Expert answer:Need statistics homework to with restaurant chain

Answer & Explanation:Hello,I have already done the work on this assignment. But I am hoping to get it looked at just to make sure I am on the right track with everything.assignment_15_questions.docxschwarz_mis86510_assignment_15.xlsxp10_04.xlsxp10_21.xlsx
assignment_15_questions.docx

schwarz_mis86510_assignment_15.xlsx

p10_04.xlsx

p10_21.xlsx

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Assignment 15 Questions
2) The owner of the Original Italian Pizza restaurant chain would like to predict the
sales of his specialty, deep-dish pizza. He has gathered data on the monthly sales of
deep-dish pizzas at his restaurants and observations on other potentially relevant
variables for each of his 15 outlets in central Indiana. These data are provided in the
file P10_04.xlsx.
a. Estimate a multiple regression model between the quantity sold (Y) and the
explanatory variables in columns C–E.
b. Is there evidence of any violations of the key assumptions of regression analysis?
c. Which of the variables in this equation have regression coefficients that are
statistically different from zero at the 5% significance level?
d. Given your findings in part c, which variables, if any, would you choose to remove
from the equation estimated in part a? Why?
18) The Undergraduate Data sheet of the file P10_21.xlsx contains information on
101 undergraduate business programs in the U.S., including various rankings by
Business Week. Use multiple regression to explore the relationship between the
median starting salary and the following set of potential explanatory variables:
annual cost, full-time enrollment, faculty-student ratio, average SAT score, and
average ACT score. Which explanatory variables should be included in
a final version of this regression equation? Justify your choices. Is multicollinearity a
problem? Why or why not?
23) The Undergraduate Data sheet of the file P10_21.xlsx contains information on
101 undergraduate business programs in the U.S., including various rankings by
Business Week. Use forward, backward, and stepwise regression analysis to explore
the relationship between the median starting salary and the following set of
potential explanatory variables: annual cost, full-time enrollment, faculty-student
ratio, average SAT score, and average ACT score. Do these three methods all lead to
the same regression equation? If not, do you think any of the final equations are
substantially better than any of the others?
2
Outlet #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Source
Model
Error
Total
Quant Sold Avg Price
Mthly Adv C D.Income per household
85.300
10,14
64.800
42.100
40.500
10,88
42.800
38.300
61.800
12,33
58.600
41.000
50.800
12,7
46.500
43.300
60.600
12,29
50.700
44.000
79.400
9,79
60.100
41.200
71.400
11,26
55.600
41.700
70.700
11,23
57.900
43.600
55.600
11,97
52.100
39.900
70.900
12,07
60.700
44.800
77.200
10,68
64.400
41.800
63.200
12,49
55.600
44.200
71.100
12,36
60.900
40.100
55.500
9,96
47.200
39.100
42.100
11,77
46.100
38.000
Deg of Free Sum of Sqr Mean Sqr
3 2305491452 768497151
11 122204548
11109504
14 2427696000 779606655
F ratio = MSR / MSE
MSR = Mean Square Regression
MSE = Mean Square Error
F ratio = 768497151 / 11109504
F ratio = 69.17
Being that the F-ratio is vey high, the model would be considered significant.
