Hi Saima,

as Vicente said, you can evaluate your predicted against observed values. In R by using e.g. lm(observed~model_predictions). But you might be more interested in the significance of your regressors (especially if you might be overfitting your model !). If you use R, you can use the summary(lm(y~x)), where x is the entire set of regressors to see the significance levels, and to find out which of your regressors really matter. Your R2 will be high if you have overfitted your model but your significance codes will tell you if a regressor is really important in the chosen setup. 

One approach to narrow down what really is important, is removing iteratively the regressors with the highest p-value until no insignificant regressors are left over (you could set the threshold to something like 0.05).

To see if you gained additional value by using so many regressors, use the anova(large_regression_model, reduced_regression_model). The anova will provide you with the results of a Fisher test, showing you if the variances of the large and reduced model are the same. 

For literature, maybe this one:

Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences

There is an ebook available.

good luck!

Hi Saima

Multiple R-squared is the variability proportion of the response variable explained for the model, you can report this value for your model (e. R2=0.34), and also reported adjused R2.

The terms included in your model can be reported for your beta-values and p-values after obtain the maximum parcimony model, or on each iteration model.

I hope help for your question.

Hi Saima,

as Vicente said, you can evaluate your predicted against observed values. In R by using e.g. lm(observed~model_predictions). But you might be more interested in the significance of your regressors (especially if you might be overfitting your model !). If you use R, you can use the summary(lm(y~x)), where x is the entire set of regressors to see the significance levels, and to find out which of your regressors really matter. Your R2 will be high if you have overfitted your model but your significance codes will tell you if a regressor is really important in the chosen setup. 

One approach to narrow down what really is important, is removing iteratively the regressors with the highest p-value until no insignificant regressors are left over (you could set the threshold to something like 0.05).

To see if you gained additional value by using so many regressors, use the anova(large_regression_model, reduced_regression_model). The anova will provide you with the results of a Fisher test, showing you if the variances of the large and reduced model are the same. 

For literature, maybe this one:

Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences

There is an ebook available.

good luck!