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).
HEIGHT 1 119.78 119.78 0.97 0.3252 AGE 1 1513.06 1513.06 12.25 0.0005 GENDER 1 36.93 36.93 0.30 0.5847 Residuals 493 60875.92 123.48 SSR(intercept, weight, height, age, gender) = 2571019+1289.38+119.89+1513.06+36.93 = 2573978 SSR(intercept, weight) = 257019+1289.38 = 2572308 SSR(height, age, gender| intercept, weight) = 2573978−2572308 = 1670
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