Question

In: Statistics and Probability

The number of plumbing repair jobs performed by Auger's Plumbing Service in each of the last...

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.

Solutions

Expert Solution

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.


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