July 2012
Intermediate to advanced
400 pages
9h 33m
English
Content preview from Statistical Inference: A Short Course12.7 Testing Hypotheses about
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12.7 Testing Hypotheses about 
and 
How do we know that X and Y are truly linearly related? Looked at in another fashion, how do we know that X actually contributes significantly to the prediction of Y? Answers to these questions can be garnered by way of testing a particular null hypothesis against an appropriate alternative hypothesis.
The most common type of hypothesis test is that of “no linear relationship between X and Y” or 
, that is, the conditional mean of Y given X does not depend linearly on X. Hence the implied null hypothesis of “no linear relationship between X and Y” is 
. Possible alternative hypotheses are:
a. If we are uncertain about the relationship between X and Y (we have no clue as to whether or not these variables vary directly or inversely), then the appropriate alternative hypothesis is 
. Clearly, this alternative implies a two-tail test with 
. If we reject H0 in ...
. Clearly, this alternative implies a two-tail test with . If we reject H0 in ...Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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