Problem 3-7 Determine a linear trend line for expected freight car loadings. (Ro
ID: 444137 • Letter: P
Question
Problem 3-7
Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 3 decimal places.)
Use the trend equation to predict expected loadings for weeks 23 and 24. (Round your intermediate calculations and final answers to 3 decimal places.)
The manager intends to install new equipment when the volume exceeds 816 loadings per week. Assuming the current trend continues, the loading volume will reach that level in approximately how many more weeks? (Round your intermediate calculations to 3 decimal places and final answer to the nearest whole number.)
rev: 02_25_2012, 03_15_2012, 01_31_2013_QC_25862, 09_05_2
Explanation / Answer
1. Let T = time , y = car loadings & t = no. of week
Now
t = 18, T = 171 , T² = 2109 , (T)² = 29241 , Y = 7129 & YT = 76947
b = (t YT - TY)/(t*T² - (T)²)
= 19.033
a = Y - b T / t
= 215.242
Y = 215.242 + 19.033 * t
2. Y 23 = 215.242 + 19.033 * 23 = 653.001
Y 24 = 215.242 + 19.033 * 24 = 672.034
3. 816 = 215.242 + 19.033 * t
Therefore, t = 31.564 weeks
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