A naval base is considering modifying or adding to its fleet of 48 standard airc

Question

A naval base is considering modifying or adding to its fleet of 48 standard aircraft. The final decision on the amount to be added depends on a comparison of the cost versus the effectiveness of the modified fleet. The data in the file Problem2.mtw contains the percentage improvement (y), the cost of modifications (x) and the location (US or Foreign). A first model proposed was a the quadratic model

y = 0 + 1x + 2x2
a) Fit the quadratic model to the data

b) Perform a test of overall model adequacy. Use =.05.
c) Is there sufficient evidence to conclude that the percentage improvement y increases more quickly for more costly modifications than less costly ones? Again, test with =.05.
d) Now consider the complete second order model

y=0+1x1 +2x2 +3x2 +4x1x2 +5 x1 x22

with x1 = cost
x2 = 1 if US base, and 0 if Foreign.

f) Fit the complete model. Is there evidence to indicate that the location of the base (US or Foreign) is a useful predictor?

Data

PERCENT   COST   BASE
18                     125        1
32                     160        1
9                         80        1
37                     162        1
6                       110        1
3                         90        0
30                     140        0
10                       85        0
25                     150        0
2                         50        0

Explanation / Answer

We can use excel to solve this

a) b)

c) There is a sufficient evidence to conclude that the percentage improvement y increases more quickly for more costly modifications than less costly ones.

d)

SUMMARY OUTPUT Regression Statistics Multiple R 0.950956 R Square 0.904318 Adjusted R Square 0.87698 Standard Error 4.548548 Observations 10 ANOVA df SS MS F Significance F Regression 2 1368.775 684.3875 33.07932 0.000271 Residual 7 144.825 20.68928 Total 9 1513.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 10.65904 14.55009 0.732575 0.487617 -23.7465 45.06453 X Variable 1 -0.28161 0.280876 -1.0026 0.349445 -0.94577 0.38256 X Variable 2 0.002672 0.001254 2.131016 0.070564 -0.00029 0.005637

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