# Coefficient of Determination

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• Oct 11th 2007, 07:25 PM
lumberjackjim
Coefficient of Determination
Im stuck on a question where I must find the coefficient of determination and then interpret the resulting value.
The value of the correlation coefficient is 0.916

Help is appreciated
• Oct 11th 2007, 07:48 PM
topsquark
Quote:

Originally Posted by lumberjackjim
Im stuck on a question where I must find the coefficient of determination and then interpret the resulting value.
The value of the correlation coefficient is 0.916

Help is appreciated

The correlation coefficient is \$\displaystyle r = 0.916\$.

The coefficient of determination is \$\displaystyle r^2 = (0.916)^2 = 0.839056\$.

So is this a good linear fit?

-Dan
• Oct 11th 2007, 07:54 PM
lumberjackjim
thanks a lot, I was unaware of how incredibly easy that is. this next one seems even more confusing to me though

Regression Analysis: Larvae versus Stumps
The regression equation is
Larvae = - 1.29 + 11.9 Stumps

Predictor Coef SE Coef T P
Constant -1.286 2.853 -0.45 0.657
Stumps 11.894 1.136 10.47 0.000

S = 6.41939 R-Sq = 83.9% R-Sq(adj) = 83.1%

Analysis of Variance
Source DF SS MS F P
Regression 1 4514.4 4514.4 109.55 0.000
Residual Error 21 865.4 41.2
Total 22 5379.8

Unusual Observations
Obs Stumps Larvae Fit SE Fit Residual St Resid
10 5.00 56.00 58.18 3.43 -2.18 -0.40 X
X denotes an observation whose X value gives it large influence.

How does the value of the Coefficient of Determination included in this
output compare with that in the previous question?
Based on the regression line obtained, predict the number of larvae clusters for a circular plot in which there were four stumps.

• Oct 11th 2007, 08:40 PM
CaptainBlack
Quote:

Originally Posted by lumberjackjim
thanks a lot, I was unaware of how incredibly easy that is. this next one seems even more confusing to me though

Regression Analysis: Larvae versus Stumps
The regression equation is
Larvae = - 1.29 + 11.9 Stumps

Predictor Coef SE Coef T P
Constant -1.286 2.853 -0.45 0.657
Stumps 11.894 1.136 10.47 0.000

S = 6.41939 R-Sq = 83.9% R-Sq(adj) = 83.1%

Analysis of Variance
Source DF SS MS F P
Regression 1 4514.4 4514.4 109.55 0.000
Residual Error 21 865.4 41.2
Total 22 5379.8

Unusual Observations
Obs Stumps Larvae Fit SE Fit Residual St Resid
10 5.00 56.00 58.18 3.43 -2.18 -0.40 X
X denotes an observation whose X value gives it large influence.

How does the value of the Coefficient of Determination included in this
output compare with that in the previous question?
Based on the regression line obtained, predict the number of larvae clusters for a circular plot in which there were four stumps.

The R^2 value is the same as in your first question to the precission it is quoted
in this question 83.9% is 0.839. The corrected R^2 is little different.

The prediction is obtained by plugging 4 in for the number of stumps in the
regression equation:

Larvae = - 1.29 + 11.9 Stumps = -1.29 + 47.6 = 46.31

RonL
• Oct 11th 2007, 08:47 PM
lumberjackjim
thanks alot