Variable
Intercept
X1
Param Esti Stand Error t-value
p-value
-33302
17898
-1,86
0,0897
-4041,534
1040,64
-3,88
0,0025
X2
X3
1,454
1,528
0,152
0,513
9,59 <.0001 2,98 0,0125 predicted Y = -33302 - 4041.534X1 + 1.454X2 + 1.528X3 e sub I = y sub I - predicted y sub I, I = 1,2,…,15 D = E sub I = 2 (e sub I - e sub i-1) ^2 / E sub i=1 esub I ^2 dsubI = 0.82 for 5% level of Significance 0.59 for 1% level of significance dsub u = 1.75 fir 5% level of significance 1.46 for 1% level of significance d = 1.542 The test is inconclusive at 5% level of significance. However the null hypothesis is accepted at 1% lev The dependent variable is following a Normal Distribution It can be concluded that there is no evidence of any violation of the key points of regression. Variable Intercept X1 X2 X3 Para est Stan. Error t-value p-value -33302 17898 -1,86 0,0897 -4041,534 1040,64 -3,88 0,0025 1,454 0,152 9,59 <.0001 1,528 0,513 2,98 0,0125 From the above table it is seen that the p-value for testing the coefficients equals to zero against no The 5% level of significance no value is greater than 0.05 except for the intercept term. Therefore, we can reject the null hypothesis of coefficients equal to zero at 5% level of significance, From the finding in the above part, there is no need to drop any variable from the regression since a 18 Yearly cost FT Enrment Med. St salar Facut stu r 9.490 655 58.000 10,4 36.847 1.669 55.000 19 37.526 2.528 61.001 11 10.848 1.050 60.000 15 4.110 1.783 50.000 19 8.932 668 55.000 26 36.390 225 60.000 3 20.364 712 55.000 19 36.336 622 55.000 10 9.354 3.942 55.000 34 37.530 1.731 52.000 16 70.000 60.000 50.000 40.000 30.000 20.000 10.000 Source Model Error Total Deg of free Sum of Sqrs Mean Sqrs F-value P-Value 5 1799281806 359856361 30,98 <.0001 96 1115126684 11615903 101 2914408489 371472264 Variable Intercept X1 X2 X3 X4 X5 Para Est Stand Error t-value p-value 6895,396 5409,071 1,27 0,2055 0,04473 0,03022 1,48 0,1421 0,62873 0,34806 1,81 0,074 -44,121 38,1264 -1,16 0,2501 7,176 8,142 0,88 0,3803 1202,973 309,759 3,88 0,0002 Predicted Y = 6895.396 + 0.04473X1 + 0.062873X2 - 44.121X3 + 7.176X4 + 1202.973X5 From the Parameter Estimate Table above the p-value shows that if we were to check the significanc Its likely that X4 should have some impact on the dependent variable, but it is also clear that X4 and It is to be anticipated that the annual cost, full time enrollment, and faculty student ratio not to affe Therefore, all variable except for the ast one that is the final of the regression equation should only If it is condered the final version of the regression then it will become a simple linear regression whe 23 09 Rank 08 Rank 1 2 3 4 5 6 Regression Table Constant Avg ACT Score 2 3 1 6 7 11 Sch Name Location Va McIntire Charlottsvile N.Dame/Mendoza IND Pa Wharton Philidelphia MI (Ross) Ann Arbor Brig Yg Provo, UT UCB Berkeley,CA Type Public Private Private Public Private Public Coefficient Std Error t-value p-value 7900,22133 3464,70023 2,2802 0,0247 1531,98379 127,879295 11,9799 <0.0001 Median Starting salary = 7900.22 + 1531.98Average ACT score ANOVA Table Explained Unexplained Deg of Free Sum of Sqrs Mean of Sqrs F-Ratio 1 1717617060 1717617060 143,5185 100 1196791429 11967914,3 Regression Table Constant Annual Cost Avg ACT Score Coefficient 9672,72541 0,04924834 1432,08515 Std Error t-value p-value 3581,89966 2,7004 0,0081 0,02857613 1,7234 0,0879 139,273781 10,2825 <0.0001 Median Starting Salary = 9672.72 + 0.04Annual Cost plus 1432.08Average Act score ANOVA Table Explained Unexplained Deg of Free Sum Sqr Mean of Sqr F-Ratio 2 1752476627 87623833 74,6581 99 1161931862 11736685,5 Regression Table Constant Avg ACT Score Coefficient Std Error t-value p-value 7900,22133 3464,70023 2,2802 0,0247 1531,98379 127,879295 11,9799 <0.0001 Median Starting Salary = 7900.22 + 1531.98Average ACT Score ANOVA Table Explained Unexplained Deg of Free Sum of sqr Mean of sqr f-ratio 1 1717617060 1717617060 143,5185 100 1196791429 11967914,3 It is seen that the forward and stepwise regression analysis are having the same regression equation 70000 60000 50000 