Lecture 5 Hypothesis Testing in Multiple Linear Regression
Lecture 5Hypothesis Testing in Multiple LinearRegressionBIOST 515January 20, 20041Types of tests Overall test Test for addition of a single variable Test for addition of a group of variables2Overall testyi= 0+xi1 1+ +xip p+ iDoes theentireset of independent variables contributesignificantly to the prediction ofy?3Test for an addition of a single variableDoes the addition ofoneparticular variable of interest addsignificantly to the prediction ofyacheived by the otherindependent variables already in the model?yi= 0+xi1 1+ +xip p+ i4Test for addition of a group of variablesDoes the addition of somegroupof independent variables ofinterest add significantly to the prediction ofyobtainedthrough other independent variables already in the model?
j 6= 0 As in simple linear regression, under the null hypothesis t 0 = βˆ j seˆ(βˆ j) ∼ t n−p−1. We reject H 0 if |t 0| > t n−p−1,1−α/2. This is a partial test because βˆ j depends on all of the other predictors x i, i 6= j that are in the model. Thus, this is a test of the contribution of x
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