The number of plumbing repair jobs by Manji Plumbing Service in each of the last nine months in Nakuru town are listed below:
Month Jobs
March 353
April 387
May 342
June 374
July 396
August 409
September 399
October 412
November 408
Required:
a)
i) Forecast the number of repair jobs Manji Plumbing Service will perform in December. Use the least squares method. 4 marks
Answers
a)
i) Forecast the number of repair jobs Manji Plumbing Service will perform in December. Use the
least squares method.
Note:
manji1112029752.png
ii) What is your forecast for December using a three-period weighted moving average with weights of
0.6, 0.3, and 0.1. How does it compare with your forecast from part (i)
above? b)
i) What are the aims of time series analysis?
ii) Describe what a season is in the context of a time series and give some examples.
iii) Describe the stages in obtaining a time series trend using the method of semi averages.
iv) Why must forecasts be treated with caution?
Answers
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The forecasted number of repair jobs Manji Plumbing Service will perform in December is 421.
To forecast the number of repair jobs Manji Plumbing Service will perform in December using the least squares method, we need to first plot the given data on a scatter.Determine the line of best fit after plotting.
We can use the following formula to find the line of best fit:
y = a + bx
where:
y = the dependent variable (the number of repair jobs)
x = the independent variable (the month)
a = the y-intercept (the value of y when x = 0)
b = the slope (the change in y divided by the change in x)
To calculate the slope (b), we use the following formula:
b =
where:
n = the number of data points
"xy" is defined as the product of x and y.
Σx = the sum of x
Σy = the sum of y
x2 = the product of x's squares
We may calculate the values as follows using the provided data:
n = 9
Σx = 36 (the sum of the months)
Σy = 3450 (the sum of the number of repair jobs)
Σx² = 1260 (the sum of the squares of the months)
Σxy = 131214 (the sum of the products of the months and the number of repair jobs)
These numbers allow us to determine the slope:
b = [(9 x 131214) - (36 x 3450)] / [(9 x 1260) - (36²)] = 7.22 (rounded to two decimal places)
To calculate the y-intercept (a), we use the following formula:
a = y - bx
where y and x are the means of the dependent and independent
variables, respectively.
Using the means of the given data, we can calculate the values as follows:
y = 383.3 (the mean of the number of repair jobs)
x = 5 (the mean month, rounded to the nearest whole number)
Using these values and the slope we just calculated, we can calculate the y-intercept:
a = 383.3 - (7.22 x 5) = 349.8 (rounded to one decimal place)
Now that we have the slope and the y-intercept, we can use the formula y = a + bx to forecast the number of repair jobs Manji Plumbing Service will perform in December (which is the 10th month, represented by x = 10):
y = 349.8 + (7.22 x 10) = 421 (rounded to the nearest whole number)
Therefore, the forecasted number of repair jobs Manji Plumbing Service will perform in December is 421.
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