# MATHEMATICS

Freight car loadings over an 18-week period at a busy port are as follows:
Week Number Week Number Week Number
1 220 7 350 13 454
2 245 8 360 14 475
3 278 9 439 15 490
4 275 10 380 16 510
5 302 11 450 17 549
6 310 12 450 18 541

a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 3 decimal places.)
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b. Use the trend equation to predict expected loadings for weeks 23 and 24. (Round your intermediate calculations and final answers to 3 decimal places.)
The forecasted demand for week 23 is _______ and 24 ________ respectively.
c. The manager intends to install new equipment when the volume exceeds 845 loadings per week. Assuming the current trend continues, the loading volume will reach that level in approximately how many more weeks? (Round your intermediate calculations to 3 decimal places and final answer to the nearest whole number.)
It would take approximately ________ more weeks.

1. The data below are the electricity consumptions in kilowatt-hours per month from ten houses and the areas in square feet of those houses: (a) Plot the data with KW on vertical axis.

(b) Write out the nonlinear equation form for a linear-quadratic segmented polynomial model. (KW is the response)

(c) To the best of your abilities, provide educated guesses for the starting values for the parameters.

(d) Fit the model and provide all parameter estimates and standard error, including the ”cut-off” point θ between the two lines. Write out the linear and the quadratic equations explicitly.

2. A repeated measures experiment was performed to decide which of the two textbooks the class should use in the future. The data are given below. (a) Should one fit a GEE or conditional GLMM model, explain which one should be used and why.

(b) What correlation structure should be used, feel free to explore more options than the one covered in class.

(c) Write conclusions on your findings.

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