Question

In: Statistics and Probability

15.28 Note: This exercise requires a computer and statistical software. The data mentioned below can be...

15.28 Note: This exercise requires a computer and statistical software. The data mentioned below can be found in several formats on your Premium Website under "Chapter datasets".

Information describing 98 of the top automobile dealership groups in the United States is provided in computer database file DEALERS. For calendar year 1999, the data include the number of dealers, the average number of retail units sold per dealer, and the total revenue for the dealership group. Determine the regression equation estimating total revenue as the dependent variable and the average retail units sold per dealer as the independent variable. (SOURCE: Automotive News, May 1, 2000, pp. 54-60.)

a. The estimated intercept is  .

b. The estimated slope is  .

c. When the average number of retail units sold per dealer is 1000, the predicted total revenue is  .

d. When the average number of retail units sold per dealer is 1000, the lower bound of the 95% confidence interval of total revenue is  .

e. When the average number of retail units sold per dealer is 1000, the upper bound of the 95% confidence interval of total revenue is  .

f. When the average number of retail units sold per dealer is 1000, the lower bound of the 95% prediction interval of total revenue is  .

g. When the average number of retail units sold per dealer is 1000, the upper bound of the 95% prediction interval of total revenue is

Name RetailUnits UsedUnits FleetUnits TotalUnits NumDealrs AvgRetail/Dealer $GroupRevenue
AutoNation Inc. 468981 238168 186470 893619 290 1617.2 20926200000
Asbury Automotive Group 102000 66000 7000 175000 84 1214.3 4231000000
V.T., Inc. 80445 58151 4886 143482 35 2298.4 3317960000
Sonic Automotive, Inc. 74065 47345 5229 126639 114 649.7 3100030000
Hendrick Automotive Group 61861 38097 3096 103054 60 1031.0 2522280000
Group 1 Automotive Inc. 60384 45630 6136 112150 47 1284.8 2364300000
Bill Heard Enterprises Inc. 34714 27037 610 62631 11 3155.8 1433200000
Planet Automotive 31511 19779 10085 61375 18 1750.6 1305980000
Lithia Motors Inc. 28645 23840 2791 55276 45 636.6 1242660000
Larry H. Miller Group 27166 31027 4589 62782 34 799.0 1360930000
Penske Automotive Group 26403 5718 6506 38627 5 5280.6 987415000
Serra Investments Inc. 22291 13272 2194 37757 19 1173.2 824130000
Rosenthal Automotive 22106 8220 191 30517 15 1473.7 791469000
DarCars Ltd. 20605 10665 1697 32967 18 1144.7 732210000
Ed Morse Automotive 20326 10991 6882 38199 18 1129.2 907398000
Herb Chambers Cos. 19871 8139 0 28010 15 1324.7 800772000
Holman Enterprises 19851 11495 54424 85770 18 1102.8 2145490000
Faulkner Organization 19239 12588 5979 37806 20 962.0 806317000
Wilson Automotive 18792 6850 1275 26917 7 2684.6 671818000
Tuttle-Click Automotive 18534 7972 902 27408 9 2059.3 684652000
Earnhardt Dealer Grp 17672 11030 0 28702 6 2945.3 680386000
Bob Rohrman Auto Group 17251 18195 2 35448 25 690.0 639300000
Galpin Motors, Inc. 16686 3867 8561 29114 4 4171.5 616372000
Toresco Enterprises 14928 5688 841 21457 6 2488.0 495067000
Braman Dealerships 14814 6060 0 20874 8 1851.8 685413000
Phil Long Dealerships 14765 15234 1799 31798 12 1230.4 638715000
Ourisman Automotive 14756 5513 2052 22321 10 1475.6 549126000
Ricart Automotive 14653 11621 638 26912 3 4884.3 491776000
Don Massey Cadillac 14217 12233 423 26873 22 646.2 920000000
West-Herr Automotive 13793 4945 1572 20310 10 1379.3 387482000
Lou Fusz Automotive 13704 7572 252 21528 11 1245.8 477370000
McCombs Automotive 13683 8661 2668 25012 8 1710.4 542509000
Gillman Cos. 13463 4332 0 17795 13 1035.6 397293000
Allen Samuels Enter. 13459 5169 3591 22219 9 1495.4 523149000
Hitchcock Automotive 13455 4592 0 18047 6 2242.5 429086000
Burt Automotive Network 13108 10005 21001 44114 6 2184.7 998760000
Ferman Automotive 13059 6630 335 20024 13 1004.5 472695000
Suburban Collection 12680 4681 586 17947 14 905.7 426689000
Holler Automotive Group 12347 6175 1242 19764 9 1371.9 397117000
Huffines Auto Group 11468 4079 281 15828 5 2293.6 431187000
Germain Motor Co. 11331 5826 120 17277 6 1888.5 439549000
Fletcher Jones Auto. Grp. 11305 5853 805 17963 7 1615.0 676774000
Wolfe Automotive Group 11302 7896 874 20072 15 753.5 422513000
Keyes Automotive Group 11259 6374 163 17796 7 1608.4 496801000
Sheehy Auto Stores 11198 4549 329 16076 7 1599.7 367675000
World Class Automotive 11128 5276 2274 18678 4 2782.0 427939000
Jeff Wyler Dealer Group 11009 6089 1374 18472 6 1834.8 361841000
Kelley Automotive Group 10976 7308 211 18495 12 914.7 446452000
Kenwood Dealer Grp. 10878 5993 0 16871 10 1087.8 350158000
Hudiburg Auto Group 10823 13633 678 25134 8 1352.9 501479000
Bob Baker Auto Group 10771 6386 886 18043 7 1538.7 434858000
Chapman Automotive 10740 6203 1639 18582 9 1193.3 519192000
Pohanka Automotive 10375 5404 0 15779 13 798.1 438126000
Wilde Automotive Group 10176 7717 16 17909 11 925.1 369823000
Miller Automotive Grp. 10162 6015 0 16177 3 3387.3 375632000
Hays Automotive Group 10035 10672 1378 22085 9 1115.0 433603000
Bergstrom Automotive 9953 8044 911 18908 19 523.8 435755000
Prestige Mgmt. Services 9805 1698 0 11503 7 1400.7 457865000
Swope Group 9767 11224 764 21755 22 444.0 442308000
Day Automotive Group 9470 5192 1239 15901 13 728.5 312666000
Ray Catena Motor Car 9197 3098 0 12295 5 1839.4 521279000
Cutter Mgmt. Co. 9196 6565 125 15886 13 707.4 372202000
Piercey Automotive Grp. 9159 3282 0 12441 4 2289.8 291500000
Lupient Automotive Grp. 9050 7900 8000 24950 12 754.2 494500000
Midway Auto Team 9007 4078 12744 25829 2 4503.5 558491000
Kahlig Enterprises 8932 5523 673 15128 4 2233.0 374281000
Boucher Group Inc. 8901 8946 761 18608 14 635.8 381249000
Warnock Automotive Grp. 8519 1769 5114 15402 6 1419.8 408300000
Scott-McRae Automotive 8393 9003 3763 21159 5 1678.6 391736000
Joe Myers Dealership 8382 4126 1058 13566 4 2095.5 293656000
Carl Gregory Enterprises 8372 8648 250 17270 14 598.0 308095000
Chapman Auto Group 8265 5820 487 14572 8 1033.1 331137000
Ancira Enterprises 8161 4764 8438 21363 9 906.8 502865000
Motorcars Group 8154 4267 0 12421 12 679.5 314134000
DeCastro Automotive Grp. 8113 4411 512 13036 6 1352.2 262453000
Performance Cos. 8084 7416 455 15955 10 808.4 390063000
Hall Auto World Inc. 7962 5140 836 13938 12 663.5 305319000
Rosatti Auto Group 7836 1736 0 9572 2 3918.0 203386000
Rick Case Enterprises Inc. 7833 4159 0 11992 9 870.3 227533000
Russ Darrow Group 7800 5800 11300 24900 11 709.1 497000000
Mel Farr Automotive Grp. 7782 6028 3893 17703 8 972.8 421665000
Ira Motor Group 7735 2842 0 10577 3 2578.3 293217000
Noarus Auto Group 7673 3733 0 11406 5 1534.6 268584000
Servco Pacific Inc. 7657 3674 1628 12959 9 850.8 264788000
Don Bohn/Bohn Bros. 7648 3073 55 10776 4 1912.0 222347000
Stewart Mgmt. Group Inc. 7632 4314 200 12146 4 1908.0 257051000
AutoFair Automotive Group 7478 3781 55 11314 5 1495.6 307117000
Lamarque Automotive Grp. 7440 5132 1145 13717 5 1488.0 315644000
Vista Auto 7276 2715 0 9991 5 1455.2 270542000
Gunn Automotive Group 7272 5201 31 12504 8 909.0 263951000
Classic Automotive Group 7087 4082 88 11257 4 1771.8 258771000
Ron Tonkin Family 7021 11372 833 19226 17 413.0 391730000
Marubani Motor Services 7015 2915 0 9930 14 501.1 305000000
Cuillo Group 6832 4210 0 11042 6 1138.7 319961000
Mathews Auto Group 6577 7160 0 13737 8 822.1 223077000
Gettel Automotive Group 6545 3654 60 10259 6 1090.8 214133000
Farmer Automotive Group 6451 5630 264 12345 4 1612.8 275564000
Kenny Ross Automotive 6428 6601 322 13351 5 1285.6 236410000

