QUESTION 1 10 points Save Answe We consider the following regression model. log(

Question

QUESTION 1 10 points Save Answe We consider the following regression model. log(TotComp) = 0+1log(Marketvalue) + u where TotComp is the total compensation of the CEO of a company (in thousands of S) and MarketValue is the total market value of the company (n millions of $). We have a data set of 1506 companies (so 1506 CEO's with their compensations and the market value of the company they manage). The regression analysis yields A = 0.235 This coefficient means 0 A 1% increase of market value increases the CEO's compensation by S235000 0 b. A S1 million increase of market value increases te CEO's compensation by 23.5%. c. A $1 million increase of market value increases the CEO's compensation by S235000. d. A 1% increase of market value increases the CEO's compensation by 0235%.

Explanation / Answer

The correct answer would be d). Please see the explaination below:

We know that: The logarithmic function y = logb(x) is the inverse function of the exponential function, x = by

So, if we assume that all other constants as zero then, the total compensation (say x) can written as log10x = b1log10(MarketValue)

Let's start with the first case only that is study the impact of increasing the market value by 1%

Let's say the initial market value of the firm is: $ 1,000,000. So multiplying the same by 0.235 (assuming all other constants as zero) 0.235*log10(1000000) = 1.41. Assuming the log base of 10, we get x = 101.41 = 25.70395783

Now increase the market value by another 1%. So multiplying the same by 0.235 we get 0.235*log10(1010000) = 1.411015435. Assuming the log base of 10, we get x = 101.411015435 = 25.76412722.

Difference in 2 values results 0.060169393. If expressed in % terms we get: 0.060169393/25.70395783 = 0.00235 or (0.235%)

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