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# Bus & Economic Statistics II QMB 3200

USF

GPA 3.64

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This 18 page Class Notes was uploaded by Adrien Osinski I on Wednesday September 23, 2015. The Class Notes belongs to QMB 3200 at University of South Florida taught by Terry Sincich in Fall. Since its upload, it has received 31 views. For similar materials see /class/212699/qmb-3200-university-of-south-florida in Quantitative Methods at University of South Florida.

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Date Created: 09/23/15

Exam 2 for Practice BACKGROUND INFORMATION A marketing researcher is investigating a customer s motivation to use discount coupons A company named ValPak distributes these discount coupons via both the mail and the Internet A sample of 133 coupon users was randomly selected and each was asked a series of questions regarding their coupon usage The following variables were measured for each user loyalty tocouponusage score 70point scale annual income thousands ofdollars age years gendermale or female and type of coupon user mail only lnternet only or both The researcher used STATISTIX to 1 build a regression model for predicting loyalty score and 2 investigate the relationship between gender and type of coupon user Use the following STATISTIX printouts to answer the exam questions STUDENT EDITION OF STATISTIX 70 PRINTOUT 1 Descriptive Statistics Variable N Mean SD Minimum Maximum AGE 133 46789 14532 22000 84000 INCOME 133 53383 25530 13100 10980 VPLOYAL 133 45203 17036 10000 70000 STUDENT EDITION OF STATISTIX 70 PRINTOUT 2 Scatter Plot of VPLOYAL VS AGE VPLOYAL 8 IKBE STUDENT EDITION OF STATISTIX 70 PRINTOUT 3 Correlations Pearson VPLOYAL AGE 03034 Cases Included 133 Missing Cases 0 STUDENT EDITION OF STATISTIX 70 PRINTOUT 4 ChiSquare Test for Heterogeneity or Independence for NUMBER GENDER VPCUST VPCUST GENDER BOTH MAIL NET F Observed 1 42 1 13 1 48 1 103 Expected 1 4802 1 1704 1 3795 Cell Chi Sq 1 075 1 096 1 266 M Observed 1 20 1 9 1 1 1 30 Expected 1 1398 1 496 1 1105 Cell Chi Sq 1 259 1 329 1 914 62 22 49 133 Overall ChiSquare 1939 PValue 00001 Degrees of Freedom 2 STUDENT EDITION OF STATISTIX 70 PRINTOUT 5 UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF VPLOYAL PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT39S T P CONSTANT 618440 478023 1294 00000 AGE 035566 009760 364 00004 RSQUARED 00920 RESID MEAN SQUARE MSE 265538 ADJUSTED RSQUARED 00851 STANDARD DEVIATION 162953 SOURCE DF SS MS F P REGRESSION 1 352609 352609 1328 00004 RESIDUAL 131 347854 265538 TOTAL 132 383115 CASES INCLUDED 133 MISSING CASES 0 STUDENT EDITION OF STATISTIX 70 UNWEIGHTED LEAST SQUARES LINEAR REGRESSION OF VPLOYAL PRINTOUT 6 PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT39S T P VIF CONSTANT 680097 566794 1200 0 0000 AGE 036364 009662 376 0 0003 10 INCOME 010850 005500 197 0 0506 10 RSQUARED 01184 RESID MEAN SQUARE MSE 259803 ADJUSTED RSQUARED 01049 STANDARD DEVIATION 161184 SOURCE DF SS MS F REGRESSION 2 453715 226858 873 0 0003 RESIDUAL 130 337744 259803 TOTAL 132 383115 STUDENT EDITION OF STATISTIX 70 PRINTOUT 7 PREDICTEDFITTED VALUES OF VPLOYAL LOWER PREDICTED BOUND 83133 LOWER FITTED BOUND 36724 PREDICTED VALUE 40414 FITTED VALUE 40414 UPPER PREDICTED BOUND 72516 UPPER FITTED BOUND 44104 SE PREDICTED VALUE 16226 SE FITTED VALUE 