In: Statistics and Probability
The number of plumbing repair jobs performed by Auger's Plumbing Service in each of the last nine months are listed below.
Month Jobs Month Jobs Month Jobs
March 353 June 374 September 399
April 387 July 396 October 412
May 342 August 409 November 408
a. Assuming a linear trend function, forecast the number of repair jobs Auger's will perform in December using the least squares method.
b. What is your forecast for December using a three-period weighted moving average with weights of .6, .3, and .1? How does it compare with your forecast from part (a)?
In excel if possible.
a)
x | y | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
1 | 353 | 16.00 | 1133.44 | 134.67 |
2 | 387 | 9.00 | 0.11 | -1.00 |
3 | 342 | 4.00 | 1995.11 | 89.33 |
4 | 374 | 1.00 | 160.44 | 12.67 |
5 | 396 | 0.00 | 87.11 | 0.00 |
6 | 409 | 1.00 | 498.78 | 22.33 |
7 | 399 | 4.00 | 152.11 | 24.67 |
8 | 412 | 9.00 | 641.78 | 76.00 |
9 | 408 | 16.00 | 455.11 | 85.33 |
ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
total sum | 45 | 3480 | 60 | 5124.0 | 444.00 |
mean | 5.00 | 386.67 | SSxx | SSyy | SSxy |
sample size , n = 9
here, x̅ = Σx / n= 5.00 ,
ȳ = Σy/n = 386.67
SSxx = Σ(x-x̅)² = 60.0000
SSxy= Σ(x-x̅)(y-ȳ) = 444.0
estimated slope , ß1 = SSxy/SSxx = 444.0
/ 60.000 = 7.4000
intercept, ß0 = y̅-ß1* x̄ =
349.6667
so, regression line is Ŷ =
349.6667 + 7.4000
*x
Ŷ = 349.66667 +
7.400000 * 10 =
423.667
b)
Month | Demand | Moving average= 0.1 * 353 + 0.3 * 387 + 0.6 * 342 |
1 | 353 | |
2 | 387 | |
3 | 342 | |
4 | 374 | 356.6 |
5 | 396 | 365.7 |
6 | 409 | 384 |
7 | 399 | 401.6 |
8 | 412 | 401.7 |
9 | 408 | 407.8 |
10 | 408.3 |
Please note that we have give maximum weightage to recent month sales as itwightage order is not given.
Forecast in Part(a) is more than Part(b)
Please revert back in case of any doubt.
Please upvote. Thanks in advance.