Pearson eText Business Statistics: First Course -- Instant Access (Pearson+)
8th Edition
ISBN: 9780136880974
Author: David Levine, David Stephan
Publisher: PEARSON+
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We have data from 209 publicly traded companies (circa 2010) indicating sales and compensation
information at the firm-level. We are interested in predicting a company's sales based on the CEO's
salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable
salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to
estimate the linear regression
sales; = a + ßsalary; + ei
and get the following regression results:
regress sales salary
.
Source
Model
Residual
Total
sales
salary
_cons
SS
337920405
2.3180e+10
2.3518e+10
df
1
207
208
Coef. Std. Err.
.9287785 .5346574
5733.917 1002.477
MS
337920405
111980203
113066454
t
Number of obs
F(1, 207)
Prob> F
R-squared
Adj R-squared
Root MSE
P>|t|
1.74 0.084
5.72 0.000
209
3.02
-.1252934
3757.543
0.0838
0.0144
0.0096
10582
[95% Conf. Interval]
1.98285
7710.291
This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary.
Suppose a CEO of a company…
We have data from 209 publicly traded companies (circa 2010) indicating sales and compensation
information at the firm-level. We are interested in predicting a company's sales based on the CEO's
salary. The variable sales; represents firm i's annual sales in millions of dollars. The variable
salary; represents the salary of a firm i's CEO in thousands of dollars. We use least-squares to
estimate the linear regression
sales; = a + ßsalary; + ei
and get the following regression results:
. regress sales salary
Source
Model
Residual
Total
sales
salary
cons
SS
337920405
2.3180e+10
2.3518e+10
df
1
207
208
Coef. Std. Err.
.9287785 .5346574
5733.917 1002.477
MS
337920405
111980203
113066454
Number of obs
F (1, 207)
Prob > F
R-squared
t P>|t|
=
Adj R-squared =
Root MSE
1.74 0.084
5.72 0.000
=
=
-.1252934
3757.543
=
209
3.02
0.0838
0.0144
0.0096
10582
[95% Conf. Interval]
1.98285
7710.291
This output tells us the regression line equation is sales = 5,733.917 +0.9287785 salary.
Interpret the…
A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.
Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.
Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.
Predict the number of days absent for an employee that lives 5 miles from the hospital.
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