40000 Series1 Series2 30000 Series3 20000 10000 0 0 3,5 20.000 40.000 60.000 80.000 100.000 3,5 3 2,5 2 1,5 Series1 1 0,5 0 1,454 0,152 9,59 <.0001 -4041,534 1040,64 -3,88 0,0025 -33302 17898 -1,86 0,0897 In the above graph there is no such pattern. Therefore, there is no heteroscedasticity present. pothesis is accepted at 1% level of significance. y points of regression. nts equals to zero against not equal to zero. intercept term. o at 5% level of significance, which implies that all of the variables in regression equation have the regression coefficients stat e from the regression since all of the independent variables have regression coefficients significantly different from 0 at 5% le 70.000 60.000 50.000 Series1 40.000 Series2 30.000 Series3 Series4 20.000 10.000 0 1 2 3 4 5 6 7 8 9 10 11 4 + 1202.973X5 were to check the significance of the regression coefficient of every variable at 5% level of significance, than variables from X5 but it is also clear that X4 and X5 are highly correlated. culty student ratio not to affect too much the dependent varaibleof the average median salary. ession equation should only have the variable of X5. simple linear regression where multicollinearity won't be in violation. However there would be a problem in X4 and X5 as the p-value <0.0001 erage Act score p-value <0.0001 p-value <0.0001 he same regression equation, but the regression equation of the backward is different from the forward and stepwise. he regression coefficients statistaically different from 0 at 5% level of significance. Outlet Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Quantity Sold 85,300 40,500 61,800 50,800 60,600 79,400 71,400 70,700 55,600 70,900 77,200 63,200 71,100 55,500 42,100 Average Price $10.14 $10.88 $12.33 $12.70 $12.29 $9.79 $11.26 $11.23 $11.97 $12.07 $10.68 $12.49 $12.36 $9.96 $11.77 Monthly Advertising Expenditures $64,800 $42,800 $58,600 $46,500 $50,700 $60,100 $55,600 $57,900 $52,100 $60,700 $64,400 $55,600 $60,900 $47,200 $46,100 Disposable Income per Household $42,100 $38,300 $41,000 $43,300 $44,000 $41,200 $41,700 $43,600 $39,900 $44,800 $41,800 $44,200 $40,100 $39,100 $38,000 This is fictitious data. Business Week The MBA data are self-reported data from the schools. The top 30 schools are listed in order of their BusinessWeek ranking. The next 15 "second tier" schools are listed in alphabetical orders, as are the last 25 "non-ranked" schools. Note that there is missing data for some schools in some columns. All we can infer is that these schools chose not to report this data. To get the letter grades for the undergraduates in the last three columns, the top 20% among all 101 ranked programs got A+s. The next 25% got As, the next 35% got Bs, and the bottom 20% got Cs. Fulltime Business Week Ranking 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Second Tier Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked Not Ranked School Name University of Chicago Harvard University Northwestern University University of Pennsylvania University of Michigan Stanford University Columbia University Duke University Massachusetts Institute of Technology University of California-Berkeley Cornell University Dartmouth College New York University UCLA Indiana University University of Virginia University of North Carolina-Chapel Hill Southern Methodist University Carnegie Mellon University University of Notre Dame University of Texas -- Austin Brigham Young University Emory University Yale University University of Southern California University of Maryland University of Washington Washington University Georgia Institute of Technology Vanderbilt University Arizona State University Babson College Boston University George Washington University Georgetown University Illinois at Urbana-Champaign Michigan State University Ohio State University Purdue University Thunderbird School of Global Management University of California, Irvine University of Connecticut University of Iowa University of Minnesota University of Rochester American University Boston College Case Western Reserve University College of William and Mary Florida