Liens de Service canadien des forêts

Coefficient de corrélation, coefficient de régression et paramètre R² ajusté

Correlation Coefficient

The correlation coefficient measures the measures the strength of the  linear association between two interval/ratio scale variables. (Bivariate  relationships are denoted with a small r.) Though it does  not distinguish explanatory from response variables and is not affected  by changes in the unit of measurement of either or both variables (Moore and McCabe, 1993).

Multiple correlation coefficients, R

-1 < = r < = 1, whereas 0 < = R < = 1

(or the multiple coefficient of determination, 0 < = R2 < = 1)

the proportion of dependent variable (Y) that can be attributed to the combined effects of all the X independent variables acting together.

- for net effects (multivariate), assess R, R2,
- for individual effects (bivariate) assess r, r2.

R - simple correlation between residuals,

R2 - denotes the percentage of variation in the dependent variable accounted for by the independent predictor variables.

Adjusted R-Squared

An adjusted R-squared, takes the size of the sample into effect. Use when need to compare the results of models which had a differing number of observations or independent variables, or to temper the results of an analysis with suspect results due to a small number of observations.

adjusted R2 = R2 - (k - 1) / (n - k) * (1 - R2)

Where:

n = # of observations,
k = # of independent variables,

Accordingly:

smaller n, decreases R2 value,
larger n, increases R2 value,

smaller k, increases R2 value,
larger k, decreases R2 value.