Question

Cruise Speed of Selected Piston Aircraft (n = 55, k = 4)
	Obs	Mfgr/Model	Cruise	Year	TotalHP	NumBlades	Turbo
	1	Cessna Turbo Stationair TU206	148	1981	310	3	1
	2	Cessna 310 R	194	1975	570	3	0
	3	Piper 125 Tri Pacer	107	1951	125	2	0
	4	Maule Comet	115	1996	180	2	0
	5	Cessna P210	186	1982	285	3	0
	6	Piper Dakota	147	1979	235	2	0
	7	Cessna 1825 Skylane	140	1997	230	3	0
	8	Cessna 421B	234	1974	750	3	0
	9	Cessna T210K	190	1970	285	3	1
	10	Piper Super Cab	100	1975	150	2	0
	11	Cessna 337G Skymotor II	170	1975	420	2	0
	12	Piper Seneca V	174	1997	440	2	0
	13	Mooney M20C	156	1965	200	2	0
	14	Beech Baron 58P	241	1984	650	3	0
	15	Piper Archer III	129	1997	180	2	0
	16	Cessna 172 R Skyhawk	122	1997	160	2	0
	17	Cessna T303 Crusader	190	1983	500	3	1
	18	Piper Seneca III	180	1982	440	3	1
	19	Piper Saratoga II TC	186	1998	300	3	1
	20	Cessna Turbo Skylane RG	159	1979	235	2	1
	21	Mooney 231	170	1982	210	2	1
	22	Beech Sierra	141	1972	360	2	0
	23	Piper Malibu Mirage	213	1998	350	3	0
	24	Lancair Columbia 300	191	1998	310	3	0
	25	Bellanca Super Viking	161	1973	300	2	0
	26	Cessna 172 RG Cutlass	129	1982	180	2	0
	27	Beech Duchess	164	1982	360	2	0
	28	Piper Aztec F	191	1980	500	2	0
	29	Cessna Cardinal	124	1970	180	2	0
	30	Beech Baron D55	199	1968	570	2	0
	31	Sky Arrow 650 TC	98	1998	81	1	0
	32	Cessna 414A	223	1985	620	3	0
	33	Cessna U206H	143	1998	300	3	0
	34	Cirrus SR20	160	1999	200	3	0
	35	Cessna 152	107	1978	110	2	0
	36	Mooney Eagle M205	175	1999	244	2	0
	37	Socata TB20 Trinidad	163	1999	250	2	0
	38	Rockwell Commander 114	151	1976	260	2	0
	39	Piper Malibu Mirage	215	1989	350	2	1
	40	Piper Turbo Lance	176	1979	300	2	1
	41	Cessna 182Q Skylane	144	1977	230	2	0
	42	Beech Baron 58	200	1984	600	3	0
	43	Cessna 170B	104	1953	145	2	0
	44	Beech Bonanza B36 TC	174	1982	300	3	1
	45	Mooney Ovation 2 M20R	188	2000	280	2	0
	46	Extra Extra 400	235	2000	350	4	1
	47	AMD CH 2000	100	2000	116	2	0
	48	Piper Satatoga SP	148	1980	300	2	0
	49	Cessna Turbo Skylane T182T	160	2001	235	3	1
	50	Piper Seneca V	186	2002	440	3	1
	51	Tiger AG-5B	143	2002	180	2	0
	52	Diamond C1 Eclipse	140	2002	125	2	0
	53	OMF Aircraft Symphony	128	2002	160	2	0
	54	Liberty XL-2	132	2003	125	2	0
	55	Piper 6X	148	2004	300	3	0

Variable Names: Year = year of manufacture, Cruise = best cruise speed (knots indicated air speed) at 65%-75% power, TotalHP = total horsepower (both engines if twin), NumBlades = number of propeller blades, Turbo = 1 if turbocharged, 0 otherwise

Using Cruise as the response variable and the other variables as predictor variables, use Minitab to perform the necessary regression calculations. Write a concise report answering the following questions. Insert tables and graphs in your report as appropriate.

1.      Use Minitab to perform multiple regression.   Use Cruise as the dependent variable, and the other variables, (Year, TotalHp, NumBlades, and Turbo) as predictor variables.

2.      Is multicollinearity a problem? Support your answer.

3.      Is the model significant? Support your answer. What does this tell you?

4.      Find the sample regression equation and interpret the coefficients in terms of the problem.

5.      Find and interpret the coefficient of determination.

6.      Test each regression coefficient for significance and interpret the results.

7. Which variable is the indicator (dummy) variable? Give and compare the sample regression equations for both levels of the dummy variable.

8.      Give a 95% confidence interval for average cruise speed for all airplanes manufactured in 1990, with 600 horsepower, 3 blades, and turbocharged. Interpret your interval. Give and interpret a 95% prediction interval using the same values.

9.      Examine the residual plots and discuss.

Answer 1

Calculations are done using Minitab:

1. The regression equation is
cruise = - 697 + 0.393 year + 0.179 HP + 8.83 blades + 16.0 turbo

2.

Correlations: year, HP, blades, turbo

year HP blades
HP -0.154
0.261

blades 0.180 0.491
0.190 0.000

turbo 0.030 0.096 0.388
0.829 0.485 0.003

Cell Contents: Pearson correlation
P-Value

So, turbo and blades, HP and blades are slightly correlated, but correlation is less than 0.5. Hence, Multicollinearity won't be much of a problem here.

3.

Analysis of Variance

Source   DF SS MS F P
Regression 4 54233 13558 41.40 0.000
Residual Error 50 16375   328
Total 54 70608

As, p value is 0.000 < 0.05, the model is significant. Hence, the independent variables are affecting the response significantly.

4.

cruise = - 697 + 0.393 year + 0.179 HP + 8.83 blades + 16.0 turbo

for one year increase, other remaining same, cruise speed increases about 0.393 unit

for unit HP increase, other remaining same, cruise speed increases about 0.179 unit

for one blade increase, other remaining same, cruise speed increases about 8.83 unit

for presence of turbo, other remaining same, cruise speed increases about 16 unit

5. 0.768 is the coefficient of determination.

Hence, 76.8% of the variance is explained by the model.

6.

Predictor Coef SE Coef T P
Constant -696.9 393.3 -1.77 0.083
year 0.3927 0.1991 1.97 0.054
HP 0.17871 0.01949 9.17 0.000
blades 8.827 5.753 1.53 0.131
turbo 15.975 6.296 2.54 0.014

Hence, at 10% level of significance, all the variables, except blades is significant.

7. Turbo is the indicator variable. Presence of a turbo increases the speed by 16 unit on an average, given others remain same