2013
FORECASTING
Brad Fink
CIT 492
3/20/2013
Operations Management
FORECASTING
Executive Summary
Woodlawn hospital needs to forecast type A blood so there is no shortage for the week of 12
October, to correctly forecast, a 3-week moving average, a 3-week weighted moving average and
an exponential smoothing forecast will be completed.
An undisclosed business which will be referred to as case 4.2 has provided data for a plotted
graph to determine any trends, cycles or random variations in sales. Again a moving average and
weighted moving average will be utilized to see the differences.
Telco Batteries, Inc., has provided monthly sales for the current year. The General Manager
wants a simple plot, a Naïve forecast, a moving and weighted moving forecast for the month of
January of the next year.
The Omaha Emergency Medical Clinic has given the past six weeks of patient demand and
would like to see what a forecast in week seven may be. A weighted moving forecast will be
performed to give the best possible data available.
Dell uses the CR5 computer chip in some of their laptops. With twelve months of data on the
price of this chip, Dell would like to see a 2-month and 3-month moving average plotted on a
graph to determine which is best, as well as a exponential smoothing average.
Coffee Palace’s manager, Joe Felan has determined that the price on a cup of Mocha Latte
influences the sales, based on his observations, Joe wants to know what the number of cups sold
might be if a cup costs $2.80.
Marty and Polly Starr runs a bed and breakfast with a bar. The number of guest for the past four
weeks have be provided and the Starr’s would like to know what to expect in bar sales if the
number of guest reaches twenty.
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FORECASTING
Contents
Woodlawn Hospital .........................................................................................................................3
Case 4.2 ............................................................................................................................................6
Telco Batteries, Inc. .........................................................................................................................9
Omaha Emergency Medical Clinic ................................................................................................13
Dell .................................................................................................................................................15
Coffee Palace .................................................................................................................................18
Marty & Polly Starr………………........……………………………...................…......................21
Summary……...…………………………………………..............................................................23
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3/20/2013
FORECASTING
Woodlawn Hospital
Running short on supplies of type (A) blood, Woodlawn Hospital needs to ensure the supply is
on demand for the weekend of October the 12th. The best possible solution is to conduct a 3week moving forecast. To accomplish this, the past five weeks of blood in pints have been
provided in Table 1, which shows the calculations, with the October 12 result.
To find how much type (A) blood is needed, take the pints
used for the weeks of Aug 31 to Sep 14, add the pints used
and dived the sum by 3; this will give a slightly higher
number of pints than what was actually used during that
time frame. This is not a bad thing, a little more is better
than ending up with a shortfall. To complete this cycle
Oct 12 will have the sum of weeks 21 Sep to 5 Oct divided
by 3 giving a forecast of 374 pints of type (A) blood
needed.
To check and see if the forecast could be more precise or
at least see another point of view, the E.R. Administrator
has decided to get a weighted moving average. A
weighted moving average indicates the subjective
importance placed on past or recent data. Weights can be
from 0.0 to 1.0; the higher the weight, then the higher
importance it has on the most recent data.
12 Oct Forecast: 3-Week
Moving Average
Period
31-Aug
7-Sep
14-Sep
21-Sep
28-Sep
5-Oct
12-Oct
Pint
Used
360
389
410
381
368
374
3-Week
Moving
Avgerage
386
393
386
374
Table 1-3-Week Moving
Average
In this case, the weights being used are 0.1 for three weeks ago, 0.3 for two weeks past and 0.6
for the previous week. Just like Table 1, the administrator wants a forecast for the week of 12
Oct.
The first thing needed is to find the total of the weights, (0.1, 0.3 and 0.6) summed up the result
is 1.0. Since the three previous weeks are being used, the first calculation will begin with 21
Sep. Simply multiply the pints of blood used during 31 Aug by 0.1 and add that to the pints used
during 7 Sep multiplied by 0.3 and add that to the pints used during 14 Sep, divide the result by
the total weight of one which gives the final forecast of 399 pints of type (A) blood needed,
again slightly higher than that actually used. Table 2 continues the calculations until the 12 Oct
results are finished
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3/20/2013
FORECASTING
Woodlawn Hospital
.
