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## Applied Regression Analysis

by: Mrs. Triston Collier

40

0

4

# Applied Regression Analysis STAT 333

Mrs. Triston Collier
UW
GPA 3.57

Staff

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COURSE
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Staff
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4
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KARMA
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## Popular in Statistics

This 4 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 333 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/205078/stat-333-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.

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Date Created: 09/17/15
Stat 333 Spring 2004 482004 Discussion 10 1 Transformation of the Response Variable 11 BoxCox Power Transformation Yquot i 1 W A for A 31 0 lnY for A 0 The alternative form is Yquot i 1 i for A 31 0 V AyAei YlnY for A0 where Y Y1Y2 Yn1 is the geometric mean of Yi 12 Maximum Likelihood Method of Estimating A First calculate W and obtain the LSE of 6 BW X X 1X W Second obtain the residual sum of squares SSEAW W i XB W i XBW Then form the normalized residual sum of squares ssno W ssno V WM The maximum likelihood estimate of A is the value that minimize SSEA V 13 Example Exercise 13C 4268 CSSC ting listatwiscedu Ting Li Lin Stat 333 Spring 2004 4182004 Regression Analysis Y2 versus x1 x2 x3 x4 The regression equation is Y2 422 825 x1 483 x2 7 567 x3 7 308 x4 Predictor Coef SE Coef T P Constant 42242 1986 2127 0000 X1 82500 07989 1033 0000 X2 48333 07989 605 0001 X3 756667 07989 7709 0000 X4 730833 07989 7386 0008 S 391384 R Sq 9727 R Sqadj 9537 AualySiS of Variance Source SS MS F P Regression 319300 79825 5211 oooo Residual Error 6 9191 1532 Total 10 328491 Source DF Seq x1 1 163350 x2 1 56067 x3 1 77067 x4 1 22817 DurbiuWat50u statistic 223288 Residuals Versus the Fitted Values Normal Probability Plot of the Residuals respunse is m respunse is m 5 n 2 2 5 1 g E E a El 3 a s 72 5 7 0 72 75 n In 2n 3 in 5D 7n n 75 74 n 4 5 lled Value Residual Bostox Power Transformation when 1 7115701500151151 Row lambda15 lambda05 lambda0 lambda05 lambda15 1 1 0662398 162861 336730 87703 447 2 0 663304 1 65700 3 52636 9 6619 131502 3 0 663447 1 66194 3 55535 9 8322 137375 4 0 659213 55279 2 99573 6 9443 58962 5 0 659739 1 56356 3 04452 71652 63489 6 0662609 163485 340120 89545 108878 7 0 661915 1 61510 3 29584 8 3923 92864 8 0 664723 1 71429 3 89182 12 0000 228000 9 0 665478 1 75746 4 21951 14 4924 373162 10 0662609 163485 340120 89545 108878 11 0665619 176750 430407 152047 423715 4268 CSSC tingslistatwiscedu TingsLi Lil Stat 333 Spring 2004 48 2004 Summary of the results SSE W R2 F SSE V 15 000000302586 929 0000547 0 000436 0674 8355 05 05 15 1969 13180 63148 16563 2596 151462407 22785625 5239247 23364210 241021203 989 998 991 945 Note Y 34665 Residuals Versus the Fitted Values Normal Probability Plot of the Residuals respnnse 15 w when 157555521 5 resp5n5e 15 w when 157555521 5 5 5515 2 5 5555 1 E E B D g o o m VD EIEIEIS 1 e2 55 5515 5 555 5 551 5 552 555 5 554 5 555 5 555 5 557 55 5515 55 5515 55 5555 5 5555 5 5555 5 5515 tled Value Residual Residuals Versus the Fitted Values Normal Probability Plot of the Residuals respnnse 15 w when 157555525 5 resp5n5e 15 w when 157555525 5 5 515 2 5 555 1 E E 5 D 1 5 5 VD DDS 1 VB BID 0 392 155 155 155 175 175 155 55 52 551 555 551 552 tted Value Residual Residuals Versus the Fitted Values Normal Probability Plot of the Residuals respnnse 15 w when lambda resp5n5e 15 w when lambda 5 55 2 El D5 5 54 1 5 55 E m i n 52 5 n a 5 K n m o 51 5 51 u 52 0 392 55 52 54 55 55 45 42 44 55555 55525 5555 5525 5555 tted Value Residual 4268 0880 ting listatwiscedu Ting Li Lin Stat 333 Spring 2004 482004 Residuals Versus the Fitted Values Normal Probability Plot of the Residuals respunse is w when lambda 5 respense is w when lambda 5 El 4 o 2 u 2 u 2 1 El 1 o E o g a D m m ix in 71 VB 2 rm 2 e2 ru 4 5 7 a m 11 12 14 is VB is nu 5n nu 25 u m u 25 a 5n lled Value Residual Residuals Versus the Fitted Values Normal Probability Plot of the Residuals respunse is w when lambda1 5 respense is w when lambda1 5 5n 2 4n 2n 1 2D 39g m o a a D m m ix rm 71 2m in 0 72 in a mu 2m 2m 4m en Eu lled Value 03 i l O 950 39 V I 8 o l C I a x Vquot 0 C o D i 03 I 1 l l lambda 4268 CSSC ting listatwiscedu Ting Li Lin

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