 Figure 1: Rating versus Complaints. 50 14.376 .755 Unstandardized Coefficients B Std. Error (Constant) Complaints a. Dependent Variable: Rating Table 1: Regression output. Rating versus Complaints 6.620 .098 60 Complaints Coefficients Standardized Coefficients Beta .825 70 t 2.172 7.737 Sig. .039 .000 80 90 95.0% Confidence Interval for B Lower Bound Upper Bound 27.937 .954 .816 .555
27. In Figure 1, two different departments have a Complaints percentage of 70%. Under this regression analysis,
which one of the following statements about these two departments is true?
They have the same observed Rating percentages.
They have different observed Rating percentages and different 95% prediction intervals.
O They have the same 95% prediction intervals and different residuals.
O They are not independent of each other.
O They have the same residuals and different observed Rating percentages.
Transcribed Image Text:27. In Figure 1, two different departments have a Complaints percentage of 70%. Under this regression analysis, which one of the following statements about these two departments is true? They have the same observed Rating percentages. They have different observed Rating percentages and different 95% prediction intervals. O They have the same 95% prediction intervals and different residuals. O They are not independent of each other. O They have the same residuals and different observed Rating percentages.
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