Consider the following relationship between the annual salary (salary) in thousa

Question

Consider the following relationship between the annual salary (salary) in thousand of
dollars of CEOs and a measure of their performance indicated by the average return on
equity (roe) in percentage terms (this is net income of the firm as a percentage of
common equity)
salaryi = B0 +Bi * roei + ui
This is a cross-section data set on the above variables:
CEO roe (%) salary
(thousand of $)
1 14.1 1095
2 23.5 1122
3 13.8 1368
4 16.4 1078
5 10.5 1237
6 25.9 567
7 14.8 1339
8 56.3 2011
You need to do the necessary calculations by hand with the help of a calculator at most.
We want to see your calculations. Follow the working format that will be shown in class.
Do not use Eviews yet but you could check whether your answers are right by running
the OLS procedure in Eviews.
i. Estimate the relationship between salary and roe using OLS; that is, obtain
the intercept and the slope estimates in the equation
salaryi = ^B0 + ^Bi * roei + ^ui
Comment on the direction of the relationship. What is the meaning of the
intercept? How much higher is the salary predicted to be if the roe increases
by 2%?
ii. Compute the fitted values and residuals for each observation, and verify that
the residuals (approximately) sum to zero.
iii. What is the predicted value of salary when roe is 18%?

Explanation / Answer

(1) intercept:885.9854

slope:15.5683

The equation is Salary =885.9854+15.5683*CEO roe

Since the value of the slope is positive, there is a positive relationship between CEO roe and salary

The meaning of the intercept is no meaning.

How much higher is the salary predicted to be if the roe increases
by 2%:

885.9854+15.5683*2=917.122

(2) Yes, the residuals (approximately) sum to zero

(3)the predicted value of salary when roe is 18%:

885.9854+15.5683*18=1166.215

Regression output


confidence interval variables coefficients std. error    t (df=6) p-value 95% lower 95% upper Intercept 885.9854 235.3374 3.765 .0093 310.1354 1,461.8353 CEO roe 15.5683 9.0748 1.716 .1371 -6.6369 37.7734

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