Ec 120B ECONOMETRICS B LECTURE NOTES
Foster, UCSD April 10, 2014
TOPIC 10. INTRO TO CORRELATION & REGRESSION
A. Covariance, Correlation, and Statistical Inference
1. Review of Population Covariance and Correlation:
a) X and Y are jointly distributed random variables.
1) Marginal distributions f(x) and f(y) have parameters μ axd σ , x ynd σ .y
2) Joint distribution f(x, y) has parameters:
• Covariance σ xy Cov(X, Y) = E[X–μ )(Y–x )]; y∞ t(3) = 3.182 in right tail. M and G are not
4. Interpretation and Abuses of Correlation:
a) Correlation is a measure of direction and strength of the linear relationship between two jointly
distributed random variables.
1) Graph sample pairs xi i in a scatter plot. The closer the points are to a straight line, the stronger
the (linear) correlation between X and Y (and the cxyser r to ±1).
• |r| > 0.8 ▯ strong relationship• |r|