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Applied Linear Regression

by: Vance Bode Sr.

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4

Applied Linear Regression 22S 152

Vance Bode Sr.
UI
GPA 3.72

Staff

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COURSE
PROF.
Staff
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Class Notes
PAGES
4
WORDS
KARMA
25 ?

Popular in Natural Sciences and Mathematics

This 4 page Class Notes was uploaded by Vance Bode Sr. on Friday October 23, 2015. The Class Notes belongs to 22S 152 at University of Iowa taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/228085/22s-152-university-of-iowa in Natural Sciences and Mathematics at University of Iowa.

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Date Created: 10/23/15
2281152 More on Transformations Lecture 15 October 25 2002 Kate Cowles 374 SH kcoWlesstatuiowaedu Variance stabilizing transformations 0 Sometimes scienti c or statistical theory indicates that the variance of the response variable varies with either 7 value of response variable itself 7 value of predictor 0 Example if response variable is counts of something then variance is proportional to expected value 7 square root transformation will stabilize variance 7 V37 7 Y Y 1 if some Y s are zero or very small 2 Plotting the Back Transformed Predicted Val ues 0 To look at the nonlinear relationship between PCB concentration and age 7 transform predicted values from regression equa tion using transformations back to their original scale y 7 plot these back transformed values vs age the untransformed predictor variable ovum l m m 4 Example the snow geese data Aerial survey methods are regularly used to estimate the number of snow geese in their summer range areas west of Hudson Bay in Canada To obtain estimates small aire craft fly over the range7 and when a flock of geese is spot ted7 an experienced person estimates the number of geese in the flock To investigate the reliability of this method of counting7 an experiment was conducted in which an airplane carrying two observers flew over n 45 flocks7 and each obserer made an independent estimate of the number of birds in each flock Also7 a photograph of the flock was taken so that an exact count of the number of birds in teh flock could be made The resulting data are given in the dataset snowgeesdat Cooka nd Jacobi sen7 1978 The variables are 0 photo 7 count based on photo 0 obs1 7 observer 17s count 0 obs2 7 observer 27s count data geese 56 50 4o mflle groupItppubkcowlesdatasetssnowgeesdat 38 25 30 Input photo o 51 obs2 25 so 40 5 beta sqrt photo 48 35 45 sobsl sqrtltobs1gt 38 25 so sobs2 sqrtltobs2gt 22 2o 20 In 22 12 2o 42 34 35 34 20 30 14 10 12 30 25 30 9 10 10 18 15 18 25 20 30 62 40 50 26 30 20 88 75 120 56 35 60 11 9 10 66 55 80 42 30 35 30 25 30 90 40 120 119 75 200 165 100 200 152 150 150 205 120 200 409 250 300 342 500 500 200 200 300 73 50 40 123 75 80 150 150 120 70 50 60 7 E 90 60 100 Regression Without transformation 110 75 120 95 150 150 Plot of photo wbsl Symbol used 1s 11 57 40 40 43 25 35 photo 55 100 110 400 325 200 400 114 60 120 83 40 40 91 35 60 9 1a proc reg 1 Remdual v5 predJcced values model photo ops1 1 run 1 The REG Proceuure WEI ue 111mm R Depenuent Varlable photo 7 9 name or I E t Sum of Mean 3 Source DF suuares suuare F Value Pr gt 1 1 Mode 1 54769 254769 12920 lt000 quotE39E39 Error 43 34790 197186A76 Corrected Total 44 9560 mm 2mm mu Root MSE 4440563 Rquuare 07503 Piphotoi1 Depenuent Mean 3931111 Ad Peso 07445 Coeff Var 4972022 Parameter Estlmates Parameter stanoaru Varlable DF Estlmate Error t Value Pr gt 1H Intercept 1 2664957 861A43 309 00035 ops1 1 033256 007764 1137 lt0001 11 12 Regression with square root transformations of beglnx verbatlm proc r g response Varlable and predlctor mo 1 5mm sob r n 1 Plot of sphotowsobsl Symbol useo 5 m Depenoent Varlable spnoto sphoto 1 2o 1 Analysls of Varlance 1 1 Sum of Mean 1 Source DF sauaree sauare F Value Pr gt 1 1 1 Mode 1 57274519 57274519 21515 000 1 rror 43 11445752 255204 1 correcteu Total 44 53121231 1 10 1 1 Root 1152 153151 aesauare 03334 1 oepenuent Mean 350453 auJ Ha 032 1 coefr Var 1335159 1 1 1 Parameter Estlmates 1 1 Parameter stanuaru 0 Varlable DF Estlmate Error t Value P gt 1H Intercept 1 161030 053529 301 00044 sops1 1 093132 006353 1467 lt0001 m crycram 1 m 15 2E Pisphot072

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