The data are on airfares for 1,000 routes serviced by U.S. airlines. The dependent variable is fare, measured in dollars, and the key independent variables are concen (fraction of the market share of the largest carrier) and dist (miles between destinations). This is the Regression output of the data. USE FOLLOWING TABLE TO SOLVE THE QUESTIONS. NO DATA IS MISSING SUMMARY OUTPUT Regression Statistics 0.584129524 explain the most important difference between eq. (1.2) and eq. (1.3). Which model provides a better fit to the data and why? 8) Now consider the model fare = 0 + 1concen + 2dist + 3dist2 + u. eq. (1.4) What signs should the parameters have for dist to have an initially positive, but diminishing, ceteris paribus effect on fare? Estimate the equation by OLS and see if the estimated effect is positive but diminishing Multiple R R Square Adjusted R Square Standard Error 0.3412073 0.33988575 60.39936195 Observations 1000 ANOVA df SS MS Regression 2 Residual Total 997 1883776.595 941888.2976 258.1871951 3637138.676 3648.082925 999 5520915.271 Intercept concen dist Significance F 4.42859E-91 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 77.20718353 9.483851305 8.140910379 1.16317E-15 58.59658361 95.81778344 58.59658361 95.81778344 54.03489109 11.38229307 4.747276383 2.36319E-06 31.69889112 76.37089106 31.69889112 76.37089106 0.081329928 0.003781502 21.50730902 1.36561E-84 0.073909312 0.088750544 0.073909312 0.088750544 1)Estimate the simple regression and write the results in equation form. fare 0+ 1concen + eq. (1.1) 2) Now estimate the multiple regression and again write the results in equation form. If concen increases by .20, how much is fare predicted to increase, holding dist fixed? Is this a large economic effect? fare = 0+ 1concen + 2dist+, eq. (1.2) 3) What is the sample correlation between concen and dist? Does this help you reconcile your findings from parts (i) and (ii)? 4) What percentage of the variation in fare is explained by concen and dist in this sample? Is this a lot? 5) What happens to the OLS estimates if we decide to measure airfare in hundreds of dollars rather than dollars? Explain. 6) The last route in the sample has concen = .7443 and dist = 861. Find the predicted fare for this route and compare it with the actual fare. Do you over- or under-estimate? 7) Now, estimate the model fare 0+ 1concen+ 2log(dist) + u = eq. (1.3) 9) Based on your estimates of eq. (1.3), and (1.4), does dist seem to have a diminishing marginal effect on fare? Explain. 10) Now estimate the model log(fare) = 30+ 1concen + 2log(dist) + u eq. (1.5) Report the results in equation form. Interpret the slope coefficients. 11) Does the estimated equation in part (x) imply a diminishing marginal effect of dist on fare? Explain. 12) Based on goodness-of-fit, can you say you prefer eq. (1.3) to eq. (1.5), or vice versa? Can you compare these two equations? Explain.