<t>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 t...

Even if the sample size is 1 it is still a z test. T test is used when you don't know the population standard deviation so you have to use sample standard deviation instead.

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