Hypothesis Testing -- for regression coefficent --- Help

CFA Level II
#1

Hi All, While caluclating t-test for regression coefficent, how would we know whether to use two-tailed test or one tailed test ? As eventhough null test has one choice(e.g. x=0), schwsner book uses two tailed test, is that becuase decision to use tailed test is based on alternate hypothesis ? Please help clarify my Level I concept regarding hypothesis testing especially for how many tailed test should be considered ? -Thanks

#2

If the null hypothesis is "="us two-tailed. Ex. Ho:b1=3 or Ho:b1=0. If the null is anything else, use one tailed.

#3

Yeah, you can come up with one-tail tests that make sense but usually the question is “is there any effect?”. That question is lwebb’s “Ho:b1=0” which is the most usual hypothesis test. The larger story here is that most of these single variable tests don’t make lots of sense anyway so they aren’t used that much. In the case of linear regression, the “Ho:b1=0” t-test is exactly equivalent to the F-test (square the t-statistic to get the F statistic). In multivariate regression, the single variable test assumes that the variables are independent which is just not usually a good assumption.

#4

Hello, Isn’t that true that if alternative hypthesis has more than on possilibility of value(Ha:b1<=0), use two sided, if it has one value(Ha:b1=0) use one sided ? Is this correct ? -Thanks

#5

cfausa you will always have the = sign in the Null Hypothesis. TWO TAILED: use a two tailed test for this scenario: H0: b1 = 0 HA: b1 <> 0 ONE TAILED: Use the One tailed test for following scenarios: H0: b1 <= 0 HA: b1 > 0 or H0: b1 >= 0 HA: b1 < 0

#6

Thanks cpk. What is the logic behind using = only in NULL hypothesis but not in alternate ? -Thanks

#7

Am I being to academic here? Why not ALWAYS use a 2-tailed test with regression co-efficents? If you have interactions in the model, you may be wrong about the direction of the coefficent. Worse comes to worse, you are being conservative. Plus, if a coefficent is signficant at .05 with a 1-tailed test but not a 2-tailed test you may consider dropping it from a risk model anyway. “.05” is pretty arbitrary. Dan

#8

cfausa Wrote: ------------------------------------------------------- > Thanks cpk. > > What is the logic behind using = only in NULL > hypothesis but not in alternate ? > > > -Thanks That is the rule. The null hypothesis is what you are testing for - - you want to know if it equals something.

#9

The answers are for the most part correct. However, remember that an F-test is one sided even if the null hypothesis is =. Also there is no difference between a > and >= or < and <= for purposes of hypothesis testing. The reason for this is that the probability of a single value is not defined, probabilities are defined only over ranges.