As shown in the Table to the left, the 12 Oct forecast
has provided a result of 373 pints of type (A) blood
needed by using the 3-week weighted moving
3-Week average. To recap, the formula used was:
Period Pint Used Weights
WMA (381*0.1) + (368*0.3) + (374*0.6) 1 = 373
12 Oct Forecast: 3-Week
Weighted Moving Average
31-Aug
7-Sep
14-Sep
21-Sep
28-Sep
5-Oct
12-Oct
360
389
410
381
368
374
0.1
0.3
0.6
399
391
376
373
Table 2 -3-week Weighted Moving
Average/Forecast
To get a visual idea of how this looks the E.R. administrator wants a graph, but does not want to
show his superiors extreme spikes and drops. An exponential smoothing graph showing the
forecast will do exactly that.
Again a weight is needed, for this graph the weight of 0.2 is being used. The formula which will
(
) . In which, is the new
capture the smoothing average is
forecast,
is the previous period’s forecast, is the smoothing (weighted) constant of (0.2),
and
is the previous period’s actual demand. Easier yet, for those who despise math, the
new forecast = the last period forecast + 0.2 *(last period actual demand – last period forecast).
Figure 1 shows the smoothing graph for Woodlawn Hospital.
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3/20/2013
FORECASTING
Smoothing Forecast
420
410
400
390
380
370
360
350
340
330
Pints Used
12-Oct
5-Oct
28-Sep
21-Sep
14-Sep
7-Sep
Smoothing Forecast
31-Aug
Pints Used
Woodlawn Hospital
Figure 1 –Woodlawn Hospital’s Smoothing Graph
Figure 1 is represented using the data from Table 3. Notice the forecast could not be done on the
first week; the week of 7 Sep forecast will begin with the previous week’s actual demand. Using
the formula and working down the formula will look as
Pint
Smoothing
so: 14 Sep forecast equals 360 + 0.2 (31 Aug pints
Period
Used
Forecast
actually used – 7 Sep forecast, or (14 Sep forecast =
360+0.2 (389-360).
31-Aug
7-Sep
14-Sep
21-Sep
28-Sep
5-Oct
12-Oct
360
389
410
381
368
374
360
366
375
376
374
374
Table 3 –Smoothing Average
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3/20/2013
FORECASTING
Case 4.2
Having been asked to plot a graph on data which has been provided in Table 4, whether or not
any trends, cycles or random variations has also been requested. Taking the data that was
providing, an easy graph was completed and is displayed in Figure 2.
Year
Demand
1
7
2
9
3
5
4
9
5
13
6
8
7
12
8
13
9
9
10
11
11
7
Table 4 –Data provided for graphing
Trend, Cycle, Random Variation Chart
14
12
10
Demand
The starting point
(year 1), has a
reoccurring cycle
at the end of year
11 and beginning
of year 12, this
pattern appears to
cycle every 12
years. All other
graphing data
shows no real
trends or cycles,
there are a few
random variations
but nothing out of
the ordinary.
8
6
Trendline
4
Demand
2
0
1
2
3
4
5
6
7
8
9
10
11
Year
Figure 2 –Trend Chart
Along with the graph in Figure2, a 3-Year moving forecast has also been requested. While
looking at the 3-Year moving forecast below Figure 3, take notice how it has smoothed the
appearance of the actual demand forecast. To achieve this 3-Year moving average had to be
completed, which can be seen in Table inside Figure 3.
Taking the sum of the demand in years 1, 2 and 3 then divide that by three, the result will be year
four’s moving average. To complete this simply move down the line, the important thing to pay
attention to is the moving average is equal to the previous 3 year demands divided by 3, Table 5
shows the completed calculations.
