In my understanding, R2 is the worst way to evaluate models, at least in regression analysis. R2 is defined as the ratio of the sum of squares of the model and the total sum of squares, times 100, in order to express it in percentage. It is often called the coefficient of determination.

The problem is that whenever you add independent variables to the model R2 will always increase. Therefore it has been suggested the use of adjusted R2. It may occur for example, that incorporating variables to the model the a sum of squares of the model increases, as it should be expected, but the loss of degrees of freedom for the estimation of the error, does not compensate the reduction in the sum of squares of the error and you may have a larger experimental error and therefore the possibility of not detecting some true significant differences between the effects, when they are really true.

To better enlighten suppose you have two independent variables, rename one of them and insert it to the model twice, you will have an R2 of 100 %, but that model does not work because you have a problem of linear dependence.

In my research I usually see, what are the R2 values often reported in similar situations. For example, an R2 of 30 % would be good as long as you worry about the statistical analysis, as well as, of your experimental technique. I do suggest you to look at other statistics for evaluating models.

Hope this can help.

R squared tells you how good the "fit" of your model is or better said how well the line you might draw through your points fits. Its a regression thing.

A simple explanation for this can be found here:

http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit

Btw: Your question has been posted in something called R Statistical Package. This is a program used for statistical analysis (its free btw). So you might think of removing this topic from your question.

Cheers,

O.

R squared is the percentage of the variance of the outcome variable explained by the predictor variable

Evans - R2 can be a little tricky. Willett and Singer pointed out in a couple of papers in The American Statistician (or at least one was in there) that it is redefined when you change models, and the R2s then cannot be compared directly. Also, you will notice that with regression through the origin and one point, you get R2 = 100%. I have noticed it being quite unstable to a small change in the data when using a statistical software package. In short, I don't pay a huge amount of attention to R2. Variance of the prediction error, for example, seems more important. Also, you can't beat a scatterplot for giving you some ideas. - Jim

Thank you you all for having given attention to my question

In my understanding, R2 is the worst way to evaluate models, at least in regression analysis. R2 is defined as the ratio of the sum of squares of the model and the total sum of squares, times 100, in order to express it in percentage. It is often called the coefficient of determination.

The problem is that whenever you add independent variables to the model R2 will always increase. Therefore it has been suggested the use of adjusted R2. It may occur for example, that incorporating variables to the model the a sum of squares of the model increases, as it should be expected, but the loss of degrees of freedom for the estimation of the error, does not compensate the reduction in the sum of squares of the error and you may have a larger experimental error and therefore the possibility of not detecting some true significant differences between the effects, when they are really true.

To better enlighten suppose you have two independent variables, rename one of them and insert it to the model twice, you will have an R2 of 100 %, but that model does not work because you have a problem of linear dependence.

In my research I usually see, what are the R2 values often reported in similar situations. For example, an R2 of 30 % would be good as long as you worry about the statistical analysis, as well as, of your experimental technique. I do suggest you to look at other statistics for evaluating models.

Hope this can help.

R square helps the prediction of dependent variables in research models.

It is better to use Adj R2. It is measure of percent variation explained by the predictors. Very high as well as low value of Adj R2 indicate problems with model.

a good value for R-squared. It depends on how you measure it! If you measure it as a percentage of the variance of the "original" (e.g., deflated but otherwise untransformed) series, then a simple time series model may achieve an R-squared above 90%. On the other hand, if you measure R-squared as a percentage of a properly stationarized series, then an R-squared of 25% may be quite respectable. (In fact, an R-squared of 10% or even as little as 5% may be statistically significant in some applications, such as predicting stock returns.) If you calculate R-squared as a percentage of the variance in the errors of the best time series model that can be explained by adding exogenous regressors, you may be disillusioned at how small this percentage is! Here it was less than 4%, although this was technically a "statistically significant" reduction, since the coefficients of the additional regressors were significantly different from zero.

R square values in regression shows the total variation explained in the regression and also show how good fit the model is. The higher value of R square shows that variables included in the line are good. I do not know how excel gives regression. Better to regression analysis. May be due to round of figures at various steps gives different values

R2 does just tell a distance of the points to a model curves… that means… absolutely nothing if trying to validate a curve…

EXELL MISCALCULATES IT DO NOT TRUST A EXELL COMPUTATION (especially with non linear, personal experience and observation)

Thank you for your Capital remark.

Hummm, in such situation, which software do you use for computing this coefficient

Kind regards

According to my understanding, R^2 gives an idea how much the selected trend line is fitted wit the set of data.On the other hand that is given the accuracy of the correlation of data set.  But this technique is no longer valid if the data points are too much scattered. At that time, we have to use another way to recognize the correlation of data set.

Coefficient of determination (R^2)

• The coefficient of determination is a measure of the amount of variance in the dependent variable explained by the independent variable(s). A value of one (1) means perfect explanation and is not encountered in reality due to ever present error. A value of .91 means that 91% of the variance in the dependent variable is explained by the independent variables.

• The amount of variation explained by the regression model should be more than the variation explained by the average. Thus, R2 should be greater than zero.

• R2 is impacted by two facets of the data:

o the number of independent variables relative to the sample size. For this reason, analysts should use the adjusted coefficient of determination, which adjusts for inflation in R2 from overfitting the data.

o the number of independent variables included in the analysis. As you increase the number of independent variables in the model, you increase the R2 automatically because the sum of squared errors by regression begins to approach the sum of squared errors about the average.

For linear regression, R2 should be fine.

Another recommended methods to assess the quaility of non-linear models?

Thanks,

Wenbin