Reading 11 Correlation and Regression - page 298 of Example relation, between, example

luckygiftvn

On page 298, Example 14 showed how to compute the t-statistic for the GM beta hypothesized parameter, which results a t-stat value of 0.8318 (using formula 10). However, later the example also states that in Table 9, the t-stat for Beta is 5.0795.
I wonder what the relation is between these two values. I thought they should be the same number..
Thanks in advance.

Spongebob

Excellent answer, now the explanation in the textbook makes sense to me. Thank you!

grharmeyer

Whenever you run a regression (in Excel or any other statistical software), the results for the t-stat that are presented to you assume that the null hypothesis tests for a parameter equal to zero. This is something you need to remember for the exam as well… if the CFAI doesn’t explicitly state the null and it supplies you with a regression output, you know that the default test is for parameters equal to zero.
So in the example you pointed to, the value in table 9 reflects the fact that you’re testing against H0: B = 0. This implies t-stat = (Estimated B - Hypothesized B) / (Standard Error) = (1.1958 - 0)/0.2354 = 5.0795.
However, the example explicitly asks you test for H0: B = 1. This implies t-stat = (1.1958 - 1)/0.2354 = 0.8318.
To reiterate, if they haven’t supplied any other information and simply supplied a regression output, you need to know that the output implies a hypothesized value of 0 for the parameters.
Hope this helps.