topic Re: OLS results interpretation in ArcGIS GeoStatistical Analyst Questions

OLS results interpretation

ROMANFILOZOF — Thu, 11 Apr 2013 11:25:04 GMT

Hello,
Can't understand some of OLS results, they don't correspond to each other. One of independent variables has a positive relationship with the depend if I look at the Coeffitient column in Summary of OLS Results table, but it has a negative relationship if I look at the Variables Distribution and Relationships graph. What result should I trust? Why there are such mismatches?

Re: OLS results interpretation

EricKrause — Thu, 11 Apr 2013 14:42:20 GMT

This can happen if several of your independent variables are highly correlated. This is called multicollinearity. The variables distribution and relationships graph will give a better sense of how the independent variable is related to the dependent variable.

Re: OLS results interpretation

ROMANFILOZOF — Wed, 17 Apr 2013 09:20:13 GMT

Okey...
So do I understand correctly? If I'd like to prognoze some value of dependent variable in the future I should:
1. Select independent variables that have no multicollinearity (or use the models with less of variables).
2. Find the correlations between independent variables and dependent one.
3. Use correlations with prognostic values of independent variables to prognoze dependent value.

And the correlation coefficients I can get from OLS result? That "Coefficient (a)"?

Re: OLS results interpretation

ROMANFILOZOF — Wed, 17 Apr 2013 10:00:47 GMT

I've just tested if "Coefficient (a)" is the correlation coefficient (which should be used in Regression equation) and haven't received the value of dependent variable... So looks like I absolutely don't understand how can I make a prognoze using OLS and Exploratory regression tool :confused:

Re: OLS results interpretation

EricKrause — Wed, 17 Apr 2013 16:44:25 GMT

The "Coefficient" values are the coefficients in the linear equation. "Correlation coefficients" are something different; they measure the degree of correlation between the dependent variable and a single independent variable.

When you say that you "haven't received the value of dependent variable," do you mean that the linear equation doesn't perfectly predict the dependent variable? If so, OLS does not make perfect predictions. If your model is good, it should predict something close to the true value, but it won't be perfect.

Re: OLS results interpretation

ROMANFILOZOF — Thu, 18 Apr 2013 13:23:39 GMT

Actually I used some kind of equation like described here http://resources.arcgis.com/en/help/main/10.1/index.html#//005p00000023000000. So betha in that link are the same as Coefficient (a)?

The difference between real and calculated value is about 10-30% (real about 19000 calculated about 13000). Is that ok?

Re: OLS results interpretation

EricKrause — Thu, 18 Apr 2013 14:26:27 GMT

The Coefficient values are the coefficients in the linear equation in the section titled "Regression analysis terms and concepts." They're the B's in the equation.

As for whether 10-30% error is acceptable, only you can answer that question. It depends on your goals coming into this analysis.

Re: OLS results interpretation

ROMANFILOZOF — Fri, 19 Apr 2013 10:24:09 GMT

Thanx a lot,
Unfortunately there's no detailed explanation in help about the algorythm of prognozing values and my math level is weak to understand everything on-flight so I have to disturb some people who know 🙂
Now looks like I see the whole picture and I'm going to work to get the acceptable result.

Re: OLS results interpretation

ROMANFILOZOF — Thu, 25 Apr 2013 10:40:01 GMT

Sorry, the last question I hope 🙂
Does that intercept value in the coeffitient table is "Bo" (betha zero) in the equation?
If not, than where should I get it? And where should I get Random Error Term/Residuals (epsylon)?

Re: OLS results interpretation

EricKrause — Thu, 25 Apr 2013 14:17:31 GMT

Yes, B₀ is the intercept term.

Re: OLS results interpretation

ROMANFILOZOF — Thu, 25 Apr 2013 14:23:33 GMT

And what about the epsylon?

Re: OLS results interpretation

EricKrause — Thu, 25 Apr 2013 20:34:24 GMT

The epsilon is the residual (or error) in the prediction. Recall that OLS does not make perfect predictions, and epsilon is the difference between the true value and the predicted value.