Question

Cruise	TotalHP
100	116
200	600
241	650
199	570
174	300
164	360
141	360
161	300
107	110
104	145
122	160
129	180
144	230
194	570
170	420
223	620
234	750
124	180
186	285
190	285
190	500
159	235
160	235
148	310
143	300
160	200
140	125
235	350
191	310
132	125
115	180
170	210
175	244
156	200
188	280
128	160
107	125
148	300
129	180
191	500
147	235
213	350
186	300
148	300
180	440
186	440
100	150
176	300
151	260
98	81
163	250
143	180

Use Data Set D, Single Engine Aircraft Performance (Airplanes), on page 535 of your textbook to answer the following questions. The first column is X, or the independent variable and the second column is Y, or the dependent variable. Use MINITAB to obtain the simple regression equation, confidence interval, prediction interval, and required graphs. Insert tables and graphs in your report as appropriate. Use Minitab and produce the appropriate output to answer the following questions. Attach or include the Minitab output.

Construct a scatter plot. Recalling what scatter plots are used for, write a couple of sentences addressing what you observed from the plot. Be sure to relate your observations to the purpose of using scatter plots in regression. (4 points)

Can we conclude that total horse power (TotalHP) helps in predicting cruise speed (Cruise)? Follow the 7 steps for hypothesis testing. (10 points)

Find the sample regression equation and interpret the coefficients. Remember your interpretations should be in terms of the problem. (4 points)

Find the coefficient of determination, and interpret its value. (3 points)

Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)

Does the simple linear model appear to be useful tool in predicting cruise speed for airplanes? If not, explain why not. If so, estimate with 95% confidence the average cruise speed of all airplanes with a total horsepower of 650 knots. Predict with 95% confidence the cruise speed of an airplane with total horsepower of 650 knots. Write at least one sentence using your confidence interval and at least one sentence using your prediction interval. (6 points)

Verify that the p-value for the F is the same as the slope’s t statistic’s p-value, and show that t2 = F. (3 points)

Answer 1

1.

Scatter plots helps in identifying the relationship between 2 variables, where one is the predictor and other is the response. High or less scatter from the best fit plot suggests the presence of the relationship between the 2 and if the relationship is strong.

2. Hypothesis testing

Step 1 - Null hypothesis Ho = There is no significant relationship between cruise speed and total HP

Step 2 - Alternate hypothesis Ha = There is a significant relationship between cruise speed and HP

Step 3 - Let Alpha risk be 0.05 (Confidence level - 95%)

Step 4 - Data is available

Step 5 - Test statistic

Regression Analysis: Cruise versus TotalHP

The regression equation is
Cruise = 103.1 + 0.1931 TotalHP

Model Summary

S	R-sq	R-sq(adj)
20.5958	68.39%	67.76%

Analysis of Variance

Source	DF	SS	MS	F	P
Regression	1	45896.2	45896.2	108.20	0.000
Error	50	21209.3	424.2
Total	51	67105.4

Fitted Line: Cruise versus TotalHP

Step 6 - Analysis of variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
TotalHP	28	62831	2244.0	12.07	0.000
Error	23	4275	185.9
Total	51	67105

Step 7 - Conclusion

Since p-value is less than the level of significance (0.05), we reject the null hypothesis an conclude that, there is a significant relationship between cruise speed and total HP

3. The regression equation is
Cruise = 103.1 + 0.1931 TotalHP

Slope - 0.1931

Constant - 103.1

4. Coefficient of determination R-Sq = 68.4%

we can assume that 68.4% of the variation in the outcome of the response can be explained by the predictor

5.

Residual plot analysis

- Data tends to follow normality, this means the relationship can be trusted

- Since there is no obvious trend in the versus fit - there is no hetroscadicity

6. Prediction intervals

Confidence intervals

Means

TotalHP	N	Mean	StDev	95% CI
81	1	98.00	*	(69.80, 126.20)
110	1	107.0	*	(78.8, 135.2)
116	1	100.0	*	(71.8, 128.2)
125	3	126.33	17.21	(110.05, 142.62)
145	1	104.0	*	(75.8, 132.2)
150	1	100.0	*	(71.8, 128.2)
160	2	125.00	4.24	(105.06, 144.94)
180	5	128.00	10.15	(115.39, 140.61)
200	2	158.00	2.83	(138.06, 177.94)
210	1	170.0	*	(141.8, 198.2)
230	1	144.0	*	(115.8, 172.2)
235	3	155.33	7.23	(139.05, 171.62)
244	1	175.0	*	(146.8, 203.2)
250	1	163.0	*	(134.8, 191.2)
260	1	151.0	*	(122.8, 179.2)
280	1	188.0	*	(159.8, 216.2)
285	2	188.00	2.83	(168.06, 207.94)
300	7	162.29	16.68	(151.63, 172.95)
310	2	169.5	30.4	(149.6, 189.4)
350	2	224.0	15.6	(204.1, 243.9)
360	2	152.5	16.3	(132.6, 172.4)
420	1	170.0	*	(141.8, 198.2)
440	2	183.00	4.24	(163.06, 202.94)
500	2	190.500	0.707	(170.558, 210.442)
570	2	196.50	3.54	(176.56, 216.44)
600	1	200.0	*	(171.8, 228.2)
620	1	223.0	*	(194.8, 251.2)
650	1	241.0	*	(212.8, 269.2)
750	1	234.0	*	(205.8, 262.2)