I have to analyse the data of three to four variables through multiple regressions analysis, Does the analysis gives me separate R square values for every variable or just one variable. please help to understand this.
Hi Alan,
The coefficient of determination (i.e., R^2) is a summary statistic that measures how much of the total variance of your dependent variable is explained by the variance of your independent variables. Therefore, there is just one R^2 value for the multiple regression model. There are no R^2 values for specific variables.
The value will lie between 0 & 1. A value of 0 indicates that 0% of the variance of your independent variables is associated with the variance of your dependent variable. A value of 1 indicates that 100% of the variance of your independent variables is associated with all of the variance of your dependent variable. Most instances of multiple regression, due to error, will produce R^2 values somewhere in between 0 & 1.
If you're interested in seeing how much variance a specific variable explains in your model, you may remove or add a variable in your regression and see how the R^2 value changes. If adding a variable to your regression causes your R^2 to increase by a reasonable amount, then there is some evidence that the variable is worth keeping in the regression model. However, if you use this method to assess model fitness, then I would advise using adjusted-R^2 values (which are usually given along with R^2 in most statistical software), since regular R^2 weakly increases as your number of independent variables increases. This fact is due to the algorithm for calculating residual sums of squares being 'greedy', where it wants to explain the variance of the dependent variable using the provided independent variables. The adjusted-R^2 value is more resistant to this greediness.
I hope this explanation helps answer your question.
Hello Alan,
I absolutely agree with Joshua. Additionally, you can calculate the specific coefficients of determination (along with their levels of significance) for all pairs of variables individually, which is called a correlation matrix. Using SAS, I recommend the 'proc corr' procedure, for example. In some cases, this allows for manually selecting reasonable variables (i.e. those which do not correlate among each other) to the model. A similar method was used within the attached publication, for example.
Please notice, when adding a variable to the multiple regression analysis (done by a statistical program) the variable-specific level of significance very likely appears different from how it was within the correlation matrix since it strongly depends on the other variables already put to the model.
Regards, Moritz
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Thanks Joshua for your nice explanation, it really helps me undertsnad the multiple regression better and Thanks further to Moritz for your added explanation, Thanks also to Huda.
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