Question

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

Week Number Week Number Week Number
1 390 7 480 13 630
2 410 8 520 14 640
3 430 9 560 15 680
4 410 10 540 16 700
5 430 11 580 17 720
6 440 12 620 18 740

Obtain a linear trend line for expected freight car loadings, and use it to predict expected loadings in the following weeks. Specifically, what's your forecast on the expected loadings in Week 20 using the linear trend approach? (Round your answer to a whole number.)

Answer 1

To find the expected freight car loadings for Week 20, we use the least squares method to calculate the slope and intercept of the linear trend line. After computing these, we can predict future loadings by plugging in the week number into the trend line equation.

Step-by-step explanation:

To obtain a linear trend line for the expected freight car loadings, we can use the method of least squares to fit a line to the data provided. This line can be expressed in the form y = mx + b, where y represents the freight loadings, m is the slope, x is the week number, and b is the y-intercept.

First, calculate the slope (m) using the formula:

m = (N∑xy - ∑x∑y) / (N∑x− - (∑x)^2)

Where:

• N is the number of data points (18 weeks)
• ∑xy is the sum of the product of each week number and its corresponding loading
• ∑x is the sum of the week numbers
• ∑y is the sum of the loadings
• ∑x− is the sum of the square of the week numbers

Next, calculate the y-intercept (b) using the formula:

b = (∑y - m∑x) / N

After calculating m and b, you can then obtain the forecasted loadings for Week 20 (x = 20) by substituting this value into the trend line equation.

Rounding the result to the nearest whole number will give the estimated weekly loading for Week 20.