Problem Set 6 (1)

Problem Set 6 (With instructions) Individual or group. Use SWA_PS6_Soth west airlines file 1. Do a multiple regression using JetFuel ($/gal), DPI ($B), Recession and AirTran to predict Revenue for Southwest Airlines using data in the Data2 tab . Then use the results to predict Revenue on CEI tab 2012 with a 95% prediction interval estimate when JetFuel = 3.07, DPI = 10337, Recession = 0 and AirTran = 1. Write up a report of your analysis. You should include the following in your report: Interpretation of R-squared, Adjusted R-squared, Mutiple R, and standard error and what these say about how good the regression is for predicting Revenue from the independent variables. Write he model, the equation Next interpretation of the 4 slopes. Which of these variables decrease revenues and which increase revenues? Use the proper units when you do the interpretations. Take care to interpret slopes for dummy variables appropriately. Tests including hypotheses and confidences for the entire equation and each variable separately, 5 sets of tests in all. State hypotheses and write a one sentence interpretation for each of the five. Use α =.05 for all. Should any terms be dropped? If so, which ones and why? Check the assumptions of linearity for JetFuel and DPI (no need for the 2 dummy variables), This is Linearity, independence, Normality, and constant variability. All plots are given to you in the Residuals tab in the excel results file. PHStat does not create the linearity plots. Write a statement detailing what you found and recommendations for addressing any issues present. A statement explaining the results of the 95% prediction interval. Now test statistically if there is evidence of an interaction for this by adding the interaction term Flights x Airtran and run the regression with all the terms. Explain the results and if this suggests you should add the interaction term to your model. Don't forget to explain why or why not! Make sure you include relevant excel results you used for each part above. ( 6 pts ) Note: writing a case report like this may be a problem on the final exam. - R-squared: R2=0.9438, 94.38% of variation in revenue is explained by the variation in JetFuel, DPI, Recession, and Airtran. - Adjusted R-squared: 0.9348, 93.48% of the variation of the revenue is explained by variation of Jet-Fuel, DPI, Recession, Airtran. - Multiple R: 0.9715, 97.15% of the relationship with revenue has to do with the variables Jet-Fuel, DPI, Recession, Airtran. - Standard Error: 192.2927, the data can vary with a range of positive or negative 192.2927 million. Y = -10322 + 60.35(x) + 1.3(x) - 251(x) + 1119(x) + or - 192.3

Ho B1=B2=B3=B4=0 H1 One of the slopes not equal to zero H0: B1 = 0 Fuel is not related to Revenue. H1: B1 ≠ 0 Fuel is related to Revenue. P-value is above 0.05, there is insufficient evidence to reject the null hypothesis. H0: B1 = 0 DPI is not related to Revenue. H1: B1 ≠ 0 DPI is related to Revenue. P-value is below 0.05, so we can reject the null hypothesis. H0: B1 = 0 Recession is not related to Revenue. H1: B1 ≠ 0 Recession is related to Revenue. P-value is below 0.05, so we can reject the null hypothesis. H0: B1 = 0 Airtran is not related to Revenue. H1: B1 ≠ 0 Airtran is related to Revenue. P-value is below 0.05, so we can reject the null hypothesis. It was hypothesized that fuel price, DPI, Merger, and recession would not affect revenue. There is significant evidence to reject the null hypothesis. The significant F is at 0 which is below the level of significance 0.05. I am 99.99% confident that one of the slopes is not equal to zero. 94% of the increase or decreases in revenue are attributed to the increase or decrease in the independent variables. When you adjust for fuel price, DPI, recession, and mergers (R2) and the sample size the percentage is 93% The slopes for the independent variables indicate (coefficients) If fuel was free, no DPI, no merger, and no recession the income would be -10 million, and for every dollar you increase the fuel price, the revenue will increase by 60 million. Similarly for every billion dollars of DPI, the revenue will increase by 1.3 million, and if we had a merger our income would increase by 118 million dollars and if there was a recession, the revenue would decrease by 251 million dollars.

