Some years ago, an economist estimated a multiple linear regression to examine the effect of firm...

 

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Some years ago, an economist estimated a multiple linear regression to examine the effect of firm performance and industry (which has three categories: financial, hotel or other) on the salaries of chief executive officers (CEO). He found the results of the estimation scribbled down on a piece of paper, but the value of the intercept is smudged out. The estimated regression and a few summary statistics are: In = +0.0157 X₁ +0.158X2, +0.181X, s.e. (0.30) (0.0032) (0.089) (0.085) Σχ., = 25 ΣΧ. = 0.17 Σχ. =0.17 ΣΧ., = 0.32 Cov(XnX,)=-0,5 R² = 0.357, n=209 where Y Salary of CEO per year X₁ = Sales revenue for the firm at which the CEO works (in millions of dollars) X₂2= a dummy if the CEO works in the financial industry X3 = a dummy if the CEO works in the hotel industry (a) Given the mean of InY is 9.4, determine the value of . Is it statistically significant? [5] (b) Interpret the coefficients on X₁ and X₂. Test whether they are significantly different from zero. [8] (c) Compute a 95% confidence interval estimate for B₁. What does this interval tell you? [5] (d) Test the hypothesis that the effect of sales revenue on CEO salary is less than 2%. [5] (e) Predict the salary for a CEO who works at a financial firm that generates sales of $950 million. [4] (f) Comment on the explanatory power of the model, i.e. interpret r-square. [2] (g) How would you modify the equation to see if white CEOs are better paid than black ones? [2] (h) Suppose you wish to convert sales revenue to billions of dollars (from millions of dollars). How would each of the estimates and standard errors change? Would the R2 change? Why or why not? [8] (i) Is X₂ a relevant variable? Why? What are the consequences if it is not a relevant variable? [4] (i) Test the hypothesis that B₂ <B,. Show full hypothesis testing procedure. Use p-value approach. [10] (k) Why would an economist not include in the regression above a third dummy that equals 1 if CEO works in 'other' industry? [2] Some years ago, an economist estimated a multiple linear regression to examine the effect of firm performance and industry (which has three categories: financial, hotel or other) on the salaries of chief executive officers (CEO). He found the results of the estimation scribbled down on a piece of paper, but the value of the intercept is smudged out. The estimated regression and a few summary statistics are: In = +0.0157 X₁ +0.158X2, +0.181X, s.e. (0.30) (0.0032) (0.089) (0.085) Σχ., = 25 ΣΧ. = 0.17 Σχ. =0.17 ΣΧ., = 0.32 Cov(XnX,)=-0,5 R² = 0.357, n=209 where Y Salary of CEO per year X₁ = Sales revenue for the firm at which the CEO works (in millions of dollars) X₂2= a dummy if the CEO works in the financial industry X3 = a dummy if the CEO works in the hotel industry (a) Given the mean of InY is 9.4, determine the value of . Is it statistically significant? [5] (b) Interpret the coefficients on X₁ and X₂. Test whether they are significantly different from zero. [8] (c) Compute a 95% confidence interval estimate for B₁. What does this interval tell you? [5] (d) Test the hypothesis that the effect of sales revenue on CEO salary is less than 2%. [5] (e) Predict the salary for a CEO who works at a financial firm that generates sales of $950 million. [4] (f) Comment on the explanatory power of the model, i.e. interpret r-square. [2] (g) How would you modify the equation to see if white CEOs are better paid than black ones? [2] (h) Suppose you wish to convert sales revenue to billions of dollars (from millions of dollars). How would each of the estimates and standard errors change? Would the R2 change? Why or why not? [8] (i) Is X₂ a relevant variable? Why? What are the consequences if it is not a relevant variable? [4] (i) Test the hypothesis that B₂ <B,. Show full hypothesis testing procedure. Use p-value approach. [10] (k) Why would an economist not include in the regression above a third dummy that equals 1 if CEO works in 'other' industry? [2]

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a The value of B is 00157 This is not statistically significant because it is not significantly diff... View the full answer