What is Adjusted R Squared in Anova

anova

#1

hello,

In minitab the output of an ANOVA is:

The R-Sq is SS(seating)/SS(Total) = 1674/110936.
Proportion of variation in the data explained.
But how is adj-rsq being calculated here?
I mean there is no concept of taking only the significant variables(or means) in this case?
Can someone please help me out on this??`


#2

Hi,

One of the disadvantage of R-squared is that it can only increase as predictors are added to the model. This increase is artificial when predictors are not actually improving the model’s fit. To cure this, we use “Adjusted R-squared”.

Adjusted R-squared is nothing but the change of R-square that adjusts the number of terms in a model. Adjusted R square calculates the proportion of the variation in the dependent variable accounted by the explanatory variables. It incorporates the model’s degrees of freedom. Adjusted R-squared will decrease as predictors are added if the increase in model fit does not make up for the loss of degrees of freedom. Likewise, it will increase as predictors are added if the increase in model fit is worthwhile. Adjusted R-squared should always be used with models with more than one predictor variable. It is interpreted as the proportion of total variance that is explained by the model.

Regards,
Imran