Problem 3-7 Freight car loadings over an 18-week period at a busy port are as fo

Question

Problem 3-7 Freight car loadings over an 18-week period at a busy port are as follows: 13 14 15 405 16 525 17 48518 545 335 375 415 490 495 515 290 9 10 310 300 310 315 445 535 12 a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.) b. Use the above trend equation to predict expected loadings for Weeks 20 & 21. (Round your final answers to 2 decimal places.) The forecasted demand for Week 20 is and for Week 21 is c. The manager intends to install new equipment when the volume exceeds 870 loadings per week Assuming the current trend continues, in which week (at the earliest) should the loading volume reach that level? (Use the rounded answers, as required, from any previous part of this problem. Do not round any other intermediate calculations. Round your final answer to 2 decimal places.) it should reach 870 loadings in Week References eBook & Resources Worksheet Dimiçulty 2 Medium Problem 3-7 Learning Objective; 03-11 Prepare a lineat trend forecast Check my work

Explanation / Answer

Part a.

Use following R-code to fit a linear trend:

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> mod

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Required linear trend:::      Yhat = 245.3 + 17.4 * t      ;    Ans (a)

Part b.

We plug in t=20, to get Yhat = 593.3; Forecasted demand for week 20 is 593.3.

We plug in t=21, to get Yhat = 610.7; Forecasted demand for week 21 is 610.7.

Part c.

Now, we want value of t such that Yhat = 870 on that t.

Therefore,   870 = 245.3 + 17.4 * t

        Hence, t = 35.90, so t = 36 week. Hence, demand will be 870 in week 36.

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