Question

Table 1 below shows the number of lawn mowers sold by Mangi Enterprises over a period of three years.

Table 1: Sales Data of Lawn Mowers

	Jan	Feb	March	April	May	June	July	Aug	Sept	Oct	Nov	Dec
20016	238	220	195	245	345	380	270	220	280	120	110	85
2017	135	145	185	219	240	420	520	410	380	320	290	240
2018	205	230	340	370	395	505	540	500	402	360	310	280

REQUIRED:

Based on the number of lawn mowers sold over the 36 months provided in Table 1, compute the following:

1 The three-month moving average forecast (MA-3).

2 The six-month moving average forecast (MA-6).

3 On the same graph, plot the actual sales as well as the MA-3 and MA-6 forecasts.

4 Comment briefly, but meaningfully, on the graph plotted in question 3.

5 Determine the linear regression equation that describes the relationship between the month of sales and the units of lawn mowers sold monthly and use it to predict the number of units of lawn mowers to be sold in quarter 1 of the 2019 financial year.

Answer 1

Formula for Moving Average is:

Where n would be the period for which moving average is to be calculated

1. Here n = 3, Since 3 months are not yet completed in January and February of 2016, no moving average will be calculated for it. 3 month MA will start from March 2016.

For March we will add Sales of Jan, Feb & March and divide by 3. Similarly for April, it would be sum of sales of Feb, March, April divided by 3 and so on.

2016	January	238	-
	February	220	-
	March	195	217.67
	April	245	220.00
	May	345	261.67
	June	380	323.33
	July	270	331.67
	August	220	290.00
	September	280	256.67
	October	120	206.67
	November	110	170.00
	December	85	105.00
2017	January	135	110.00
	February	145	121.67
	March	185	155.00
	April	219	183.00
	May	240	214.67
	June	420	293.00
	July	520	393.33
	August	410	450.00
	September	380	436.67
	October	320	370.00
	November	290	330.00
	December	240	283.33
2018	January	205	245.00
	February	230	225.00
	March	340	258.33
	April	370	313.33
	May	395	368.33
	June	505	423.33
	July	540	480.00
	August	500	515.00
	September	402	480.67
	October	360	420.67
	November	310	357.33
	December	280	316.67

2) n = 6. Calculation starts from June 2016 since for earlier months 6 months data is not available.

2016	January	238	-
	February	220	-
	March	195	-
	April	245	-
	May	345	-
	June	380	270.50
	July	270	275.83
	August	220	275.83
	September	280	290.00
	October	120	269.17
	November	110	230.00
	December	85	180.83
2017	January	135	158.33
	February	145	145.83
	March	185	130.00
	April	219	146.50
	May	240	168.17
	June	420	224.00
	July	520	288.17
	August	410	332.33
	September	380	364.83
	October	320	381.67
	November	290	390.00
	December	240	360.00
2018	January	205	307.50
	February	230	277.50
	March	340	270.83
	April	370	279.17
	May	395	296.67
	June	505	340.83
	July	540	396.67
	August	500	441.67
	September	402	452.00
	October	360	450.33
	November	310	436.17
	December	280	398.67

3)

4) We can see that actual sales always drop below the forecasted sales from September to December of any year. At the end of the Period actual sales are much less than forecasted sales.

5) Linear equation is in the form of

y = mx + c

where y = no. of units of lawn

x = month of sale

m is the slope on the regression line and c is the value at given point.

From graph

y = 6.1438x + 192.22

y = 198.3638 for January 2019

y = 204.507 for Feb 2019

y = 210.6514 for March 2019