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FORECASTING
Case 4.2
3 Year Moving Forecast
14
12
10
Demand
8
6
4
2
0
1
Year
1
Demand
7
Moving Forecast
2
2
9
3
3
5
4 5 6 7 8
4 5 6 7 8
9 13 8 12 13
7 8 9 10 11
9
9
9
11
10
10
11
11
11 12
11 12
7
11 9
Figure 3 -3 Year Moving Average & Forecast
The last forecast needed to weigh all options is the weighted average. By placing a weight
standard on each year’s demand, a forecast may seem more realistic than that of the 3-Year
moving forecast. The weights associated with the demands normally are numbers ranging 0 to
1.0, with the biggest number being associated with the nearest month, since a 3-Year average is
still in effect, there will be three different weighted numbers. The predetermined numbers given
are (0.1, 0.3 and 0.6). Again using the formula (0.6*last month demand)+(0.3*demand 2 months
ago)+(0.1*demand 3 months ago) / 1, which is represented in Figure 4.
After doing all the equations, the weighted average can then be placed into the graph in Figure 3.
The weighted average that is placed into the graph will be referred to as the weighted forecast in
Figure 4.
Taking a good look at all three graphs, the Trend graph, 3-Year moving forecast and the
weighted forecast, the weighted forecast gives a better depiction of a good accurate forecast.
Following the green graphing line, it is not only a medium of the actual demand and the moving
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3/20/2013
FORECASTING
Case 4.2
forecast. Notice that it is not as smooth as the 3-Year forecast and yet it does not give a presence
of drastic declines as does the actual demand.
Taking a good look at all three graphs, the Trend graph, 3-Year moving forecast and the
weighted forecast, the weighted forecast gives a better depiction of a good accurate forecast.
Following the green graphing line, it is not only a medium of the actual demand and the moving
forecast. Notice that it is not as smooth as the 3-Year forecast and yet it does not give a presence
of drastic declines as does the actual demand.
Weighted Forecast
14
Demand
12
10
8
6
4
2
0
Time in Years
1
2
3
4
5
6
7
8
9
10
11
Trend
1
2
3
4
5
6
7
8
9
10
11
Demand
7
9
5
9
13
8
12
13
9
11
7
Moving Forecast
7
8
9
10
11
11
11
11
9
Weighted
6
8
11
10
11
12
11
11
8
12
Figure 4 –Weighted Forecast
8
3/20/2013
FORECASTING
Telco Batteries
The monthly sales have been provided for a one year time frame, the general manager wants to
see a graph for the years sales, so he has asked for a simple sales chart. Taking the data given by
the GM, in Table 5 and monthly sales chart has been provided shown in Figure 5.
Sales Chart
25
20
Sales
15
10
Sales
5
Dec
Nov
Oct
Sep
Aug
Jul
Jun
May
Apr
Mar
Feb
0
Jan
Month Sales
Jan
20
Feb
21
Mar
15
Apr
14
May
13
Jun
16
Jul
17
Aug
18
Sep
20
Oct
20
Nov
21
Dec
23
Table 5 –Telco Sales
Figure 5 –Telco Batteries Monthly Sales Chart
After looking at the sales the GM wanted to see what a simple forecast of sales would be for the
next January, a Naïve forecast is the simplest method of determining a forecast by taking the last
month’s sales and placing the value as next month’s forecast, Table 6 shows January sales
forecast using the Naïve method.
Month Jan Feb Mar Apr May Jun
Sales
20
21
15
14
13
16
Table 6 –Telco Jan Naïve Forecast
Jul
17
Aug Sep
18
20
Oct Nov Dec
20
21
23
Jan
23
By taking the sales during December, a store can use that data in predicting the next month’s
sales as is with the last January in Table 6 equaling that of the previous month in December.
Now that the Telco GM has seen the sales and the Naïve forecast, he wanted to see a forecast
with a little more accuracy. To do this a 3-month moving forecast has been calculated, and
plotted for his viewing. Figure 6 will show both the 3-month moving average inserted into the 3month moving forecast chart.
