An Exponential Trendline in Business Objects

This is going to be the third type of Trendline and I just noticed, Excel has six of them. I’m not sure how many really are used, or if there is a specific need for any in particular. So, for now, I’m gonna keep this at three, unless there is a demand for the other three. (Polynomial, Power and Moving Average).

I am going to add those three eventually, just for fun, but I’m going to keep them for a cold winter evening. Or when the question arises.

So, here’s the Exponential Trendline.

The magic number for the Exponential trendline is e. I’ve been reading about the constant e on Wikipedia and it’s a great story. You should read it too. One of the things I noticed is the amount of history that lies at the base of these trendlines. Amazing.

First, the formula:

Where c and b are constants. Each time when they say that (and here is where I find that info) I’m a bit pissed off. Especially, because they’re not constants at all. They’re calculated values. All of them.

c, as usual, is the intercept point but this time, it uses the Natural Logarithm of Y and the value (non Logarithm) of X. In fact, the calculation uses the EXP function, which is the inverse of a Natural Logarithm.

So, if i = ln(x), then exp(i) = x.

b is the coëfficient which we calculated in both other trendlines before, but this time, it uses the ln of  y.

(ah, on a sidenote, I wrote 2011 in my report, but on the test-databases that come with Business Objects, the numbers are identical for 2003 or 2006 –amazing huh )

So, I take the ln on Sales Revenue and I call it LnY

The formulas are:

=ln(<Sales revenue> in body) in report (which is called LnY)

=Average(<LnY> in body) in Report (which I call AverageLnY)

Like in the linear trendline, we calculate X-AverageX where X is a Runningcount of the Month.

=((RunningCount(<Month>) In <Month>) - <AverageX>) In <Month>

=(<LnY> - <AverageLnY>) In <Month> becomes the variable LnY-AverageLnY

and we multiply those two :

=<LnY-AverageLnY>*<X - average X>

After which we add them up. As before, we now have the top of our division:

=Sum((<LnY-AverageLnY> * <X - average X>) In  Body) In Report

For the bottom part of our division, we need the Square of X-AverageX added up.

=Power(<X - average X>, 2) In <Month>

Now we divide those numbers

There, that’s our b-variable which we can use to calculate our c variable.

=<LnY>-(<LnCoeff>*<xvalue>)

There we go, we have both variables to put into our formula.

e = 2.71828, I found that on Wikipedia.

Now, one more thing needs to be done, and it’s probably why this is called the exponential trendline, we need to take the EXP of our intercept point (our c-variable)

=Exp(<InterceptLn>) In Report

=<ExpIntercept>*(Power(2.71828 ,(<LnCoeff>*<xvalue>)))

this is the formulat shown at the top, turned Business Objects. We add that one and convert it to a table. That gives us the following chart:

And excel does this :

Again, a perfect match.

There. That gives you Linear, Logarithmic and Exponential trendlines to add to your charts.

Enjoy

Binabik

Logarithmic Trendline in Business Objects

Right, looks like I overestimated this one. After doing the previous one, Logarithmic just sounded a bit more scary. It really isn’t. In fact, it was the Microsoft site that got me a bit going. They mentioned something called “Linear Regression”. I looked up the math and it looked impressive. I had no idea, that was what I had already done in the previous article.

That has been my experience so far. A series of terms is unknown to me. This makes it fun to figure out how this stuff works because I really have to figure it out for myself.

Like the function in excel to calculate the Intercept point. On one site, I found this construction :

=index(linest(A1:A20;B1;B20);1)

Then, I found that the intercept function does exactly that. =intercept(A1:A20;B1:B20)

Ah well. it’s an amazing journey – and I’m enjoying every stop along the way.But without further ado, here’s the Logarithmic Trendline.

First off, the math is exactly the same as we had in the Linear trendline except that we don’t use x but ln(x). which is the natural logarithm of x.

for this, I use the function =Ln(runningcount(<Month>)) in <Month>

As with last time, I try to avoid using the month in a calculation, although it would work just the same.

Next up, we calculate the average of that column. In fact, that’s the only difference with the linear trendline.

=Average(LnX in Body) in Report is the function I use for that one.

Like with the linear trendline, we then need to make the difference between X and average X (this time with the logarithms of course) and Y- averageY.

