R-squared adj. in multiple linear regression of 75% = high correlation?

I have a response column and a column of categorical predictors (around 25 categories) and I get with minitab linear regression analysis a R-sqr adjusted of 75%.

For simple linear regression analysis the R-sqr is equal to the coefficient of determination, is this also true for multiple linear regression analysis? Can I conclude that the two columns have a coefficient of determination of 75% which gives a correlation of around 0.9?

(Most of the predictors / terms have a p-value of >0.05, so the created linear model is not useful.)

• It doesn't really make sense to talk about the correlation between more than two random variables. For example, what is the correlation that the R would be measuring in multiple regression? sqrt(R^2) is only the correlation in the simple linear regression. Edit: Apparently there is this: en.wikipedia.org/wiki/Multiple_correlation – wolfsatthedoor Nov 9 '14 at 21:00
• Yes R-sqr "is equal to the correlation between the dependent variable and the regression model’s predictions for it" But if the model prediction is 75 % it means that there is a correlation between the two columns or not necessarily ? – mike Nov 9 '14 at 21:06
• "Most of the predictors/terms have a p-value of >0.05 so the created linear model is not useful" is puzzling. – Scortchi Nov 9 '14 at 21:08