Regression Coefficient Interpretation (OLS)
April 8, 2010 4:11 PM
In an OLS regression the coefficient is b = cov(X,Y)/var(X). What is the plain english interpretation of this coefficient in terms of variations (ie. b is the variation in Y that can be explained by variation in X)?
How does this relate to r^2?
The plainest English interpretation of b is that it is the expected change in Y if you increase X by one.
posted by ROU_Xenophobe at 5:32 PM on April 8, 2010
posted by ROU_Xenophobe at 5:32 PM on April 8, 2010
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Remember, R^2 is always between 0 and 1. The regression coefficient is not, and depends on the units of X and Y. Mathematically in simple model (i.e. y = a + b x), b and R^2 are mathematically related as follows:
b = R (SDy / SDx) where SD is standard deviation.
posted by drpynchon at 5:09 PM on April 8, 2010