# Multiple regression

CFAI q. 6b, i don’t understand when your critical value from the t-table is 1.66 that you reject the null when the test statistic is less than -1.66, instead of 1.66. where did the minus sign come from and is there a hard and fast rule for dealing with these one tailed t-tests?

Do you mean two-tailed test? If so, just focus on the absolute value because the normal distribution is symmetrical.

no its a one tail test, i understand the difference

The Key Concepts in Kaplan Schweser say this : "For a two-tailed test of a regression coefficient, if the t-statistic is between the upper and lower critical t-values, we cannot reject the null hypothesis. We cannot conclude that the regression coefficient is statistically significantly different from the null hypothesis value at the chosen significance level.

[For a one-tailed test] If the t-statistic is greater than the upper critical t-value or lower than the lower critical t-value, we can reject the null hypothesis and conclude that the regression coefficient is statistically significantly different from the null hypothesis value at the specified significance level."

Therefore, since the one-tailed test’s Alternative hypothesis is looking to see if a regression coefficient (intercept, b1) is LESS than some value X, you should use the lower critical t-value (put a minus sign in front of the number you get from the table). If the computed t-stat is less than the (negative) t-value, reject the null hypothesis and conclude that the regression coefficient is statistically less than value X. If the computed t-stat is more than the (negative) t-value, conclude that you cannot reject the null hypothesis (not statistically different). If the one-tailed test’s Alternative hypothesis is looking to see if a regression coefficient is MORE than some value Z, you should use the upper critical t-value (positive number you get from the table). If the compued t-stat is more than the (positive) t-value, reject the null hypothesis and concluded that the regression coefficient is statistically greater than value Z. If the computed t-stat is less than the (positive) t-value, conclude that you cannot reject the null hypothesis (not statistically different). Hope this helps.