Statistics - Adjusted R-Squared

Statistics – Adjusted R-Squared

R-squared measures the proportion of the variation in your dependent variable (Y) defined by your impartial variables (X) for a linear regression mannequin. Adjusted R-squared adjusts the statistic primarily based on the variety of impartial variables within the mannequin.R2R2 reveals how properly phrases (information factors) match a curve or line. Adjusted R2R2 additionally signifies how properly phrases match a curve or line, however adjusts for the variety of phrases in a mannequin. Should you add an increasing number of ineffective variables to a mannequin, adjusted r-squared will lower. Should you add extra helpful variables, adjusted r-squared will enhance.

Adjusted R2adjRadj2 will all the time be lower than or equal to R2R2. You solely want R2R2 when working with samples. In different phrases, R2R2 is not mandatory when you will have information from a whole inhabitants.

Formulation

R2adj=1[(1R2)(n1)nk1]Radj2=1−[(1−R2)(n−1)n−k−1]

The place −

  • nn = the variety of factors in your information pattern.
  • okayokay = the variety of impartial regressors, i.e. the variety of variables in your mannequin, excluding the fixed.

Instance

Downside Assertion:

A fund has a pattern R-squared worth near 0.5 and it’s doubtlessly providing larger threat adjusted returns with the pattern dimension of 50 for five predictors. Discover Adjusted R sq. worth.

Resolution:

Pattern dimension = 50 Variety of predictor = 5 Pattern R – sq. = 0.5.Substitute the qualities within the equation,

R2adj=1[(10.52)(501)5051]=1(0.75)×4944,=10.8352,=0.1648