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##### Devry MATH 533 Final Exam Two Problems

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solution

**Question**

Question;1.(TCO E) The management of JAL;Airlines assumes a direct relationship between advertising expenditures and the;number of passengers who choose to fly JAL. The following data is collected;over the past 15 months of performance by JAL Airlines. Note that X=ADEXP;(Advertising Expenditures in $1,000s), and Y=Passengers (number of passengers;in 1,000s). The MINITAB printout can be found below.;ADEXP;PASSENGERS;PREDICT;100;15;120;120;17;250;80;13;170;23;100;16;150;21;100;14;140;20;190;24;100;17;110;16;130;18;160;23;100;15;120;16;Correlations;ADEXP, PASSENGERS;Pearson correlation of ADEXP;and PASSENGERS = 0.968;P-Value = 0.000General;Regression Analysis: PASSENGERS versus ADEXP;Regression Equation;PASSENGERS = 4.38625 + 0.108132;ADEXP;Coefficients;Term Coef SE;Coef T P 95%;CI;Constant 4.38625 0.991282;4.4248 0.001 (2.24472, 6.52779);ADEXP 0.10813 0.007726 13.9949 0.000 (0.09144;0.12482);Summary of Model;S =;0.906780 R-Sq =;93.78% R-Sq(adj) = 93.30%;PRESS = 14.6535;R-Sq(pred) = 91.47%;Analysis of Variance;Source DF Seq;SS Adj SS Adj;MS F P;Regression 1 161.044 161.044 161.044 195.858;0.000000;ADEXP 1 161.044;161.044 161.044 195.858 0.000000;Error 13 10.689 10.689 0.822;Lack-of-Fit 8 4.989;4.989 0.624;0.547 0.786417;Pure Error 5 5.700;5.700 1.140;Total 13 171.733;Fits and Diagnostics for;Unusual Observations;Obs PASSENGERS Fit SE;Fit Residual St Resid;10 17 15.1994 0.301894 1.80058 2.10582 R;R denotes an observation with a;large standardized residual.;Predicted Values for New;Observations;New;Obs Fit SE;Fit 95%;CI 95%;PI;1 17.3621 0.236890 (16.8503;17.8738) (15.3373, 19.3868);2 31.4192 0.996288 (29.2668;33.5715) (28.5088, 34.3295);Values of Predictors for New;Observations;New Obs ADEXP;1 120;2 250 XX;XX denotes a point that is an;extreme outlier in the predictors.a. Analyze the above output to determine the;regression equation.;b. Find;and interpret BETA SUB 11in the context of this problem.c. Find and interpret the coefficient of;determination (r-squared).;d. Find and interpret coefficient of;correlation.;e. Does the data provide significant evidence (a=.05) that advertising expenditures can be used;to predict the number of passengers? Test the utility of this model using a;two-tailed test. Find the observed p-value and interpret.f. Find the 95% confidence interval for the mean;number of passengers when advertising expenditures were $120,000. Interpret;this interval.;g. Find the 95% prediction interval for the;number of passengers when advertising expenditures were $120,000. Interpret;this interval.;h. What can we say about the number of;passengers when advertising expenditures were $250,000? (Points: 48);Question 1.1.(TCO;E) The management of an international hotel chain is in the process of;evaluating possible sites for a new hotel on a beach resort. As part of the;analysis, management is interested in evaluating the relationship between;the distance between a hotel and the beach, (Distance, X1 in miles), the;number of golf courses on the premises (Golf, X2), and the average;occupancy rate (Rate, Y as a %). A sample of 14 existing resort hotels is;selected yielding the following results.;Distance;Golf;Rate;0.1;2;92;0.1;2;95;0.2;3;96;0.3;3;90;0.4;3;89;0.4;2;86;0.5;2;90;0.6;1;83;0.7;1;85;0.7;1;80;0.8;0;78;0.8;0;76;0.9;0;72;0.9;0;75;Correlations: Distance, Golf;Rate;Distance Golf;Golf -0.859;0.000;Rate -0.944 0.895;0.037 0.982;Cell Contents: Pearson;correlation;P-Value;Regression Analysis: Rate;versus Distance, Golf;The regression equation is;Rate = 91.3 - 18.0 Distance +;2.13 Golf.;Predictor;Coef SE Coef;T P;Constant;91.262 3.924 23.26 0.000;Distance -18.013;4.561 -3.95 0.002;Golf 2.132 1.119 1.91;0.083;S = 2.39278 R-Sq;= 91.8% R-Sq(adj) = 90.3%;Analysis of Variance;Source;DF SS;MS F P;Regression;2 701.38 350.69 61.25 0.000;Residual;Error 11 62.98 5.73;Total 13;764.36;Predicted Values for New;Observations;New;Obs Fit SE;Fit 95%;CI 95%;PI;1 86.518 0.832 (84.688, 88.349) (80.943;92.094);Values of Predictors for New;Observations;New Obs;Distance Golf;1 0.500 2.00;a. Analyze the above output to determine the multiple regression equation.;b. Find and interpret the multiple index of determination (R-Sq).;c. Perform multiple regression;t-tests on beta sub 1 and beta sub 2. Use two tailed test with (ae =.10).;Interpret your results;d.Predict the average occupancy;for a single hotel that is.5 miles from the beach and has two golf courses;on the premises. Use both a point estimate and the appropriate interval;estimate. (points 31);c. Perform the multiple regression t-tests on??1,??2 (use two;tailed test with (a=.10). Interpret;your results.;d. Predict the average occupancy rate for a single hotel that is.5 miles;from the beach and has two golf courses on the premises. Use both a point;estimate and the appropriate interval estimate. (Points: 31);c. Perform the multiple regression t-tests on??1,??2 (use two;tailed test with (a=.10). Interpret;your results.;d. Predict the average occupancy rate for a single hotel that is.5 miles;from the beach and has two golf courses on the premises. Use both a point;estimate and the appropriate interval estimate. (Points: 31);c. Perform the multiple regression t-tests on??1,??2 (use two;tailed test with (a=.10). Interpret;your results.;d. Predict the average occupancy rate for a single hotel that is.5 miles;from the beach and has two golf courses on the premises. Use both a point;estimate and the appropriate interval estimate. (Points: 31);c. Perform the multiple regressiont-tests on??1,??2 (use two tailed test with;(a=.10). Interpret your results.;d. Predict the average occupancy rate for a single hotel that is.5 miles;from the beach and has two golf courses on the premises. Use both a point;estimate and the appropriate interval estimate. (Points: 31)

Paper#60821 | Written in 18-Jul-2015

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