International University Fordham University Howard University Northeastern University Pepperdine University Rice University Rutgers University Texas A & M Texas Christian University The Pennsylvania State University The University of Tennessee at Knoxville Tulane University University at Buffalo University of Arizona University of Colorado at Denver University of Florida University of Georgia University of Miami University of Pittsburgh University of Wisconsin-Madison Wake Forest University State Illinois Massachusetts Illinois Pennsylvania Michigan California New York North Carolina Massachusetts California New York New Hampshire New York California Indiana Virginia North Carolina Texas Pennsylvania Indiana Texas Utah Georgia Connecticut California Maryland Washington Missouri Georgia Tennessee Arizona Massachusetts Massachusetts Washington D.C. Washington D.C. Illinois Michigan Ohio Indiana Arizona California Connecticut Iowa Minnesota New York Washington D.C. Massachusetts Ohio Virginia Florida New York Washington D.C. Massachusetts California Texas New Jersey Texas Texas Pennsylvania Tennessee Louisiana New York Arizona Colorado Florida Georgia Florida Pennsylvania Wisconsin North Carolina Type Private Private Private Private Public Private Private Private Private Private Public Private Private Public Public Public Public Private Private Private Public Private Private Private Private Public Public Private Public Private Public Private Private Private Private Public Public Public Public Private Public Public Public Public Private Private Private Private Public Public Private Private Private Private Private Private Public Private Public Public Private Public Public Public Public Public Private Public Public Private Enrollment Avg GMAT 1144 713 1801 720 1200 711 1651 714 898 706 739 726 1234 878 696 780 708 500 714 593 694 506 712 832 708 731 711 473 663 644 693 562 678 201 642 392 690 316 677 552 681 315 673 373 680 382 718 525 692 257 660 225 688 294 681 156 681 382 656 159 676 387 630 315 680 201 643 521 678 198 639 214 642 274 674 293 662 589 610 204 675 119 627 140 653 199 663 350 675 137 202 661 163 606 175 601 84 560 337 610 86 557 154 609 294 637 250 667 160 643 164 643 94 610 187 646 151 615 131 654 176 619 139 622 33 574 142 677 140 199 631 234 626 231 666 149 629 Resident Tuition, Fees 97165 101660 93918 104410 80879 97842 94104 95000 46784 66475 93000 91905 89184 66590 40882 84000 43503 81384 93840 77340 48800 18530 82856 93098 88800 60583 43556 83172 17816 81076 34082 72184 73996 65550 83868 42004 40937 47277 37700 78255 55629 21188 29224 58387 80010 Pct International Pct Female 35 35 33 38 34 36 44 36 27 34 43 36 33 32 40 39 36 35 39 30 27 39 31 33 32 41 32 34 37 26 30 29 32 32 18 28 23 21 28 24 24 31 10 20 42 39 28 34 34 29 35 29 18 36 34 37 19 27 18 25 26 25 41 37 32 45 27 45 24 30 45 34 30 22 33 27 45 27 45 32 40 37 38 25 38 29 19 32 55 33 Pct Asian American Pct Minority 16 7 25 7.8 21 13 9 13 12 19 14 29 15 8 14 14 12 6 5 7 25 10 11 13 12 9 4 7 13 15 6 13 9 10 8 12 9 11 5 14 11 6 11 5 12 5 6 4 11 8 4 5 15 13 7 6 9 1 9 4.8 5 26 8 14 23 18 15 7 7 7 3 14 14 9 17 16 22 13 13 7 18 5 2.4 6 15 66604 70666 42800 30490 69878 36380 72198 73630 76500 45061 25603 58500 38036 23612 74900 18156 31668 31606 17132 20 46 37 39 20 27 41 36 29 27 26 25 33 12 38 30 32 7 23 36 37 30 49 29 56 45 43 37 38 21 26 38 25 23 30 27 42 32 9 7 0 4 9 3 10 25 18 19 13 0 4 3.5 22 9 59 5 97 3 4 11 9 16 6 13 6 18 1 5 7 11 68626 36836 22957 70600 32 48 13 15 36 31 30 33 19 1.5 6 8 21 7 9 8 8 0 4 13 Pct with job offers 92 94 95 89 89 94 87 92 92 90 84 94 84 80 88 92 82 80 96 80 88 78 82 89 88 81 85 81 98 83 80 62 88 68 91 75 86 79 83 51 62 57 86 84 80 Avg starting base salary 107091 124378 108064 112186 103608 121171 107450 100136 111184 108967 100700 110305 101063 101306 92000 103963 95647 84828 103012 89660 96537 88958 93620 99562 91863 85225 86426 90775 93403 89891 86065 92296 89543 83746 94137 90317 90951 89584 83614 84295 81500 95120 82380 87539 18712 83 60 88 37 87140 84671 78222 49770 77659 80525 72061 75711 93006 83092 86700 71153 87444 71932 83558 55276 77376 49 72 84 