18651 UNUSUALNESS LEVERAGE 00134 PERCENT COVERAGE 950 CORRESPONDING T 198 PREDICTOR VALUES AGE 55000 INCOME 70000 Identify each ofthe following for this study Experimental unit 2 pts Quantitative variables measured give units of measurement for each 6 pts Qualitative variables measured give levels for each 4 pts Multiple Choice Give the null hypothesis for determining whether the two qualitative variables measured in the study are related A B C D E Ho Ho Ho Ho Ho 3 lots Type of customer and Gender are independent Loyalty score is linearly related to Gender True mean loyalty score 0 True mean loyalty score and Type of customer are independent Type of customer and Gender interact Give the appropriate conclusion at at 01 for the hypothesis test of question 2 3 pts SX PO 4 The analyst wants to predict a coupon user s loyalty score based on the user s age Write the equation ofthe hypothesized straightline model for Ey Be sure to identify the variables that represent y and X 5 pts Hypothesized model Ey y X True or False The line shown on the scatterplot PO 2 is the true line of means forthe dependent variable y 2 pts Practically interpret the y interceptofthe least squares line If no practical interpretation is 6 possible explain why 5 pts SX PO 7 Practically interpret the slope ofthe leastsquares line If no practical interpretation is possible explain why 5 pts SX PO 8 Provide the following elements for testing for a negative linear relationship in the simple linear straight line model hypothesized in question 4 10 pts H0 at evalue Ha pvalue SX PO Conclusion 9 Practically interpret the value ofthe correlation coefficient relating y to X 4 pts SX PO 10 Multiple Choice Who is known as the quotfather of regressionquot for his work with Frances Galton on the relationship between fathers39 and sons39 heights 3 pts A B l3 0 quotquot Derrick Brooks HG Wells Mario Monteleone Karl Pearson R A Fisher 13 First give the least squares prediction equation for the multiple regression model that is t in P0 6 Then identify the variables that represent y X1 and X2 4 pts Prediction equation yhat Variables y X1 X2 Provide the following elements for testing the overall adequacy ofthe multiple regression model identi ed in question 11 10 pts Ho devalue Ha pvalue SX PO Conclusion Give a reason why conducting a series of ttests on the individual parameters in a multiple regression model is a dangerous strategy 3 pts 14 Give a practical interpretation ofthe 95 prediction interval fory using the multiple regression model Your interpretation should begin with We are 95 con dent 6 pts SX PO 15 Explain theoretically the meaning ofthe phrase quot95 con dentquot in the above interval 6 pts Multiple Choice The researcher wants to estimate the mean loyalty score for all users of age 50 years and with an annual income of 70 thousand dollars How should he proceed 3 pts A Form a 95 prediction interval for y using X1 50 and X2 70 B Form a 95 confidence interval for Ey using X1 50 and X2 70 C Form a 95 con dence interval for 32 in the multiple regression model D Since X1 50 and X2 70 are both outside the range ofthe sample data he should collect data for users with similar Xvalues before attempting to make the estimate E Form a 95 confidence interval for u using the Central Limit Theorem 20 Give the value ofthe standard deviation 3 for the multiple regression model and