Reading 11, 3.5 Hypothesis Testing (Part b)

Level 2, Volume 1, Quantitative methods, Reading 11, Correlation & Regression, 3.5

This is Part B of Reading 11, 3.5, Part A

The most common way to test a hypothesis using a regression model is with a t-test of significance.

The formula for testing the hypothesis is just a rearrangement of the formula used previously in Part A.

The initial formula is:

 b1 equals:

But we are trying to calculate t (test statistic) and not the critical value. So t replaces tc

Therefore the equation changes to:

b1- bˆ1 = t .sbˆ1

t = (b1- bˆ1) / sbˆ1

Example 1: Calculate t for b1 from Part A

For bˆ1

= (0.005 - 0.004473) / (0.00002)

= 26.35

Because t (26.35) >  tc (5.841) , we reject the null hypothesis that b1 = 0.005

Example 2: Calculate t for bo from Part A

For bˆ0

= (-19 +20.9637) / (1)

= 1.9637

Because t (1) <  tc (3.182) , we accept the null hypothesis that b0 = 19