9
3/20/2013
FORECASTING
Telco Batteries
3-Month Moving Forecast
25
20
15
10
5
Actual Sales
Jan
Dec
Nov
Oct
Sep
Aug
Jul
Jun
May
Apr
Mar
Feb
Jan
Month
0
3-Month Moving
Month Sales 3-Month
Jan
20 Moving
Feb
21 Average
Mar
15
Apr
14
19
May
13
17
Jun
16
14
Jul
17
14
Aug
18
15
Sep
20
17
Oct
20
18
Nov
21
19
Dec
23
20
Jan
21
Figure 6 –Telco Batteries 3-Month Moving Average/Forecast
By taking the sum of sales for Jan(20), Feb(21) and Mar(15) that value needs to be divided by
three, this will give the 3-month moving average for April, this will continue until the end, so the
Jan 3-month forecast will be (Oct + Nov + Dec) divided by 3, or (20+21+23)/3 which will give
Jan a 3-month moving forecast of 21.
Now that the GM has seen how the 3-month moving forecast correlates with the actual sales, he
has also asked to see what a 6-month forecast would look like, To help in accomplishing this
some weights have been assigned to each six previous months, these weighted numbers will be
within a normal weight range of zero to one.
In the case of Telco Batteries, the weights that correspond to each month is (.1, .1, .1, .2, .2
and .3); the first series of 0.3 being applied to the most recent month and working down to 0.1
that applies to the farthest month. All these weights summed up have a value of 1.0 which will
be used in the division of the formula.
Figure 7 will show the data table along with the forecast chart to show a more precise upward
trend compared to that of the 3-month moving forecast in Figure 6. To reach these results the
weights are multiplied to corresponding sales for that month. An example of how this is achieved
10
3/20/2013
FORECASTING
Telco Batteries
the following formula is used; (the actual sales for
Jan*0.1)+(Feb*0.1)+(Mar*0.1)+(Apr*0.2)+(May*0.2)+(Jun*0.3)/1. Remember that the divisor
was the sum of all numbers of weights. This will be the results for the 6-month weighted
forecast for the month of July, the next forecast for August will be the same except the formula
will skip the sales of January and start with February.
25
6-Month
Weighted
Forecast
20
15
10
5
0
Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan
Sales 20 21
15 14 13 16 17 18 20 20 21 23
6-Month Weighted Average
15.8 15.9 16.2 17.3 18.2 19.4 20.6
Figure 7 -6-Month Weighted Average and Forecast
With the exception of the January forecast being off slightly between the 3-month moving
forecast and the weighted forecast there is really no difference, this is why the GM has requested
a smoothing forecast, this should give him what the forecast suggests, a smoothing effect to the
forecast from the two previous forecasts already done. Figure 8 will show both data table and
chart to show Telco Batteries smoothing forecast chart.
11
3/20/2013
FORECASTING
Telco Batteries
Smoothing Forecast with Trend Line
25
Sales
20
15
Sales
Smoothing
10
Trend Line
5
Jan
Dec
Nov
Oct
Sep
Aug
Jul
Jun
May
Apr
Mar
Feb
Jan
0
Figure 8 –Telco Batteries Smoothing Average and Forecast Chart
While just looking at Figure 8, the GM has noticed the forecast is much smoother while giving
almost the same exact forecast as in the prior two forecast, except the smoothing forecast has
both a gradual decline in sales forecasts as well as a gradual spike in sales. With the smoothing
forecast complete he needs to see a trend projection.
Figure 8 shows the same forecasting chart as Figure 7 with the addition of the trend line based
off the monthly sales, the trend line for Telco Batteries shows a slow but gradual positive trend
in sales for the year.
