Question

Can the cost of flying a commercial airliner be predicted using regression analysis? If so, what variables are related to this cost? A few of many variables that can potentially contribute are type of plane, distance, number of passengers, amount of luggage/freight, weather condition, direction of destination, or even pilot skill. Suppose a study is conducted using only Boeing 737s traveling 800 km on comparable routes during the same season of the year. Can the number of passengers predict the cost of flying such routes? It seems logical that more passengers result in more mass and more baggage, which could, in turn, result in increased fuel consumption and other costs. Suppose the data displayed below are the cost and associated number of passengers for thirty-six 800-km commercial airline flights using Boeing 737s during the same season of the year. We will use these data to develop a regression model to predict cost by number of passengers.

The data contains the data on the cost and number of passengers of 36 observations.

Cost	Passengers
4.24	88
3.39	95
2.6	88
2.27	66
3.28	87
3.67	88
3.09	81
1.71	60
3.48	86
4.22	93
3.24	80
4.9	96
0.77	62
1.49	61
2.36	69
3.21	76
2.59	74
3.06	86
2.71	80
4.8	98
3.42	91
2.08	59
1.62	71
3.33	84
3.63	89
3.67	92
2.43	75
4.88	92
3.07	85
2.35	74
1.72	73
4.12	90
3.67	73
2.94	73
2.3	77
1.67	69

(f) Using an αα of 5%, this data indicates that  ? Cost of flying a commercial flight using Boeing 737s the number of passengers   ? can cannot  be expressed as a linear function of  ? Cost of flying a commercial flight using Boeing 737s the number of passengers .

(g) Find a 95% confidence interval for the slope term of the model, β1β1.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

(i) With 95% confidence, find the average cost of flying a commercial flight using Boeing 737s when the number of passengers is 70.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

Answer 1

using excel>addin>phstat>multiple sample >Regression 'we have

Regression Analysis
Regression Statistics
Multiple R	0.855594769
R Square	0.732042409
Adjusted R Square	0.724161304
Standard Error	0.524781565
Observations	36
ANOVA
	df	SS	MS	F	Significance F
Regression	1	25.58033541	25.58033541	92.88575052	2.97542E-11
Residual	34	9.36345348	0.275395691
Total	35	34.94378889
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-3.221712613	0.651399143	-4.945834897	2.01893E-05	-4.545514945	-1.897910282
Passengers	0.077737471	0.008065956	9.637725381	2.97542E-11	0.061345476	0.094129466

Confidence Interval Estimate
Data
X Value	70
Confidence Level	95%
Intermediate Calculations
Sample Size	36
Degrees of Freedom	34
t Value	2.032245
XBar, Sample Mean of X	80.02778
Sum of Squared Differences from XBar	4232.972
Standard Error of the Estimate	0.524782
h Statistic	0.051533
Predicted Y (YHat)	2.21991
For Average Y
Interval Half Width	0.242102
Confidence Interval Lower Limit	1.977808
Confidence Interval Upper Limit	2.462012
For Individual Response Y
Interval Half Width	1.093619
Prediction Interval Lower Limit	1.126291
Prediction Interval Upper Limit	3.313529

(f) since p value 0.000<0.05 so we conclude that Cost of flying a commercial flight can be expressed as a linear function of using Boeing 737s the number of passengers .

(g) 95% confidence interval for the slope term of the model, β1β1.

Lower Bound =0.061

Upper Bound =0.094

(i) With 95% confidence, find the average cost of flying a commercial flight using Boeing 737s when the number of passengers is 70.

Lower Bound =1.126

Upper Bound =3.314