Question

Freight car loadings over a 12-year period at a busy port are as follows: Number 13 245 360 14 475 15 500 10 16 275 380 510 300 17 310 12 541 a. Determine a linear trend line for expected freight car loadings. b. Use the trend equation to predict expected loadings for weeks 20 and 21 c·The manager intends to install new equipment when the volume exceeds 800 loadings per week. Assuming the current trend continues, the loading volume will reach that level in approximately what week?

Answer 1

a)

Linear trend line is determined using least square method as below:

Simple Linear Regression (Least Squares Regression Method 220 220 245 490 280 840 9 16 275 1100 300 1500 25 6 310 1860 36 49 350 2450 2880 360 64 81 9 400 3600 10 100 380 3800 420 4620 121 12 450 5400 144 460 13 169 5980 196 14 475 6650 225 15 500 7500 16 510 8160 256 17 525 8925 289 324 18 541 9738 75713 7001 2109 Regression Equation: y = a bx, where x- Week (Independent variable) y - Freight car loadings (dependent variable) a intercept point of regression line and y-axis b slope of regression line 2109 18 (Zx)^-29241 7001 2xy-75713 Slope (b) - N Ex - (Ex) Intercept (a) Regression Equation: y : 208.48 + 18.996x

b)

For week 20, Predicted expected loadings = 208.48+18.996*20 = 588

For week 21, Predicted expected loadings = 208.48+18.996*21 = 607

c)

For given expected loadings (y) of 800,

Week, x = (800 - 208.48)/18.996

= 31

The loading volume will reach 800 in approximately week 31