Question

After tallying the receipts for their first year of operation, the owners of the Taco Barn are encouraged. Sales of their artisnal tacos, made from such exotic ingredients as ground beef, cheese, and beans, have been strong and seem to give hope to the coming year. Taco sales by month are shown in the table.



Armed only with his fingers, the owner decides that the safest forecasting approach is a linear trend line. Generate a forecast for the year using this technique and then calculate forecast errors using MSE. What is the mean squared error for this forecasting approach?

1217

1033

1148

1282

Answer 1

Answer:

Information given in the question is:

Month	Artisnal Taco Sales
Month 1	18
Month 2	21
Month 3	15
Month 4	23

Using Linear Trend, Sales forecast is to be determined.

Input the data in EXCEL:

x	Month	Sales
1	Month 1	18
2	Month 2	21
3	Month 3	15
4	Month 4	23

Step 1	Select the month and sales data
Step 2	Click on Insert and then “Line”
Step 3	On the line graph, do right click and select “Add Trendline”
Step 4	Then from the menu, click on the “Display Equation on chart” checkbox.

Following graph will be displayed:

Thus, equation for linear trend is:

y = 0.9x + 17

where,

y = Ft = Forecast

x = t = Month or time period number

Using formula y = 0.9x + 17

Forecast for month 1 = (0.9*1)+17 = 17.90

Forecast for month 2 = (0.9*2)+17 = 18.80

Forecast for month 3 = (0.9*3)+17 = 19.70

Forecast for month 4 = (0.9*4)+17 = 20.60

If forecast for more months are to be calculated, the same equation can be continued.

x	Month	Sales	Forecast y = Ft
1	Month 1	18	17.90
2	Month 2	21	18.80
3	Month 3	15	19.70
4	Month 4	23	20.60

Calculation of MSE (Mean Squared Error):

Month	Actual Sales	Forecast	Errors	Absolute Errors	Absolute Errors2
	At	Ft	et = At-Ft	|et|	|et|2
Month 1	18	17.00	1.00	1	1
Month 2	21	17.00	4.00	4	16
Month 3	15	17.00	-2.00	2	4
Month 4	23	17.00	6.00	6	36
				MSE	14.25

Error = Actual Sales – Forecast

Absolute Error = |Error| or ABS(Error)

Absolute Error2 = |Error|2

MSE = Mean Squared Error = Average of all Absolute Error2

= (1+16+4+36)/4

MSE = 14.25

Mean squared error estimates the average squared delta between the estimated forecast values and the actual sales value.

Mean squared error for this forecasting approach = 14.25