# Calculate a confidence and prediction interval for DOTEST = 100.

Statistics Problems
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Using the FLAG data set (first 10 observations given), fit a model that predicts COST based on DOTEST. Use the complete data set in your analysis. Show the relevant output from Minitab in your answer. 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

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Calculate a confidence and prediction interval for DOTEST = 100. 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? Why are confidence intervals always more narrow than prediction intervals?

(2) Consider the EXPRESS data set (first 10 observations given). Use the complete data set in your analysis. Show the relevant output from Minitab in your answers. The first 10 observations are given for illustrative purposes.

Weight Distance Cost
5.9 47 2.6
3.2 145 3.9
4.4 202 8
6.6 160 9.2
0.75 280 4.4
0.7 80 1.5
6.5 240 14.5
4.5 53 1.9
0.6 100 1
7.5 190 14

a)Draw a scatterplot of Cost vs. each of the predictors. Do you see any evidence of a quadratic relationship?

b)Write a general second-order model (not including interaction terms) for Cost(y).

c)Give the null and alternative hypothesis for determining whether both of the second-order terms are statistically significant (nested model hypothesis).

d)Identify which of the two general nested models is the complete model and which is the reduced model.

e)Using Minitab, produce an output and write the least squares regression equation for the second-order model AND the reduced model that was fit in Minitab.

f)Compute the test statistic and perform the appropriate F-test. Be sure to state the degrees of freedom and the correct F critical value that you are comparing your test statistic to. Formally state your conclusion. Hint: To compute the test statistic, you need to separately fit both the complete and reduced models. To fit the complete model, you need to add the appropriate variables to your data set.

(3) Consider the EXPRESS data set (first 10 observations given). Use the complete data set in your analysis. Show the relevant output from Minitab in your answers. The first 10 observations are given for illustrative purposes.

Weight Distance Cost
5.9 47 2.6
3.2 145 3.9
4.4 202 8
6.6 160 9.2
0.75 280 4.4
0.7 80 1.5
6.5 240 14.5
4.5 53 1.9
0.6 100 1
7.5 190 14

a)Write out a complete general first-order model including an interaction term for Cost as the outcome.

b)Using Minitab, produce an output and write the least squares regression equation with the interaction term that was fit in Minitab.

c)State the null and alternative hypothesis to test if there is a significant interaction effect between weight and distance. Test the hypothesis at the α= 0.01 level. Write your formal conclusion in terms of the variable names.

d)If there is a significant interaction effect, but the individual predictors (main effects) that make up that interaction are not significant in the model, would you suggest removing the main effects? Why or why not?