df SS MS F Significan ce F Regression 4 15533797.2 889 3883449.32 22 105.02 48 0.0000 Residual 25 924412.177 8 36976.4871 Total 29 16458209.4 667 Coefficie nts Standard Error t Stat P-valu e Lower 95% Upper 95% Lower 95% Upper 95% Intercept -10322.08 17 1559.6093 -6.6184 0.0000 -13534.157 1 -7110.00 62 -13534.157 1 -7110.0062 JetFuel($/gal) 60.3484 87.0957 0.6929 0.4948 -119.0284 239.7253 -119.0284 239.7253 DPI($B) 1.3014 0.1684 7.7292 0.0000 0.9546 1.6481 0.9546 1.6481 Recession -251.2149 97.4119 -2.5789 0.0162 -451.8385 -50.5913 -451.8385 -50.5913 Airtran 1118.542 3 129.5954 8.6310 0.0000 851.6355 1385.449 0 851.6355 1385.4490 Individual or group. Use SWA 18 file 2. Do a multiple regression using Fuel ($/gal), Maintenance , Employees and Airport fees to predict Costs for Southwest Airlines using data in the Costs tab . Then use the results to predict costson CEI tab with a 95% confidence when Fuel Price = 4.00, Maintenance = 4 hours, Employees= 200,000 and AirPort fee = 7,000. Write up a report of your analysis. You should include the following in your report: a. Interpretation of R-squared, Adjusted R-squared, Multiple R, and standard error and what these say about how good the regression is for predicting Revenue from the independent variables. b. Write he model, the equation c. Next interpretation of the 4 slopes. Which of these variables decrease revenues and which increase revenues? Use the proper units when you do the interpretations. Take care to interpret slopes for dummy variables appropriately. d. Tests including hypotheses and confidences for the entire equation and each variable separately, 5 sets of tests in all. State hypotheses and write a one sentence interpretation for each of the five. Use α =.05 for all. e. Should any terms be dropped? If so, which ones and why? Check the assumptions of linearity for Fuel price and Maintenance, Employees and Airport Fees. This is Linearity, independence, Normality, and constant variability. All plots are given to you in

the Residuals tab in the excel results file. PHStat does not create the linearity plots. Write a statement detailing what you found and recommendations for addressing any issues present. A statement explaining the results of the 95% prediction interval. - R-squared: R2=0.999999, 99.99% of variation in revenue is explained by the variation in JetFuel, DPI, Recession, and Airtran. - Adjusted R-squared: 0.99999, 99.99% of the variation of the revenue is explained by variation of Jet-Fuel, DPI, Recession, Airtran. - Multiple R: 0.99999, 99.99% of the relationship with revenue has to do with the variables Jet-Fuel, DPI, Recession, Airtran. - Standard Error: 3.5014, the data can vary with a range of positive or negative 3.5014 million. Y = 4.5 - 0.01(x) + 0.002(x) + 0.001(x) + 12.13(x) + or - 3.50 Ho B1=B2=B3=B4=0 H1 One of the slopes not equal to zero H0: B1 = 0 Fuel is not related to Revenue. H1: B1 ≠ 0 Fuel is related to Revenue. P-value is above 0.05, there is insufficient evidence to reject the null hypothesis. H0: B1 = 0 Maintenance is not related to Revenue. H1: B1 ≠ 0 Maintenance is related to Revenue. P-value is above 0.05, there is insufficient evidence to reject the null hypothesis H0: B1 = 0 Employees is not related to Revenue. H1: B1 ≠ 0 Employees is related to Revenue. P-value is above 0.05, there is insufficient evidence to reject the null hypothesis. H0: B1 = 0 Airport fee is not related to Revenue. H1: B1 ≠ 0 Airport fee is related to Revenue. P-value is below 0.05, so we can reject the null hypothesis.

Regression Analysis Regression Statistics Multiple R 0.9999901 R Square 0.99998020 Adjusted R Square 0.9999770 Standard Error 3.5014 Observations 30 ANOVA df SS MS F Significance F Regression 4 15481070.4748 3870267.6187 315690.8480 0.0000000 Residual 25 306.4919 12.2597 Total 29 15481376.9667 Coeffici ents Standard Error t Stat P-value Lower 95% Upper 95% Lower 95% Upper 95% Intercept 4.5050 2.9286 1.5383 0.1365 -1.5265 10.536 6 -1.5265 10.5366 Fuel -0.0105 0.0080 -1.3212 0.1984 -0.0270 0.0059 -0.0270 0.0059 Maintance 0.0019 0.0157 0.1198 0.9056 -0.0305 0.0343 -0.0305 0.0343 Employees 0.0010 0.0028 0.3624 0.7201 -0.0047 0.0067 -0.0047 0.0067 Airport fee 12.1330 0.0238 510.4495 0.000 12.0840 12.181 9 12.0840 12.1819

For 1 Point of extra credit. Compare the output from Revenue and the Output for Costs and write a short paragraph on the Profit for the upcoming year. Remember Profit is Revenue Minus Costs. Tell me how confident you are that the Profit will be the number you state. For the given values of the equation, Fuel Price = 4.00, Maintenance = 4 hours, Employees= 200,000 and AirPort fee = 7,000. The total costs would equal 85 million dollars. For the given values of the problems equation, when JetFuel = 3.07, DPI = 10337, Recession = 0 and AirTran = 1. The revenue for the company would be 4 million dollars. From the data I have analyzed, I believe that the profit will be negative this year. 4 million in revenue minus 85 million in costs comes out to negative 81 million dollars. Company should rethink some strategical things and focus on dropping the cost of the airline fee if possible.