R Square, P-values and t-Stat

[Thomas Dugan]

One and All,

What does anyone know about these numbers (R Square, P-values and t-
Stat) in regards to linear regression? When doing a linear regression
are there acceptable values attached to these that would lend greater
signigficance / credibility in any given analysis? In addition, in
doing a "linear" regression is it incorrect or misleading to use a
trend graph that is polynomial?

Thanks, Tom D, LV, NV

[Gary Grantham]

Now those are some loaded questions. I use statistics in valuation quite a bit in our practice yet to explain them would be tough. This is therefore a good exercise for me too. We get used to running our models and forget to be able to explain the measure or their significance.

Most of our models are multiple regression rather than linear but still must be measured by their statistical significance. We use multiple regression models to aid in estimating commercial land values. When R-Squared approaches 1, it's telling us that there is a higher significance of how the data fits. In other words, it just fits / works together. Depends too on your data set. We have models that a .65 R-Sq is GREAT and others that go as high as .98. Personally, when we look at R-Sq's of linear models, they're usually quite low as statistically, the data just fits horribly wherein visually on a graph, it makes sense and we can derive some good info from it.

I know there are gurus out there who know much more about it and I too look forward to their comments.

Have you tried to do a Wikipedia yet? Good stuff sometimes.

http://en.wikipedia.org/wiki/R-squared

As far as a polynomial being misleading, it really depends on the operators input. There was a discussion on a forum about how to best represent a polynomial in terms of the order. 2nd order, 3rd order, 4th?? Rather than misleading, I think a Poly trend actually can be the opposite. It allows for a certain number of movements of the trend which I think can actually tell you more than a single linear movement. A single trend line can leave out a lot of information / movement that should be considered.

Once again, the gurus know more but this is sort of my laymans take,


Gary Grantham
Canon City, CO

[Thomas Dugan]

Gary,

Thank you for your feedback.

All the best . Tom D, LV, NV

[Matt Boxberger]

"There are three kinds of lies: lies, damned lies, and statistics." Mark Twain (from Disraeli)

Statistics is an art - given a limited amount of data , we try to figure out what the reality and relationships were between the factors we're analyzing. (Or, if you have other intentions in mind, refer to a nice little book from about 50 years ago, amazingly still in print)

I'd advise not to use or refer to the P-values and t-stats unless you're doing a very formal analysis and can defend them well.

As Gary Grantham noted, the R-squared results tells how correlated the variables are -- i.e. how well they predict the relationship you're graphing.

Based on the reality of our business (lots of unknown variables in every real estate transaction) I'd advise to use the lowest order polynomial curve possible when creating your graphs in Excel.

The order of the curve is based on how many degrees of freedom (number of unspecified parameters, or independent variables) you've controlled for in fitting the points.

If you're graphing the price change in $/SF over time, and your price per SF is also adjusted for lot size, condition, location, buyer and seller motivations etc., etc., then you could use an n-1 order curve for your n-points, so the curve goes through every point, since you really do KNOW that the only variable left is the date of sale...

I think you see my point.

If you're graphing 5 year price trends, and you know from the broader market data that there's likely been a single 'hump' as prices rose through 2006, and have fallen since, then the 'art' of applying the statistics would say you use a 2nd order curve to capture the 1 hump for your neighborhood data, but don't get too fancy and say that the data 'prove' there have been 4 swings in the market because your 5th degree polynomial curve fit through your 100 sales "proves" it. :)

Best Regards,

Matt Boxberger