practically interpret its value 5 pts SX PO Give the adjusted coef cient of determination Rzadj for the multiple regression model and practically interpret its value 5pts SX PO Which regression statistic can be arti cially forced to 1 by simply adding independent variables good or bad predictors to the model 2 pts Multiple Choice Do you recommend using this multiple regression model in practice or would you recommend searching for a better model 4 pts A B U 0 Use the model in practice the global Ftest is significant R2adj is high and 2s is small Use the model in practice the global Ftest is significant R2adj is low and 2s is large Search for a better model the global Ftest is not signi cant Search for a better model although the global Ftest is significant R2adj is too low Search for a better model although the global Ftest is significant 2s is too large lO Ryan Yates U80162272 PO 1 Data Listing Student Edition of Statistix 90 AM Exam3POs CASE GPA Hours HoursSQ HoursSQis Hoursisex 1 31 O O 2 29 13 169 O O 3 36 15 225 225 15 4 28 15 225 225 15 5 32 15 225 225 15 6 33 15 225 O O 7 26 12 144 O O 8 29 15 225 225 15 9 31 18 324 324 18 10 28 12 144 O O 11 33 12 144 144 12 12 31 15 225 O O 13 36 15 225 O O 14 26 15 225 O O 15 3 12 144 144 12 16 31 9 81 81 9 17 27 16 256 256 16 18 3 12 144 O O 19 28 14 196 196 14 20 33 15 225 O O 21 26 12 144 144 12 22 31 15 225 225 15 23 31 15 225 O O 24 3 15 225 O O 25 26 12 144 O O 26 3 12 144 144 12 27 31 14 196 196 14 28 29 16 256 O O 29 26 18 324 O 0 30 33 12 144 144 12 31 31 15 225 O O 32 26 9 81 O O 33 36 12 144 144 12 34 32 12 144 O O 35 3 12 144 144 12 36 33 15 225 225 15 37 37 15 225 225 15 38 39 15 225 O O 39 26 12 144 144 12 40 27 12 144 O O 41 25 15 225 225 15 42 27 18 324 O O 43 38 12 144 144 12 44 33 9 81 O O 45 31 6 36 O O 46 31 15 225 225 15 47 26 18 324 324 18 48 38 12 144 O O 49 3 15 225 O O 50 37 15 225 225 15 3292011 I D X HOOHHOOHOHOHOgt HHOHOOHOOgt gt OOOHHOHOHHHOOOHOHHOOHHHOO 111055 Ryan Yates U80162272 PO 2 Scatterplot of Actual Data Scatter Plot of Hours vs GPA 18 Q 0 Q 0 o C O O 6 0 O O 0 Q 0 0 w 14 O 0 Sex L o g o o o 0 o o ltgt 9 Q 0 0 I 10 Q 1 0 lt2 0 6 o 214 29 34 39 GPA PO 3 Correlation Matrix Student Edition of Statistix 90 Exam3POs 4112011 93618 PM Correlations Pearson Hours Sex Sex 009912 GPA 00540 00882 Cases Included 50 Missing Cases 0 Ryan Yates U80162272 P04 Model 1 Student Edition of Statistix 90 Exam3POs 4112011 100358 Least Squares Linear Regression of GPA Predictor Variables Coefficient Std Error 39139 P VIE Constant 229758 112318 205 00468 00 Hours 012692 018114 070 04872 670 Sex 074883 274297 027 07861 6547 HoursSQiS 000490 001495 033 07446 8822 HoursiSeX 012741 040687 031 07556 28982 HoursSQ 000515 000718 072 04771 720 R Squared 00407 Resid Mean Square MSE 014365 Adjusted R Squared 00683 Standard Deviation 037901 AICc 86745 PRESS 84474 Source DF SS MS F P Regression 5 026839 005368 037 08640 Residual 44 632041 014365 Total 49 658880 Lack of Fit 7 085641 012234 083 05704 Pure Error 37 546400 014768 Cases Included 50 Missing Cases 0 PO5 Compare Model 1 vs Model 2 Student Edition of Statistix 90 Exam3POs 4112011 103622 Best Subset Regression Models for GPA Forced Independent Variables AHours BSex CHoursiSex Unforced Independent Variables DHoursSQ EHoursSQ7S Adjusted AICc P Cp R Square Min AICc Resid SS F PF Model variables 4 31 00474 000 647862 A B C 5 41 0 0471 