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In Problem 2 in Chapter $4,$ we added the return on the firm's stock, $r o s,$ to a model explaining CEOsalary; ros turned out to be insignificant. Now, define a dummy variable, rosneg, which is equal to oneif $r o s<0$ and equal to zero if $r o s \geq 0 .$ Use CEOSALl to estimate the model$$\log (\text {salary})=\beta_{0}+\beta_{\mathrm{l}} \log (\text {sales})+\beta_{2} r o e+\beta_{3} r o s n e g+u$$Discuss the interpretation and statistical significance of $\hat{\beta}_{3}$

The coefficient of rosneg is $\hat{\beta}_{3}$ with the value $-0.225675$ with the p-value 0.0402 which is lessthan the critical p-value of 0.05 at 5$\%$ level of significance indicating that the variable rosneg isstatistically significant at 5$\%$ level of significance.

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Chapter 7

Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables

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So this is a pretty quick problem. The first thing you would want to do is create a dummy variable for Roz Neck that you really have to do, just depending on the language programming language you're using the computer application you're using. Sorry. And, um, now we just want to explain what our beta three coefficient meetings. Beta three hat means so Beta three is the same thing as the coefficient of Ross neg. And what this means is, if the return of stocks is negative between 1988 to 1990 then what is that relationship between this and, um, he salary of our CEO? So what we have is this is equal to negative point two three, about negative 0.23 So notice that we have a log salary and this log basically as a proxy, this eyes an approximation of a percent change. So what we're saying is that when we have a negative return on stock, all right, if the return on stock was negative between 1988 and 1990 then the CEO salary dropped by about 22.6%. Um, for whatever the given levels of sales and Ara, we are on DDE. We know that this is ah, significant because of our P value of 0.4 and that's less than 0.5 So at the 5% significance level, um, we have a ah, we have a signal. We have a significant coefficient value. So against summarize between 19 88 in 1990 if the return of stock was less than zero than CEO salary, um, was predicted to be if I could spell predicted as 22.6% lower, Um, then if it was positive, were equal to zero, um, for the given levels of sales and return on you, whatever that stands for.

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