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The data set in CEOSAL2 contains information on chief executive officers for U.S. corporations. Thevariable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years ascompany CEO.$$\begin{array}{l}{\text { (i) Find the average salary and the average tenure in the sample. }} \\ {\text { (ii) How many CEOs are in their first year as } \mathrm{CEO} \text { (that is, ceoten }=0 ) ? \text { What is the longest tenure }} \\ {\text { as a CEO? }} \\ {\text { (iii) Estimate the simple regression model }}\end{array}$$$$\log (\text {salary})=\beta_{0}+\beta_{1} \text { ceoten }+u$$and report your results in the usual form. What is the (approximate) predicted percentageincrease in salary given one more year as a CEO?

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Chapter 2

The Simple Regression Model

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computer exercise and Chapter two and we're gonna use the data set called CEO Sal to which contains information and chief executive officers for US corporations the variable salaries annual compensation in thousands of dollars and CEO 10. This other variable is ah, prior number of years. This company CEO All right, I have imported the data center St Uff. Let's first hit. Described to see what a data set is. As we can see, we have 177 observations, 15 lying variables, and the main variables we're gonna be dealing with this question is salary, which is, um, compensation 1990 in thousands of dollars and actually going to use that log off salary. The transformation with the natural longer than we're also gonna use the variable CEO 10 I guess a sense retainer. And it's measured in It's a discreet variable. Imagine measured in a number of years. A CEO with the company. Okay, Party s us. Has to find the average Sally in the average tenure in the sample. Well, that's very easy within a couple of times already. So we're gonna hit summarize their two variables. It is ah. Is it ever salary and CEO tenure. Okay, as we can see there No missing observations. Both haven't 107 7 Observation that mean CEO salary is, uh is this number right here? Mother played by 1000 because this $1000 So it's 865,000 864 U. S. Dollars. That's a lot of money. And the average CEO tenure is 7.9 to 5 years. Almost eight years as we're going to see, the minimum salary is 100,000 per year. No, that's not too bad. Maximum salary is five point $3,000,000. And, um, in part B, how many CEOs are in the first year? CEO? That is how many CEO tenure minor variables are equal to zero as we know already. Don't do. Ah, civil counted with a variable CEO 10 and the condition is that is equal to zero. All right, so which is half five CEOs with 10 year olds zero years on the other hands? What is the longest tenure as a CEO? We've already seemed that right here when we did the descriptive analysis of the CEO 10. Bye Mary variable. The maximum is 37 years and just out of curiosity. Let's see how many people have sealed in your 37 years. Just two people. Two people have spent basically their whole adult life. A CEO. Is that company okay? In part C, we need to estimate the simple regression model. Ah, the dependent variable would be the national law game of salary. And in the explanatory part, that right hand side, we have a constant term and CEO tenure, plus the return of a disturbance. We need to report the results in the usual form raised. Do as we explain the previous video which hit rag regression followed by the dependent variable look of salary. We did not need to include an intercept because state I includes right away automatically and then the dependent they're independent. Variable will be CEO 10 And of course, we don't need to include the sermons term. It is applied. It's include automatically and we're just going to run the simplest aggression. No robust air terms, no corrections. All right. As we can see, number of observations that correct one. The one we had. I would describe the data set so nothing went wrong. The are square. It is 0.0 13. It's extremely low. That would say, um okay. And, uh, the quantities of interest are these ones right here. The are estimated value for the constantly 6.5 and our slope coefficient with seo 10 0.0 97. So I've written down the estimate equation right here. Estimated log salaries equal to the heir to the constant term plus a slope coefficient. Time CEO 10. Number of variables at 1 77 Our score 0.0 13. Okay. And then we're being asked two, uh, to ah state. What is the approximate predicted percentage increase in salary given one more year as a CEO. All right, so remember, here we don't have ah level levels. Regression will have a love levels. Meaning that the dependent variables in drugs as your longer than an independent variable is in levels. No transformation. So we obtained the approximate percentage change in salary and by approximately mean is gonna be in love. Different. So in his approximate percent of change. And on top of that, we're doing with average pointedly, so we don't need to take his value 100% at face value. Right? Is an approximate average change, and we need to construct the difference in such a way. Uh, as in a ziff, we need to interpret as that one point change in the independent variable. So you can see if we change the independent variable was his tenure by one. Well, we multiply the coefficient and cementing her by 100. And then we get that percentage change because we have been log variable on the left inside. Therefore, one more years of seo is predicted to increase salary by almost 1% 0 for 97% almost 1%. Okay, so remember when we haven't loved levels regression, we estimate our stoke coefficient we multiplied by 100 waste made as the percentage changed in that, um dependent variable. And the last thing I would like to add is that do we Shall we take this prediction seriously? Well, the first thing we need to check is that here at sea, on tenure, the corresponding T value from the T test, the critical values very small and affords the correspondent p. Valerie's very high, which means that this estimate right here it's not statistically significant, at least in the conduct of the by virus progression we're running. And of course, there's socially flaking the very lower squared in the marginally Hi critical, a critical Bali for the F test and this critical while you tells us that our regression is slightly better than one with just a constant term. So what? Leasing this context, the CEO tenure variable does not really explain much of the variation in in log salary, and this prediction should not be taken at face value.

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