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+0.9287785salary. Interpret the numerical value of the regression slope in words that conveys the relationship between the variables sales and salary.

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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
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 numerical value of the regression slope
in words that conveys the relationship between the
variables sales and salary.
Transcribed Image Text: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 numerical value of the regression slope in words that conveys the relationship between the variables sales and salary.
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