adjusted r squared formula
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Question:My homework assignment says I can calculate the basic R2 based on the data given, to determine which of the two has a higher R2
Equation 1: adjusted R2 is .624 and N is 41
Equation 2: adjusted R2 is .532 and N is 44
Wouldn't R2 be higher for equation 1? The difference in degrees of freedom is so small it couldn't be enough for a .10 swing. Still curious how the calculation would be done!
gives the formula. If A is adjusted R-squared and R2 is ordinary R-squared, wikipedia gives:
A = 1-(1-R2) (n-1)/(n-p-1)
R2 = 1-(1-A) (n-p-1)/(n-1)
where p is the number of parameters (not counting the constant term) in the regression.
Question:I am looking for a basic definition of the statistics term: Adjusted R^2. I just need a simple down to earth example that applies to life demonstrating the concept. Thank you.
Answers:I suppose you mean an adjusted correlation coefficient?
Question:From a multiple regression analysis of stock market data, the following ANOVA table output was obtained from EXCEL.
df SS MS F
Regression 2 97.21 48.605 12.72186
Residual 17 64.95 3.820588
Total 19 162.16
Answers:First you need R-squared
R-Squared = 1 - SS(E)/SS(T) = 1- 64.95/162.16 = .40053
Adjusted = 1 - (1-R-squared)(n-1)/(n-p-1)
So a stab at this is = 1 - (.40053)(19)/17 = 0.552348
You need to check my n-1 and n-p-1, but the idea is there
Regression 3: Sums of Squares and R-squared :In this video, I give two formulas for r^2, and give one intuitive interpretation of the value of r^2.