# Sales Forecast - Least Squares Regression or Arithmetic Mean?

#### Stormin

##### New Member
Hi all,

I've built a model for total sales forecasting based on cumulative sales and using least squares regression gradient [y-intercept set to zero i.e. f(0)=0] to get the monthly 'run rate'. This works well for large, mostly consistent numbers (~300 per month).

e.g.
Code:
Month   Sales   Cml Sales
1       300     300
2       250     550
3       325     875
4       375     1250
My run rate here would be [Sum(Month * Cml Sales) / Sum(Month * Month)] = 300.8 to 1dp (this is the [Sxy/Sxx] gradient of LSR)
In comparison the arithmetic mean would be 1250 / 4 = 312.5 to 1dp

Therefore I can forecast to month 6 as:
LSR gradient: 300.8 * 6 = 1805
Mean: 312.5 * 6 = 1875
Variance between the two: 70 (3.7% of the mean)

We've found the forecast derived from the LSR gradient to be more accurate than the one from the mean.

However, now we are forecasting on a site-by-site basis, where the numbers are smaller and less consistent.

e.g.
Code:
Month   Sales   Cml Sales
1       10      10
2       5       23
3       9       32
4       30      54
LSR: 10.9 to 1dp
Mean: 13.5 to 1dp

Forecast to month 6:
LSR: 65.6
Mean: 81
Variance between the two: 15.4 (19% of the mean)

I'm worried that using this model will not work. Since I am using cumulative sales, there is bias towards the earlier months in the LSR model (the first 10 sales appear in months 1,2,3,4, yet the last 30 sales only appear in month 4). This can be seen when reversing the order of the sales:

Code:
Month   Sales   Cml Sales
1       30      10
2       9       23
3       5       32
4       10      54
LSR: 15.2 to 1dp
Mean: 13.5 to 1dp

Forecast to month 6:
LSR: 91.2
Mean: 81
Variance between the two: 10.2 (13% of the mean)

The total sales are the same, so the mean in the same, but the LSR gradient has completely changed because of this bias. My LSR forecast has changed by 25 units even though the total sales have remained constant.

Am I barking up the wrong tree using the LSR gradient as a forecasting tool? Should I just stick to the mean, or is there some better way of forecasting sales taking every month into account? I want to use the same model for all situations.

I've attached a .xlsx Excel spreadsheet with these examples on (just change the extension from .zip to .xlsx)

Cheers for any and all advice

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#### Stormin

##### New Member
Is anyone able to offer any advice?