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Hypothesis to test B0 and B1 in regression analysis


New Member
Sorry, I have another Qn from Schweser Practice Exam I do not understand. The last from me, hopefully.
Qn 74, Practice Exam 2: Greg Barns and Jill Tillman are discussing the hypothesis they wish to test with respect to the model represented by Yi=B0+B1*X+ei. They wish to use standard statistical methodology in their test. Barns thinks an appropriate hypothesis would be that B1=0 with the goal of proving it to be true. Tillman thinks an appropriate hypothesis would be that B1=1 with the goal of rejecting it. With respect to these hypothesis:
a) the hypothesis of neither researcher is appropriate;
b) the hypothesis of Barns is appropriate but not that of Tillman;
c) the hypothesis of Tillman is appropriate but not that of Barns;
d) more information is required.
Correct answer c):The usual approach is to specify a hypothesis that a researcher wishes to disprove.
I think, the goal is to reject the H0 (this part is true Tillman's) BUT shouldn't the hypothesis be H0: B1=0 (i.e no dependence) and therefore this part true Barns'? All together, both are wrong. I thought I understood hypothesis, but this I do not...
Thanks and sorry for the long text.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi Plirts,

It's an interesting question, I would love an expert statistician's view (i.e., not me) because, like you, I would find the question challenging (the longer i look at the question, the more interpretation i can find). My issue is that it mixes casual language ("appropriate" instead of null) with convention (alternative is the affirmative) yet hinges the correct answer on a technicality.

Here is my thought process, fwiw:
  • "Appropriate" hypothesis is an awkward word choice, is it null or alternative? The use of the equal sign ("=") betray this as the "null" hypothesis, such we can substitute "null" for "appropriate"
  • Answer (C), IMO, is technically correct, although not quite exactly for the reason stated: we can either REJECT the null, or FAIL to reject the null. We cannot technically accept the null. Barns is incorrect, not for specifying the null as the affirmative (IMO, it is okay to be looking to affirm the alternative!) but Barns technical mistake is to think the null can be "proven" when the best we can do is "fail to reject"
  • The null of B1=0 or B1=1 is irrelevant. For example, often the null is: B1 = 1.0 or B1 <= 1.0, in order to specify a null that the beta of the security is 1.0. It is true that our merely TYPICAL approach is the "significance test" in which our null is H0:B1=0, so that we are looking to reject no correlation (correlation is embedded in beta) and affirm that the coefficient does have non-zero linear relationship to the variable. That is TYPICAL, but we decide to anchor the null on any X such that H0: B1 = X and alternative HA: B1 <> X. The value of (X) has no relevance here, except that out typical significance test is: X = 0, and we are, by default convention, often looking to reject the null.
I hope that's helpful, thanks,