Question

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

Week	Number	Week	Number	Week	Number
1	290	7	335	13	490
2	300	8	375	14	495
3	310	9	415	15	515
4	300	10	405	16	525
5	310	11	445	17	535
6	315	12	485	18	545

a. Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.)

YˆY^ =  +  t

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              .

rev: 09_25_2014_QC_54677, 11_19_2014_QC_59433, 02_05_2015_QC_CS-1708

Answer 1

Answer a:

We have the following data table:

Where x = Independent Variable = A particular week and Y = Dependent Variable = No. of car loadings

Step 1: Find the Mean values for x and y:

Step 2: Find the three columns as mentioned below:

Where,

xy = x * y

x2 = x * x

y2 = y * y

Step 3: Find the value of byx:

Step 4: Find the linear trend equation:

y = 17.40 x + 245.26 (Rounded to 2 decimal places)

Answer b:

We will find the forecast demand for week 20 and 21 as mentioned below:

(Rounded to 2 decimal places)

Answer c:
Here, we take y = 870, in the linear trend equation as derived in answer a:

∴ 870 = 245.26 + 17.40 x

∴ 870 - 245.26 = 17.40 x

∴ x = 624.74 / 17.40

∴ x = 35.90 (Rounded to 2 decimal places) = 36th Week

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