12
3/20/2013
FORECASTING
Omaha Emergency Medical Clinic
Marc Schniederjans needs a forecast the patient demand for week seven using the data from
weeks 1 thru 6. After looking at all options, the weighted average/forecast will present more
emphasis on the data since the data given is so short. The data that Marc has given can be seen
in Table 5.
ACTUAL
WEEK
NO. OF
PATIENTS
1
65
2
62
3
70
4
48
5
63
6
52
Table 5 –
Data for a
Weighted
Forecast
The values in the forecast Table 6 will be for week seven, also this will be determined from a 4Week weighted average. The weighted numbers for the Table 5 data are (0.333 on the present
period, 0.25 one period ago, 0.25 two periods ago, and 0.167 three periods ago).
ACTUAL
WEEK
NO. OF Weighted
PATIENTS
1
65
2
62
3
70
3 Periods
4
48
Ago
5
63
0.167
6
52
61
7
55
Table 6 –Week 7 Weighted Forecast
2 Periods 1 Period
Present
Ago
Ago
0.25
0.25
0.333
Total
1
Week 7 Forecast based of the
weighted numbers (0.33, 0.25, 0.25
and 0.167)
After completing the 7-Week weighted forecast, a confirmation check is performed with
weighted number extremely out of the normal weighted range of 0 to 1.0, the number used were
(20 replacing 0.333, 15 replacing 0.25, 15 replacing 0.25 and 10 replacing 0.167) the results are
presented in Table 7.
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3/20/2013
FORECASTING
Omaha Emergency Medical Clinic
Total
ACTUAL
Weighted
WEEK
NO. OF Weighted
Periods
PATIENTS
1
65
2
62
3
70
3 Periods 2 Periods 1 Period
Present
Total
4
48
Ago
Ago
Ago
5
63
20
15
15
10
60
6
52
3640
7
3425
Using the numbers outside the normal weighted range the new 7 week forecast shows a 6,066%
increase which is substantially similar to the total weights periods of 60.
Now that the integrity check on weighted number beyond the normal range is complete a
different set of numbers are used, this time within the normal weighted range. The numbers
being used to replace the original respectively are, (0.40, 0.30, 0.20, and 0.10). Table 8 will
show the results of the changes.
ACTUAL
WEEK
NO. OF Weighted
PATIENTS
1
65
2
62
3
70
3 Periods 2 Periods 1 Period
Present
Total
4
48
Ago
Ago
Ago
5
63
0.4
0.3
0.2
0.1
1
6
52
62
Table 8 –Weighted Forecast confirmation
check
7
57
Since all number are within the normal weighted range in Table 8, and with such minor
differences, the forecast is approximately 5% greater, which coincides with the data given, the
difference is only off by 2 forecasted patients.
14
3/20/2013
FORECASTING
Dell
Dell Computers has been tracking the cost of the CR5 chip used in some of their laptops for the
past year, the tracking list has been provided and a 2-month moving average is needed as well as
plotting the information in a 2-month moving forecast, the data is provided in Table 9 with the 2month moving average.
In order to help Dell get the 2-month moving average, the values in
January and February are summed and divided by 2, this will be the
2-month moving average or forecast for the month of March. This
process will continue progressively until the months of November
and December, these two months will be for the next January. Table
9 displays the finished 2-month moving average which is needed in
order to do a plotted chart shown in Figure 9.
2-Month Moving Forecast
$1.95
$1.90
$1.85
$1.80
Price per Chip
$1.75
$1.70
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Jan
Price
2per Chip Month
$1.80 Moving
$1.67 Average
$1.70
$1.74
$1.85
$1.69
$1.90
$1.78
$1.87
$1.88
$1.80
$1.89
$1.83
$1.84
$1.70
$1.82
$1.65
$1.77
$1.70
$1.68
$1.75
$1.68
$1.73
Table 10 –2-Month
Moving Average
2-MonthMoving
Average
$1.65
$1.60
$1.55
Jan
Dec
Oct
Nov
Sep
Aug
Jul
Jun
May
Apr
Mar
Jan
Feb
$1.50
Figure 9 -2-Month Moving Forecast
Along with the 2-month moving average and forecast, Dell also needed to see what a 3-month
moving average and forecast chart would look like compared to the 2-month mmoving average
and forecast. Figure 10 shows Dell exactly what they need to help predict future cost of the CR5
computer chip.
