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The file CEOSAL2 contains data on 177 chief executive officers and can be used to examine theeffects of firm performance on CEO salary.(i) Estimate a model relating annual salary to firm sales and market value. Make the model of theconstant elasticity variety for both independent variables. Write the results out in equation form.(ii) Add profits to the model from part (i). Why can this variable not be included in logarithmicform? Would you say that these firm performance variables explain most of the variation inCEO salaries?(iii) Add the variable ceoten to the model in part (ii). What is the estimated percentage return foranother year of CEO tenure, holding other factors fixed?(iv) Find the sample correlation coefficient between the variables log(mktval) and profits. Are thesevariables highly correlated? What does this say about the OLS estimators?

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(i) $\log (\hat s{\text {alary }})=4.62+.162 \log ($ sales $)+.107 \log ($ mktrual $)$$\mathrm{n}=177$$\mathrm{R}^{2}=0.299$(ii) $\log (\hat s{\text {alary }})=4.69+.162 \log ($ sales $)+.098 \log (\mathrm{mktval})+.000036$ profits$\mathrm{n}=177$$\mathrm{R}^{2}=0.299$(iii). $\log (\hat s{\text {alary }})=4.56+.162 \log ($ sales $)+.102 \log (\mathrm{mktval})+.000029 \mathrm{profits}+.012 \mathrm{ceoten}$$\mathrm{n}=177$$\mathrm{R}^{2}=0.318$(iv) The sample correlation between $\log (m k t v a l)$ and profits is about $0.78,$ which is fairly high. As it is known, this causes no bias in the OLS estimators, although it can cause their variances to be large. Given the fairly substantial correlation market value and firm profits, it is not too surprising that the latter adds nothing to explaining CEO salaries. Also, profits is a short termmeasure of how the firm is doing while mktval is based on past, current, and expected future profitability.

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Chapter 3

Multiple Regression Analysis: Estimation

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Milena A.

September 10, 2020

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Hello, Ruben. We have Ah, this question. Computer exercise, tree infested tree. Do you have the file? See you sell to your salaries. And the first part asked us to estimate a model relating annual salary to from sales and market value. And we were asked to form this model A and B constant elasticity for which means who, like the variable single Britney full so inconstant elasticity model will have our salary. Original salary usually cool to bait of Europe plus data one l sales look great in the sales, huh? Beta two, um, market value and plus the editor. So this is all constant getting salaries to sales and mark down, do you? So I'm just and we left to right the results. So the estimates I'm just under aggression found calories on our sales and al market value. And the estimates I get is for the constant made of you had it. 4.62 beta. One head is points 1 62 and beta two hat and 0.16 Okay, The second part of the question is asking us to at the profits to this model, and, uh asked us why the stable cannot be included in your ethnic form. And the reason is that the Logan Mick function is defined on positive values. And so when you look at the salaries, definitely has to be positive. Tails has to be positive. Market values positive. So all the tables are positive, so they can be written in a rhythmic form. But the profits can technically be negative. So and since long is not defined in negative values, we cannot include processed in academic form. That's that's reason. So our new model, it's just gonna be thing we have impressed, made a tree profit for a few but not out profits. Just profit. And, uh, there's another part of this question. Which, yes, would you say that this firm performance variables explained most of the variation, your salaries and, uh, to get this, we have to look at our square and square from the regression when we'll have profits is equal to 0.29 93. So the old market value and the performances I've explained Coty, 20% variation and, uh, the salary and okay, this is for the second part. Go to deterrent punch and the variable your 10 year tenure to the model in part two. What is estimated percentage returned for another year, or CEO? 10 year holding out of factors. So we gotta have a model where we have our salary, our sales, our luck, value, profits and also see your tenure And when we're under aggression for that model. So I'm just gonna say, like, beta tree profits plus beta full your tenure, right? I'm not just gonna wait. And the estimate for the coefficient off CEO. 10 year on this aggression, it's Penner comes out 0.1 and 16. So any was asking what it estimated percentage to return for another year or see or tenure, right, Uh, are independent variable your tenure so that is not in log, but dependent table isn't long form. So to get the estimated percentage return when we have a dependent fable that is in love and an independent label that is not in love, what we have to do is we have to multiply the coefficient by hundreds night. So the estimated change in salary in percentages right when you fix the other factors and includes a CEO 10 you by one year is gonna be 100 times point till I'm 16 okay? And this is gonna be 1.16. So one more year off your tenure, it's gonna tease with Sally's by 1.6% when we kicked that affect us all right and last part. The fourth part of this question is find a simple correlation coefficient between the variables block market value and profits, right, correlation between not market value and CrossFit. So for this, like in st I just put in the command section, you are blank block market value blend profits. Andi, just table. And from that, you find a correlation is points 77 69. It's a pretty high coalition. Correlation is, and I'm in between minus one in one. And when you get closer to one or minus one means a strong relationship. And here we have 10.77 69 which is highly Cordless. And, uh, there's another part of this question. What does this say about the or less estimators? So we have logged market value we have, and we have profits, and we see that large market value and profits ah, highly correlated. Right? So if this means that if we don't include profits when we include market value, dark market value. It's not market value in profit, which when we don't include it in like in the YouTube. So lock Mark Betty also captures the effect off profits on the salaries, which means a lot market salary will be biased in that in which we say we have the omitted variable day so dismissed that we have to conclude profits for me also include look market value to, uh, do not have to have a bias. All right, I hope that helps. Thank you for watching.

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