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Freight car loadings over an 18-week period at a busy port are as follows:

Week Number Week Number Week Number
1 370 7 415 13 450
2 380 8 425 14 455
3 390 9 435 15 475
4 380 10 425 16 485
5 390 11 435 17 495
6 395 12 445 18 505

a. Determine a linear trend line for expected freight car loadings.
b. Use the above trend equation to predict expected loadings for Weeks 20 & 21.
c. The manager intends to install new equipment when the volume exceeds 950 loadings per week. Assuming the current trend continues, in which week (at the earliest) should the loading volume reach that level?

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Answer:

y = 7.678X + 357.614 ;

518.852 ; 526.53 ;

Week 78;

Explanation:

Given the data :

Week Number Week Number Week Number

1 370 7 415 13 450

2 380 8 425 14 455

3 390 9 435 15 475

4 380 10 425 16 485

5 390 11 435 17 495

6 395 12 445 18 505

The linear trend line for expected freight car loading obtained using a linear model calculator is :

y = 7.678X + 357.614

y = expected freight car loading

X = week

m = slope = 7.678 ;

c = intercept = 357.614

B.)

predicted loading for week 21:

X = 21

y = 7.678(21) + 357.614 = 518.852

Predicted loading for week 22:

y = 7.678(22) + 357.614 = 526.53

C.)

Week loading volume should exceed 950:

y = 950

950 = 7.678X + 357.614

950 - 357.614 = 7.678X

592.386 = 7.678X

X = 592.386 / 7.678

X = 77.153685

X = 78 (should exceed 950)

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