Solutions

Expert Solution

Considering only the required columns ie AvgRetail/Dealer and $GroupRevenue

When we run regression in excel we get the following result

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.006981818
R Square 4.87458E-05
Adjusted R Square -0.010367413
Standard Error 2164593622
Observations 98
ANOVA
df SS MS F Significance F
Regression 1 2.19271E+16 2.19271E+16 0.00468 0.945602158
Residual 96 4.49805E+20 4.68547E+18
Total 97 4.49827E+20
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 828663848.7 419024769.6 1.977601108 0.050841 -3093745.049 1660421442
X Variable 1 15875.08814 232060.6096 0.068409232 0.945602 -444761.5812 476511.7575

a. The estimated intercept is

828663848.7

b. The estimated slope is  

15875.08814

c. When the average number of retail units sold per dealer is 1000, the predicted total revenue is  

= intercept + x * slope = 828663848.7 + 1000 * 15875.08814 = 844538936.8

d. When the average number of retail units sold per dealer is 1000, the lower bound of the 95% confidence interval of total revenue is  

-447855326

ie a loss of 447855326

e. When the average number of retail units sold per dealer is 1000, the upper bound of the 95% confidence interval of total revenue is  .intercept + 1000 * slope at 95% upper bound

2136933200

orchestra answered 2 years ago
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