1) The data in file Prob1.csv contain results of tests of fuel consumption and various physical properties of the fuel. Investigate the extent of multicolinearity in the physical properties when used to predict consumption. (Note that you do not need to use vehicle in the model. Be sure to identify which variables might be collinear.

2) Use all possible regressions to build two models of life expectancy from all the other variables in the data set Prob2.csv except Country with 1) Cp and 2) Adjusted Rsquared as the criteria. Choose the best model for each and compare the two models. Use the best=15 option to limit your output to the best 15 models.

3) An operations analyst in a multinational electronics firm studied factors affecting production in a piecework operation where earnings are based on the number of pieces produced. Two employees were selected from each of various age groups and the data on their productivity last year are contained in the file Prob 3.csv with productivity in a coded scale. There is a more complicated relationship between productivity and age than might be expected because of changing life priorities as a person ages. In particular the investigators expected a third degree polynomial to provide a good fit. Run an analysis to check on their claim, being sure to focus on the correct degree of polynomial. Use the fitted model to find 95% confidence intervals for the mean productivity for 20, 40 and 60 year olds and a 95% prediction interval for a randomly selected 55 year old.

4) The factors that influence the breaking strength of a synthetic fiber are being studied. Four production machines and 3 operators are chosen and each operator produces two specimens on each machine for testing. The data are in file Prob4.csv. Analyze the full model including an interaction term and check model assumptions with residual plots.

**Subject Mathematics Mathematics - Other**