(1) R-square is always in between 0 and 1. DOes the same apply to the adjusted R-square?(2) What is the use of F-statistic?

For your first question:Adjusted R-SquareIt says that while R-Square is a percentace, adjusted R-Squeare in a index value.For your second question:F-statistic / F-test is used for statistical comparison of varances of two data sets.

A t-test the significance of a variable individually.,The F-test test the significance of a set of variables jointly. So if our model was y = x1 + x2 + error terms. We would have two T-test results and one F test result. The F-test of all the variables (i.e. X1 and X2) is equivalent to testing the models statistical significance. i.e. whether your model is likely to be statistically robustNote this is slighltly different from the R-square or Adj R-square which test the model's explanatory power Or rather accuracy.BTW the Adj R-square penalises you when you add irrelevant variables, whereas the R-square will always increase. Think of the Adj R-square as an R-square with an added penalty factor for including irrelevant variables into the model.

I would add: Rsquare is only between 0 and 1 when there is an intercept in your model, otherwise this may or may not be true. This is easy to show using algebra.

QuoteOriginally posted by: KLA t-test the significance of a variable individually.,The F-test test the significance of a set of variables jointly. This is a very good argument!!!! Answers all the confusions!!!

R Square is a measure of linear correlation. So if there are polynomial effects in the model then it does not give you the true picture. Adjusted R Square is also the same thing only difference being that it compensates for the increase in degrees of freedom

yes adjusted r square is also between 0 and 1. The reason adjusted r square is used because r square either increases or remains constant but never decreases. whereas adjusted r square starts decreasing if the new information added is less than the decrease in degrees of freedom. if you look at the formula of adjusted r square you will understand.F statistics is used to test the simultaneous equality of population means.

although i am a little bit late to join debate, never mind, anyway,...R-square means the percentage power of the independent variable to explain dependent variable. that is to say, u can answer such a question using R-squared: If u think that a Y variable can be explained by 100 unit of various independent factors, how many units that influencing Y are constituted by X in this 100 units? or How percentage of the impact results belong to X?With this side, R-squared is differ from correlation coefficient which define the POWER of the relationship.Good luck

If I recall well the R-square is the squared correlation between your explanatory variable and dependant variable of you have only one explanatory variable.