15
3/20/2013
FORECASTING
Dell
3-Month Moving Forecast
$1.95
$1.90
$1.85
$1.80
$1.75
$1.70
$1.65
$1.60
$1.55
$1.50
Price per Chip
2-MonthMoving
Average
3-Month Moving
Average
Figure 10 -3-Month Moving Forecast
The 3-month moving average is done with the same process as the 2-month average with the
exception that three months of values are added and the divided by three. Taking a look at the
difference between the two averages, it would appear that the 3-month moving average is just
slightly higher than that of the 2-month moving average. Since it is easier to predict a near term
forecast than it is for a farther out forecast, the 2-month average better predicts the cost of the
CR5 chips.
Dell has additionally requested an exponential smoothing forecast for each month. The weighted
numbers are within a normal weighted range. To do this each month will be calculated using
each set of numbers which are: ( =0.1, =0.3 and =0.5). In addition to these factors, the
beginning forcast for January will be $1.80. Table 11 will show the final calculations of the
smoothing forecast and using the Mean Absolute Deviation (MAD) formula, we will be able to
tell which weighted factor involved is best.
Using the formula for the forecast (New Forecast= Last forecast + (Actual Demand-Last
Forecast), the error can now be calculated by subtracting the new forecast from the actual
demand, if the value is a negative simply treat it as an absolute number.
Once all columns are completed, add all the values under the error column which will then be
divided by the number of periods, in this case twelve. Since the MAD computation has the
lowest value of $0.068, this will be the best smoothing forecast scenario, which is using the 0.5
weighted score number.
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3/20/2013
FORECASTING
Dell
0.1
0.3
0.5
Price
Month
Forecast Error Forecast Error Forecast Error
per Chip
Jan
$1.80
$1.80
$0.00
$1.80
$0.00
$1.80
$0.00
Feb
$1.67
$1.80
$0.13
$1.08
$0.13
$1.80
$0.13
Mar
$1.70
$1.79
$0.09
$1.76
$0.06
$1.74
$0.04
Apr
$1.85
$1.78
$0.07
$1.74
$0.11
$1.72
$0.13
May
$1.90
$1.79
$0.11
$1.77
$0.13
$1.78
$0.12
Jun
$1.87
$1.80
$0.07
$1.81
$0.06
$1.84
$0.03
Jul
$1.80
$1.80
$0.00
$1.83
$0.03
$1.86
$0.06
Aug
$1.83
$1.80
$0.03
$1.82
$0.01
$1.83
$0.00
Sep
$1.70
$1.81
$0.11
$1.82
$0.12
$1.83
$0.13
Oct
$1.65
$1.80
$0.15
$1.79
$0.14
$1.76
$0.11
Nov
$1.70
$1.78
$0.08
$1.75
$0.05
$1.71
$0.01
Dec
$1.75
$1.77
$0.02
$1.73
$0.02
$1.70
$0.05
MAD (Total/12)
$0.86
0.072
$0.86
0.072
Table 11 - Exponential
Smoothing Chart using
weighted Numbers (0.1,
0.3 and 0.5)
Using MAD, the
Error total divided
by 12 rates 0.068
the best choice.
$0.81
0.068
17
3/20/2013
FORECASTING
Coffee Palace
Joe Felan suspects that demand for mocha latte coffees depends on the price being charged.
Based on historical observations, Joe has gathered the following data, which show the numbers
of these coffees sold over six different price values. Using this data, Joe would like to know the
forecast if the price for a cup of coffee were $2.80. The data Joe has provided is in Table 12
below.
