Determine a linear trend line for expected freight car loadings. (Round your int
ID: 442362 • Letter: D
Question
Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.)
Use the above trend equation to predict expected loadings for Weeks 20 & 21. (Round your final answers to 2 decimal places.)
The manager intends to install new equipment when the volume exceeds 900 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.)
Explanation / Answer
a. linear trendline equation is y = ax+b
y = number of car loadings and x = week number
a = n*sum of xy - sum of x*sum of y/(n*sum of x^2 - (sum of x)^2)
= 18*74160 - 171*7275/ 18*2109 - 171^2
= 90855/8721 = 10.42
b = sum of y - a*sum of x/(n)
= 7275 - 10.41 * 171/(18) = 305.20
equation: y = 10.42x+305.20
b. week 20: x = 20. so loading (y) will be = 10.42*20+305.20 = 513.60
week 21. x = 21. so loading (y) will be 10.42*21+305.20 = 524.02
c. Here y = 900. we have to calculate x
900 = 10.42x+305.20
594.8 = 10.42x
x = 57 weeks. So the volume will reach 900 loadings at the end of 57 weeks. The new equipment will have to be installed at the beginning of the 58th week.
x y x*y x^2 1 320 320 1 2 335 670 4 3 350 1050 9 4 335 1340 16 5 350 1750 25 6 360 2160 36 7 390 2730 49 8 400 3200 64 9 410 3690 81 10 395 3950 100 11 405 4455 121 12 415 4980 144 13 425 5525 169 14 435 6090 196 15 465 6975 225 16 480 7680 256 17 495 8415 289 18 510 9180 324 Total 171 7275 74160 2109Related Questions
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