Question

Please use Minitab and follow instructions given with the problem

1. A contractor has recorded the number of jobs performed in the last seven months.
   1. Last year’s performance evaluation score

For each of the following methods, develop a forecast for the number of jobs for the 8th month.

2. A three-period moving average
3. Exponential smoothing (use Minitab default smoothing parameters)
4. A linear trend equation

Using the mean squared difference (MSD), explain which of the methods you believe results in the best forecast and make your recommendation to the contractor about what he should expect for the eighth month.

Month	Jobs
Feb	19
Mar	18
Apr	15
May	20
Jun	18
Jul	22
Aug	20

Answer 1

Solution : Given that a contractor has recorded the number of jobs performed in the last seven months.

given data is,

month   Job
Feb   19
Mar   18
Apr   15
May   20
Jun   18
Jul   22
Aug   20
Here the variable is jobs  

a) by the method of moving averages

The minitab commnds are as follows

i) enter the data in minitab

ii) click on stats

ii) click on time series and the dialogue box appers in which we have to select moving averages

iv) keep moving average lengh as 3

v ) under the graph section select

normal plot of residuals and residuals versus fits

The minitab output for moving averages is as follows

Moving Average for Job

Data Job
Length 7
NMissing 0

Moving Average

Length 3

Accuracy Measures

MAPE 8.72054
MAD 1.83333
MSD 6.50000

Here we can see that MSD is 6.5000

From the above plot we can say that the residuals versus fits are not good since the value below and above are

not randomly and equally spread.

The data follows noramality from the above plot.

moving average analysis Plot for Job is as below

b) Using the Exponential smoothing method

The minitab commnds are as follows

i) enter the data in minitab

ii) click on stats

ii) click on time series and the dialogue box appers in which we have to select exponential smoothing

v ) under the graph section select

normal plot of residuals and residuals versus fits

The minitab output for moving averages is as follows

Single Exponential Smoothing for Job

Data Job
Length 7

Smoothing Constant

α 0.229794

Accuracy Measures

MAPE 9.37972
MAD 1.71594
MSD 4.92260

The MSD is 4.92260

The residual versus fits shows that there is randomness and the poits are spread above and below the line eqaully which means that the fit is good

The data follows normality.

exponential smoothing analysis plot for actual versus predicted is as follows  

c) Using the linear trend eqaution :

The minitab commnds are as follows

i) enter the data in minitab

ii) click on stats

ii) click on time series and the dialogue box appers in which we have to select trend analysis

select linear as shown in above box

v ) under the graph section select

normal plot of residuals and residuals versus fits

The minitab output for moving averages is as follows

Trend Analysis for Job

Data Job
Length 7
NMissing 0

Fitted Trend Equation

Yt = 16.86 + 0.500×t

Accuracy Measures

MAPE 8.08588
MAD 1.44898
MSD 3.12245

Here the MSD is 3.2245

The residual versus fits shows that there is randomness and the poits are spread above and below the line eqaully which means that the fit is good

The data follows normality.

Linear trend analysis plot for actual versus predicted is as follows   

The trend line fit is good as comapred to exponential smoothing and moving average method

Here the Mean squared deviation (MSD) is always computed using the same denominator, n, regardless of the model. MSD is a more sensitive measure of an unusually large forecast error than MAD.

Notation

Term	Description
yt	actual value at time t
	fitted value
n	number of observations

Hence from the above analysis we can see that

	moving averages	Exponential smoothing	linear trend
MSD	6.5	4.9226	3.12245

Hence we will use the fit which will have minimum MSD and the linear trend gives the minimum MSD

Hence, Using the mean squared difference (MSD), linear trend fit is method we believe results in the best forecast.