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 10observations 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.