82 78 68 34 74 62 91 65 91 87 85 54 46 30 85 76559 62567 75454 88626 79392 2009 Rank 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 2008 Rank 2 3 1 6 7 11 9 4 5 10 13 20 12 21 8 15 14 24 22 16 17 18 28 19 33 25 34 NA 47 29 23 35 30 32 43 26 31 38 41 37 27 59 42 54 36 School Name Virginia (McIntire) Notre Dame (Mendoza) Pennsylvania (Wharton) Michigan (Ross) Brigham Young (Marriott) UC-Berkeley (Haas) MIT (Sloan) Cornell Emory (Goizueta) Texas (McCombs) Villanova Richmond (Robins) North Carolina (Kenan-Flagler) Wake Forest (Calloway) NYU (Stern) Washington U. (Olin) Boston College (Carroll) Miami U. (Farmer) Carnegie Mellon (Tepper) Indiana (Kelley) USC (Marshall) Illinois Babson Georgetown (McDonough) U. of Washington (Foster) Lehigh Northeastern American (Kogod) San Diego William & Mary (Mason) SMU (Cox) Santa Clara (Leavey) Bentley Texas Christian (Neeley) Maryland (Smith) Rensselaer Polytech (Lally) Texas A&M (Mays) Penn State (Smeal) Case Western (Weatherhead) Wisconsin Fordham Ohio State (Fisher) Boston U. James Madison Baylor (Hankamer) Location Charlottesville South Bend, Ind. Philadelphia Ann Arbor Provo, Utah Berkeley, Calif. Cambridge, Mass. Ithaca, N.Y. Atlanta Austin Villanova, Pa. Richmond, Va. Chapel Hill Winston-Salem, N.C. New York St. Louis Boston Oxford, Ohio Pittsburgh Bloomington Los Angeles Urbana-Champaign Babson Park, Mass. Washington, D.C. Seattle Bethlehem, Pa. Boston Washington, D.C. San Diego, Calif. Williamsburg, Va. Dallas Santa Clara, Calif. Waltham, Mass. Fort Worth College Park Troy, N.Y. College Station University Park Cleveland Madison New York Columbus Boston Harrisonburg, Va. Waco, Tex. Type Public Private Private Public Private Public Private Private Private Public Private Private Public Private Private Private Private Public Private Public Private Public Private Private Public Private Private Private Private Public Private Private Private Private Public Private Public Public Private Public Private Public Private Public Private Program Length 2 3 4 3 2 2 3 4 2 4 4 4 2 2 4 4 4 2 4 4 4 4 4 4 2 4 4 4 4 2 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 46 47 48 49 50 51 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 NA NA 40 52 49 55 55 39 46 NA 48 50 NA 60 64 NA 62 56 63 53 51 61 73 65 NA NA NA 70 81 76 80 84 NA 74 77 86 NA NA 88 89 85 95 82 90 83 NA NA Chapman (Argyros) Ohio Binghamton Syracuse (Whitman) U. of Miami Georgia Tech Georgia Tech Michigan State (Broad) Florida (Warrington) Virginia Tech (Pamplin) Minnesota (Carlson) Rutgers St. Joseph's (Haub) Delaware (Lerner) Bryant John Carroll (Boler) Purdue (Krannert) Clemson Arizona (Eller) Marquette George Washington Connecticut Colorado State Drexel (LeBow) Xavier (Williams) CalPoly (Orfalea) DePaul Arizona State (Carey) Northern Illinois Missouri (Trulaske) Massachusetts (Isenberg) Iowa (Tippie) Texas Tech (Rawls) Oregon (Lundquist) Pittsburgh Texas Oklahoma (Price) Tennessee Arkansas (Walton) Belmont North Carolina State South Carolina (Moore) Houston (Bauer) Louisiana State (Ourso) Colorado (Leeds) Rutgers Cincinnati Orange, Calif. Athens Binghamton, N.Y. Syracuse, N.Y. Coral Gables, Fla. Atlanta Atlanta East Lansing Gainesville Blacksburg Minneapolis New Brunswick, N.J. Philadelphia Newark Smithfield, R.I. University Heights, Ohio West Lafayette, Ind. Clemson, S.C. Tucson Milwaukee Washington, D.C. Storrs Ft. Collins Philadelphia Cincinnati San Luis Obispo Chicago Tempe DeKalb Columbia Amherst Iowa City Lubbock Eugene Pittsburgh Dallas Norman Chattanooga Fayetteville Nashville Raleigh Columbia Houston Baton Rouge Boulder Newark, N.J. Cincinnati Private Public Public Private Private Public Public Public Public Public Public Public Private Public Private Private Public Public Public Private Private Public Public Private Private Public Private Public Public Public Public Public Public Public Public Public Public Public Public Private Public Public Public Public Public Public Public 4 4 4 4 4 4 4 2 2 4 4 4 4 4 4 2 4 4 2 4 4 4 4 4 4 4 4 4 2 2 4 2 4 2 4 ... Purchase answer to see full attachment

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