Devry MATH 533 Final Exam Two Problems

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 = 0.000

General 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 onβ˖1,β˖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 onβ˖1,β˖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)

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Devry MATH 533 Final Exam Two Problems

MATH 533 Final Exam Questions