PRICE
$2.70
$3.50
$2.00
$4.20
$3.10
$4.05
NUMBER
SOLD
760
510
980
250
320
480
Table 12 –Coffee
Palace
Historical
Data
Using Table 12, the forecast will be determined by using a simple linear regression method based
off the price of coffee at $2.80.
The forecast will be performed in a few steps, so taking one step or mathematical equation at a
time will be the easiest way about it. First taking the data from Joe’s observation, an updated
Table will need to be done. Table 13 will help with formulating the steps.
PRICE NUMBER
x²
(x)
SOLD (y)
2.70
760
7.29
3.50
510
12.25
2.00
980
4
4.20
250
17.64
3.10
320
9.61
4.05
480
16.4025
Total:
19.55
3,300
67.1925
xy
Table 13 –x, y
Factor Chart
2,052
1,785
1,960
1,050
992
1,944
9,783
To find the values for x², simply start from top to bottom under the price column and square that
particular value, for example 2.70² will be the first value for the x² column which is 7.29.
Continue down all 6 rows until complete. The next step is to find the xy value, by multiplying
the value in price by the value in number sold the xy value will be completed.
Now that all six rows in Table 13 are complete, the next phase is ready for calculation. By
adding all the values in the price column, the result is 19.55. For all following equations the
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Coffee Palace
value for n will be the total number of observations which is six. Now that the value x and value
n as been determined, by using the next formula the value for ̅ can be computed.
̂ = Value of dependent variable, (Sales), or ( ̂
a = y-axis intercept
b = Slope of regression line
x = Independent variable (2.80)
)
The next step is to find the mean average ( ̅ ) of all the prices, to do this add all six prices and
dive that sum by (n), the next equation will give the final result.
̅=
= 3.26; ̅
, or
The next equation to be completed is finding the mean average of the number of cups sold, the
process is the same as the previous equation.
̅
= 550; ̅
=
To continue the data in Table 13 will be used to find the value of the slope of regression (b).
Taking the sum of (xy) and subtracting the total observations multiplied by ( ̅ ̅), divide that
value by the sum in x² minus the number of observation multiplied by ̅ the result will be that in
the equation below.
̅̅̅̅
̅̅̅
=
To find the value of the dependent variable follow the equation below, remember that the value
of (b) is a negative number.
a = ̅-b ̅ = 550-(-277.628)*3.26, a = 1454.604
Now that all data needed is complete, the last step is to find the value of ̂ . This will be
calculated using the value of (a), (b) and the price per cup that Joe wants forecasted, (2.80). The
equation below will finish the last step before making a plotted forecast.
Sales = a + bx = 1454.604+ (-277.628) * 2.80, ̂ = 677
With all information available, a scatter plot can now show Joe the forecast based on the data he
provided. Looking at the forecast in Figure 11, it clearly proves Joe’s theory that the cost of a
cup of Mocha latte does in fact impact the sales. With the economy being what it is, there are
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FORECASTING
Coffee Palace
fewer customers willing to spend over $3.00 per cup, and while charging only $2.00, the profits
do not justify selling a cup at such a low price.
Coffee Palace Mocha Forecast
1200
1000
Regression
Line
800
Cups Sold 600
Number sold
400
677 Cups
sold at $2.80
200
y = -277.63x + 1454.6
0
$0.00
$1.00
$2.00
$3.00
Price Per Cup
$4.00
$5.00
Figure 11 –Regression Forecast for Mocha Latte
Selling a cup of Mocha Latte at $2.80 will bring in gross sales of $1,895.60. The difference
between selling at $2.00 is $64, but after expenses, the overall profits suggests this would be a
good move, not to mention that selling a cup at $2.70 is by far the biggest gross sales of $2,052.
Joe should make this move in order to collect data for another analysis.
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FORECASTING
Marty and Polly Starr
Marty and Polly Starr have provided the data in Table 14 that pertains to the number of guest
registered in their bed and breakfast. The data was obtained from a four week period which they
consider an appropriate time frame to forecast the bar sales for twenty guests. To give the Starr’s
an accurate forecast; a linear regression will be used.