148 633585 101 03193 A B C D 5 45 0 0567 193 639427 059 04450 A B C E 6 60 0 0683 407 632041 055 05805 AB C D E Cases Included 50 Missing Cases 0 Ryan Yates U80162272 PO 5A Compare Mbdel 2 to Mbdel 4 Student Edition of Statistix 90 Exam3POs Least Squares Linear Regression of GPA Predictor Variables Coefficient Std Error T P Constant 493 037825 808 00000 Hours 000141 002767 005 09595 Sex 037046 063494 058 05624 Hours7Sex 002203 004567 048 06319 R Squared 00167 Resid Mean Square MSE Adjusted R Squared 00474 Standard Deviation AICC 90812 PRESS 75279 Source DF SS MS F P Regression 3 011018 003673 026 08533 Residual 46 647862 014084 Total 49 658880 Lack of Fit 9 101462 011274 076 06500 Pure Error 37 546400 014768 Cases Included 50 Missing Cases 0 PO 6 Best Mbdel Student Edition of Statistix 90 Exam3POs Least Squares Linear Regression of GPA Predictor Variables Coefficient Std Error T P Constant 316325 030188 1048 00000 Hours 000950 002183 043 06656 Sex 006856 010580 065 05201 R Squared 00117 Resid Mean Square MSE Adjusted R Squared 00303 Standard Deviation AlCc 93035 PRESS 72940 Source DF SS MS F P Regression 2 007741 003870 028 07575 Residual 47 651139 013854 Total 49 658880 Lack of Fit 10 104739 010474 071 07100 Pure Error 37 546400 014768 Cases Included 50 Missing Cases 0 4112011 VIE 00 16 35 372 00 014084 037529 4122011 013854 037221 105010 40015 Ryan Yates U80162272 PO 7 Prediction Confidence Intervals Student Edition of Statistix 90 Exam3POs 4122011 40058 PredictedFitted Values of GPA Lower Predicted Bound 23242 Lower Fitted Bound 29317 Predicted Value 30894 Fitted Value 30894 Upper Predicted Bound 38546 Upper Fitted Bound 32470 SE Predicted Value 03804 SE Fitted Value 00784 Unusualness Leverage 00443 Percent Coverage 950 Corresponding T 201 Predictor Values Hours 15000 Sex 10000 P0 8 List of Standard Residuals Student Edition of Statistix 90 Exam3POs 4112011 113616 PM CASE STDRES 01395275 0383445 14033506 0795242 0304054 07691024 1236342 0520418 9 01107024 10 0685994 11 05026512 12 02181577 13 15955194 14 15 16 17 OO1jLNgtJgtLAl 1159204 0325226 0132868 1050111 18 0135646 19 0819513 20 07691024 21 1429062 22 00292299 23 02181577 24 0057314 25 1236342 26 0325226 27 00031248 28 0308983 29 1119024 30 05026512 31 02181577 32 1358073 Ryan Yates U80162272 33 13305285 34 04147014 35 70325226 36 05788782 37 16781748 38 24219365 39 71429062 40 70961168 41 71619715 42 7083379 43 18824467 44 06316375 45 70019184 46 00292299 47 71304035 48 20657448 49 70057314 50 16781748 PO 9 SCATTERPLOT OF RESIDUALS VS QNX Scatter Plot of RESID vs Hours 09 0 04 D o o G 2 g z 701 0 o O o 706 o 6 10 14 18 Ryan Yates U80162272 P0 10 SCA39I39I39ERPLOT OF RESIDUALS VS PREDICTEDY Scatter Plot of RESID vs PRED 09 04 0 0 0 lt73 0 o LU c n 0 O 01 o O o O o 06 7 299 303 307 311 315 PRED P0 11 Graph of Best Model Scatter Plot of PRED vs Hours 315 0 311 0 0 D o 0 Sex E 307 0 0 O A 1 o o 303 o o 299 quot 6 m 14 18 Hours Rya n Ya tes U80162272 P0 12 STEMLEAF PLOT 0F RESIDUALS Student Edition of Statistix 90 Exam3POs 4122011 40337 Stem and Leaf Plot of STDRES Leaf Digit Unit 01 Minimum 16197 1 6 represents 16 Medi 00382 an Maximum 24219 Stem Leaves 6 1 1 10 1 443322110 16 0 988765 10 0 3333311000 24 0 0001122234 14 0 555677 8 1 34 6 1 5668 2 2 04 50 cases included 0 missing cases 50 cases included 0 missing cases

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