Transcription of Lecture 5 Hypothesis Testing in Multiple Linear Regression
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Lecture 5 Hypothesis Testing in Multiple Linear Regression
Lecture 5 Hypothesis Testing in Multiple LinearRegressionBIOST 515 January 20, 20041 Types of tests Overall test Test for addition of a single variable Test for addition of a group of variables2 Overall testyi= 0+xi1 1+ +xip p+ iDoes theentireset of independent variables contributesignificantly to the prediction ofy?3 Test 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+ i4 Test 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?yi= 0+xi1 1+ +xi,p 1 p 1+xip p+ i5 The ANOVA tableSource ofSums of squaresDegrees ofMeanE[Mean square]variationfreedomsquareRegressionS SR= X y n y2pSSRpp 2+ RX CXC RErrorSSE=y y X y n (p+ 1)SSEn (p+1) 2 TotalSST O=y y n y2n 1 XCis the matrix of centered predictors:XC=0BB@x11 x1x12 x2 x1p xpx21 x1x22 x2 x2p x1xn2 x2 xnp xp1 CCAand R= ( 1, , p).
know this through hypothesis testing as confounders may not test significant but would still be necessary in the regression model). • Adding an unimportant predictor may increase the residual mean square thereby reducing the usefulness of the model.
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