Bar
Guests
Week
Sales
(x)
(y)
1
2
3
4
16
12
18
14
Table 14 -4-Week Guest
to Bar Sales
(x) and (y) factors for the Linear
Regression Calculations
$330
$270
$380
$380
Table 14 gives the base of information needed in order to perform all further calculations; Table
15 shows the progression of the required data. Notice that the bottom row gives the total of the
number of weeks, guest and bar sales, while the furthest two columns have multiplied the
number of guest and bar sales giving a result of (xy). Again the far right column has taken the
number of guest and squared it giving the values for (x²).
Bar
Guests
Week
Sales
(x)
(y)
Totals:
xy
x²
1
2
3
4
16
12
18
14
$330
$270
$380
$380
$5,280
$3,240
$6,840
$5,320
256
144
324
196
4
60
$1,360
$20,680
920
Table 15 –Linear
Regression Chart
In a five step mathematical equation, the first step is to find the value of ( ̅ ), this is the mean
average for the number of guest, the following equation below will show what the process looks
like.
̅=
, or
= 15; ̅
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Marty and Polly Starr
Step two is to find the value of ( ̅), this will be the mean average for the bar sales, the equation
for this is below and can easily be followed.
̅
= 340; ̅
=
Step number three is to find the value of (b), this is known as the slope of the regression line,
which is the next equation below.
̅̅̅̅
̅̅̅
=
In step four, the y-axis intercept value will be determined by using the end results for ( ̅, b and
̅ ) from steps one through three in the next equation below. After step four is complete, all
results can be seen in Figure 14.
a = ̅-b ̅ = 340-(14)*15, a = 130
Using the formula a + bx, the linear regression that relates the bar
sales to the number of guest can represented by:
̅ 𝟏𝟓
𝒙
̅ 𝟑𝟒𝟎
𝒚
𝐛 𝟏𝟒
a = 130
Sales = a + bx, or Sales = 130+ 14x
Figure 14 -Linear
The Starr’s want to know what the sales in the bar might be if the
Regression Results
forecasted number of guests reaches twenty. Again, using the
equation above and substituting (x) for (20), the equation now becomes; 130 + (14 * 20) which
will give the estimated bar sales of $410. This equates to about $20.5 in bar sales per guest.
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FORECASTING
Summary
Forecasting happens in smart businesses worldwide on a daily basis, for determining how much
blood to order as in the case of Woodlawn Hospital. A poor forecast in this situation could result
in lost lives. Of course a good forecast is only as good as the data that is required to make such a
prediction. While there are several different ways to make a forecast, choosing the right method
is vital to the accuracy needed. With Woodlawn Hospital the best choice was a moving forecast
only because the information needed was good and accurate.
With past raw data, not only can a forecast can be produced, but looking at any trends in sales,
what the cycle of sales might look like or even looking into the random variations can be studied
by plotting the information on a graph. A good manager can then adjust any ordering of
products based on this type of information to avoid having an overstock of certain items which
could take valuable space for another item which traditionally sells better at a particular time of
year.
In many cases a linear regression method of forecasting can help business owners decide what
might happen to sales if the price per items were either raised or lowered, which was the case of
Joe from Coffee Palace. With linear regression forecasting future sales based on other forecasts
are possible to help determine sales in specific departments just like the Starr’s bed and
breakfast, in which the bar was one of the specific departments they were focusing on.
No matter which method of forecasting is being done, the bottom line is there is no good forecast
without a good foundation of data that is used for support. A good manager or analyst knows,
good data in equals’ good data out, not to mention, having a strong accurate record of past
history makes compiling that data much easier for forecasting, not to mention faster and more
understandable. Without the fore mentioned, forecasting truly is like trying to pick information
out of someone’s brain, an impossible task for anyone.
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