=LnX – AverageLnX in Month

=Y – AverageY in Month

Next, we multiply those two with eachother and add them up.

=LnX-AverageLnX * Y-AverageY

=Sum(LnX-AverageLnX*Y-AverageY in body) in report

That last one is going to be the first part of our division.

Like last time, we now need to Square X-AverageX, but this time, it has to be the Ln version. So, the formula would be:

=sum(ln(x)-AverageLnX * ln(x)-AverageLnX  in body)in report

That’s going to be the second part of our division.

Next, we divide those two.

And we have our Direction Coëfficient.

Next up, we need the interception.

For this one, we need to subtract from AverageY

=<AverageY> – (<AverageLnX>*<LnCoëfficiënt>)

This formula, again, is the same as Linear trendline, but we use the one where we calculate the logarithm of X.

the next formula is : (Coefficient*LnX)+ InterceptLn

And then, we convert this baby to a chart.

And, it has the typical Logarithm curvature

Here is the version Excel comes up with – and again, they are identical.

There. A logarithmic trendline is perfectly possible in Business Objects. One less reason to convert your Business Objects Report into an Excel sheet.

Next up : Exponential Trendline

Have a nice day !!

Binabik

Trendlines in Business Objects

This is what we would want.A trendline in Business Objects.

 

It is not possible to let Business Objects insert a trendline in a chart automatically. It’s a feature that is simply missing. This is what I have been living with until now, it simply isn’t possible, end of story. And that makes me rebel. I want to make it possible.

Two problems : I’m not a real good mathematician. The math to achieve trendlines isn’t easy math either.

But, good news, I figured it out – and it works. Over the next few articles, I will hand you the math to add trendlines to your charts.

Our first type of trendline : A LINEAR TRENDLINE

The functions Excel uses to calculate that trendline looks like this :

and this

That’s the sort of math that makes my head spin – but after 5 minutes, I figured out how it works and then it’s easy. In case you don’t know, the x and y with a dash over their heads are averages.

The first function gets you the “direction-coëfficiënt”, the second gives you the interception point. Both are needed to calculate the trend.

Step1:

Calculate the average on both X and Y.

In this case, I used the formula : Average(<Sales revenue) in Report. If you don’t know what the “in Report” stands for, you should have a look at the articles about contexts. It’s not an easy subject.

With that, we have the average of Y and we also need the average of X. This might be a bit strange. Basically, you just need to find the middle of the X-axis of your chart.

So, we need to count how many items there are and find the middle of that. In fact, for our 12 months the middle is not 6 but 6,5 because it’s an even number of lines. So, what I end up doing is using a runningcount function :”=RunningCount(<Month)” Which I then take an average on.

the function at the end is : =Average((RunningCount(<Month>) )) In Report. which I define as variable <AverageX>

This means, that at this point, we have the two numbers with the dashes over their heads. Next, we need to subtract the X and Y values from it.

For X, this is : =((RunningCount(<Month>) In <Month>) - <AverageX>) In <Month> which I define as a variable X – AverageX

Next, we need Y – AverageY

=(<Sales revenue> - <AverageY>) In <Month> which I define as Y – AverageY

Next, we need to multiply those : =<X - average X>*<Y - AverageY> and add them up.

This gives us the first part of our division, specified at the beginning of this document.

For our second part, we need to Square x-divisionX and add them up.

that’s :=Sum(Power(<X - average X> , 2) In  Body) In Report

Last but not least, we need to divide them to get the direction Coëfficient.

Now that we calculated b, we can proceed to calculate

This translates to :

=<AverageY> - (<AverageX>*<coefficient>)

and that’s our “Intercept” which amounts to the Intercept function in Excel.

Now we can calculate the values for our Trendline. The function in this case (for a linear Trendline is:

y = mx + b

m = direction coëfficient

b = intercept

the x-Value is our runningCount on the month (remember)

So, now we transform this to a chart :

I had a great time trying to figure this one out, so I hope it’s useful to anyone. Next up Logarithmic trendlines. It won’t be easy, I can promise you that

 

ah.. last but not least, this is what that trendline looks like in Excel

Isn’t that – entirely – identical Lovely.

Cheers

Binabik