Using Linear Regression to Calculate Growth

A few blog entries back I showed the MDX I used to calculate a seasonally-adjusted total in my chalk talk at the BI conference. This is useful but if we’re looking for a calculation that we can use for the Trend property of a KPI it’s not the whole story – we still need to find a way of expressing how much a value is growing or shrinking over time. Although previous period growth calculations are a lot more useful with seasonally-adjusted values, we can use simple linear regression (and it has to be simple because, as I said, I’m no statistician) to do a better job.

The starting point for understanding how to use linear regression in MDX is (surprise, surprise) Mosha’s blog entry on the subject:

http://sqljunkies.com/WebLog/mosha/archive/2004/12/21/5689.aspx

However, the function that’s going to be most useful here is the linregslope function. If we’re looking at the values in our time series and trying to find a line of best fit for those values with the equation y=ax+b, linregslope returns the value of a in that equation, ie the gradient – when the value of x increases by 1, y increases by the value of a. Here’s an example of how to use it:

with member measures.gradient as
linregslope(
lastperiods(3, [Date].[Calendar].currentmember) as last3
, [Measures].[Internet Sales Amount]
,rank([Date].[Calendar].currentmember, last3)
)

select {[Measures].[Internet Sales Amount], measures.gradient} on 0,
[Date].[Calendar].[Month].members on 1
from [Adventure Works]

The trick with using this function in MDX with a time series is to be able to work out what values you want to pass in for the x axis. Here I’ve used the lastperiods function to get a set containing the current member on the Calendar hierarchy, the previous member on the Calendar hierarchy and the member before that, in the first parameter of the function; at the same time I’ve declared a named set and then used that with a rank function in the third parameter to return the values 1, 2 and 3 for each of these three members.

This gets us the slope, then, but I was thinking it would be better to express this value as a percentage – but of what? The current period’s value? Or one of the preceding two periods values? I have to admit I don’t know which would be correct. Can someone help me out here? Please leave a comment..