Question

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

Week	Number	Week	Number	Week	Number
1	360	7	430	13	505
2	375	8	450	14	515
3	390	9	470	15	545
4	375	10	455	16	560
5	390	11	475	17	575
6	400	12	495	18	590

a. Determine a linear trend line for expected freight car loadings.

YˆY^ =  +  t

b. Use the above trend equation to predict expected loadings for Weeks 20 & 21.

The forecasted demand for Week 20 is? and for Week 21 is ?

The manager intends to install new equipment when the volume exceeds 940 loadings per week. Assuming the current trend continues, in which week (at the earliest) should the loading volume reach that level?

It should reach 940 loadings in Week?

Answer 1

The given data is as below. Here the independent variable (x) is the week and the dependent variable (y) is the number of loadings.

The regression equation to forecast the sales is of the form y = a+bx, where the value of a and b is calculate as per below formulas

where y is the dependent variable, x is the independent variable and n is the number of observations

Using these values in the above equations, we get

Hence the regression equation is Y = 334.4118+13.6584t

b. The loadings for week 20 and 21 can be determined by substituting t= 20 and t=21 in the above equation. Hence we have the below

Loadings for week 20 = 334.4118+13.6584*20 = 607.5798

Loadings for week 21 = 334.4118+13.6584*21 = 621.2382

c. To find the week in which the loadings reach 940, we need to consider Y as 940 in the regression equation and solve for t. Hence we have the below

940 = 334.4418+13.6548t

13.6548t = 940-334.4418 = 605.5582

t = 605.5582/13.6548 = 44.3476 which is the 45th week.

Hence it should reach 940 loadings in week 45th.