Judging Variable Significance

The standard error of the estimate indicates the precision with which the regression model can be expected to predict the dependent Y variable. The standard deviation (or standard error) of each individual coefficient provides a similar measure of precision for the relation between the dependent Y variable and a given X variable. When the standard deviation of a given estimated coefficient is small, a strong relation is suggested between X and Y. When the standard deviation of a coefficient estimate is relatively large, the underlying relation between X and Y is typically weak.

A number of interesting statistical tests can be conducted based on the size of a given estimated coefficient and its standard deviation. These tests are based on alternate versions of the previously described t statistic. Generally speaking, a t test is performed to test whether the estimated coefficient b is significantly different from some hypothesized value. By far, the most commonly tested hypothesis is that b = 0. This stems from the fact that if X and Y are indeed unrelated, then the b slope coefficient for a given X variable will equal zero. If the b = 0 hypothesis can be rejected, then it is possible to infer that b ^ 0 and that a relation between Y and a given X variable does in fact exist. The t statistic with n - k degrees of freedom used to test the b = 0 hypothesis is given by the expression

Was this article helpful?

0 0
Your Retirement Planning Guide

Your Retirement Planning Guide

Don't Blame Us If You End Up Enjoying Your Retired Life Like None Of Your Other Retired Friends. Already Freaked-Out About Your Retirement? Not Having Any Idea As To How You Should Be Planning For It? Started To Doubt If Your Later Years Would Really Be As Golden As They Promised? Fret Not Right Guidance Is Just Around The Corner.

Get My Free Ebook

Post a comment