Question

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.

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

1. Use residual analysis to check the validity of the model and fully explain your findings and conclusions. (6 points)
2. 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)
3. 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

Regression Analysis: TotalHP(=Y) versus Cruise (=X)

The regression equation is
TotalHP = - 271 + 3.54 Cruise

Predictor Coef SE Coef T P
Constant -270.57 56.10 -4.82 0.000
Cruise 3.5413 0.3404 10.40 0.000

S = 88.1914 R-Sq = 68.4% R-Sq(adj) = 67.8%

Analysis of Variance

Source DF SS MS F P
Regression 1 841536 841536 108.20 0.000
Residual Error 50 388886 7778
Total 51 1230422

Coefficient of determination=0.684 i.e. 68.4% of total variation in Y is explained by X.

From the above plot we conclude that the residual follow normal distribution.

From above plot we see that residuals are almost scattered against fitted values so we can conclude that fitting is good. Hence the simple linear model appears to be useful tool in predicting cruise speed for airplanes.

t for slope=10.40 and F=108.20 =10.40²=t² F_0.05,1,50=4.03, t_0.05,50=1.68, F_0.05,1,50= t²_0.05,50