Question

In: Statistics and Probability

Problem 2. Consider the FLAG data set. The first 10 observations are given for informational purposes....

Problem 2. Consider the FLAG data set. The first 10 observations are given for informational purposes.

CONTRACT

COST

DOTEST

STATUS

1

1379.43

1386.29

1

2

134.03

85.71

1

3

202.33

248.89

0

4

397.12

467.49

0

5

158.54

117.72

1

6

1128.11

1008.91

1

7

400.33

472.98

1

8

581.64

785.39

0

9

353.96

370.02

0

10

138.71

174.25

0

b) Calculate a confidence and prediction interval for DOTEST = 110.

c) Interpret the confidence and prediction intervals given in the output. Do you see any problems with the interpretation of the prediction interval in terms of what we are trying to predict?

d) Why are confidence intervals always more narrow than prediction intervals?

Solutions

Expert Solution

The regression equation is defined as,

The least square estimate of intercept and slope are,

CONTRACT COST, Y DOTEST, X X^2 XY
1 1379.43 1386.29 1921800 1912290
2 134.03 85.71 7346.204 11487.71
3 202.33 248.89 61946.23 50357.91
4 397.12 467.49 218546.9 185649.6
5 158.54 117.72 13858 18663.33
6 1128.11 1008.91 1017899 1138161
7 400.33 472.98 223710.1 189348.1
8 581.64 785.39 616837.5 456814.2
9 353.96 370.02 136914.8 130972.3
10 138.71 174.25 30363.06 24170.22
SUM 4874.2 5117.65 4249222 4117915

Form the data values, the values are calculated as,

b)

The confidence interval is defined as,

The standard error of regression is calculated as,

CONTRACT COST, Y DOTEST, X Y-hat=-22.236+0.99588X (Y-Y-hat) (Y-Y-hat)^2
1 1379.43 1386.29 1358.3411 21.0889 444.7427
2 134.03 85.71 63.1208 70.9092 5028.1181
3 202.33 248.89 225.6283 -23.2983 542.8112
4 397.12 467.49 443.3275 -46.2075 2135.1291
5 158.54 117.72 94.9989 63.5411 4037.4762
6 1128.11 1008.91 982.5163 145.5937 21197.5366
7 400.33 472.98 448.7948 -48.4648 2348.8401
8 581.64 785.39 759.9174 -178.2774 31782.8276
9 353.96 370.02 346.2591 7.7009 59.3034
10 138.71 174.25 151.2959 -12.5859 158.4049
SUM 67735.1899

The prediction interval is obtained using the formula,

c)

The prediction interval gives the interval where the next predicted data would be.

The confidence interval gives the interval of mean value of input variable

orchestra answered 2 years ago
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