Question

Consider an equation to explain salaries of CEOs in terms of annual firm sales in million dollars, return on equity (roe, measured in percentage points as the unit), and return on the firm's sock (ros, measured in percentage points as the unit):

  

Asume that the following equation was obtained by OLS:

By how much is salary predicted to increase on average if ros increases by 30 percentage points while all other variables are held constant?

(Please indicate the solution this way: "66" and do not write down the symbol %. Indicate an increase with the number and a decrease with a "-" in front of the number)

Answer 1

As per above question, we have one dependent variable and 2 independent variable . Let us assume and denote symbols as per below.

Y : SALARY IN TERMS OF ANNUAL FIRM SALES IN TERMS OF MILLION DOLLAR

X1 : RETURN ON EQUITY

X2 : RETURN ON STOCK

b0 : Intercept term which is positive, has no economic meaning and has no impact on dependent variable.

b1 : Coefficient of X1 ( RETURN ON EQUITY). It shows if X1 change by 1 unit , the average value of Y will change by b1 unit.

b2 : Coefficient of X2 ( RETURN ON STOCK) . It shows if X2 change by one unit, the average value of Y will change by b2 unit.

E : The error term which shows impact of all the variables that are not take into account.

The regression equation is as per below

Y = b0 + b1X1 +b2X2 +E

OLS ( ORDINARY LEAST SQAURE) is the method in Regression analysis which states that b1 and b2 ( Slope Coefficients) to be selected in such a way that sigma square of E is minimized.

Here we are keeping b2 ( slope coefficient of Reurn on equity Constant) as per assumption made in question.

Now there is an increase in 30 percentange in return of stock which will constitute slope coefficient of Return on Stockas 0.3 ( 30/100) .We can rewrite equation as

Y = b0 + b1X1+ 0.3X2 +E

The above equation states that if X2 ( Return on stock) increase by 1 unit , the average value of Y ( SALARY IN TERMS OF ANNUAL FIRM SALES IN TERMS OF MILLION DOLLAR) will get increased by 0.03 units.

Now salary has been stated in terms of million dollar. It means value of salary in terms of million dollar is (1000000*0.3) which is equal to INR 300000.

To calculate the percentage increase in salary, we canculate as below

(1000000-300000/1000000)*100 = 70

Hence the annual salary will get increased by 70 percentage if return on stock will inreased by 30 percentage.