F15-IntroductoryMLR

F15-IntroductoryMLR - PubH 7405: REGRESSION ANALYSIS...

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PubH 7405: REGRESSION ANALYSIS INTRODUCTORY MULTIPLE REGRESSION
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SIMPLE LINEAR REGRESSION The method we have learned so far is called SIMPLE LINEAR REGRESSION ”( ± simple correlation). It’s “ linear because we assume that the relationship is represented by a straight line. It’s “ simple because it only allows us to investigate the role of “ one predictor at a
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Most of the times, we have more than just two measurements ; may be only one “Response” but many Predictors at least many “ Potential Predictors ”. Then you could ask why predicting the response from just one predictor? Or, if there are more than one predictors, then which predictor? Or which would be the most valuable one? Can we take advantage of their availability to use them all?
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In a study of Lung Health using FEV (Forced Expiratory Volume) as the Outcome or Response Variable, we could investigate the role of Age, Height, and Weight, etc… as potential predictors .
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In investigating “ severity ” of prostate cancer, potential predictors include age at diagnosis and level of serum acid phosphatase, X-ray reading , grade (pathology reading of a biopsy of the tumor obtained by needle), and stage (a rough measure of the size and location of the tumor obtained by palpation with fingers via the rectum).
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Statistically, is there any problem with using one predictor at a time using Simple Linear Regression? (A similar but more simple question: suppose we want to compare several population means, what is the problem with using the two-sample t-test to compare two means at a time?) – A few problems in addition to the obvious loss of opportunities.
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White Blood count Survival Time White Blood Count Survival Time (WBC) (weeks) (WBC) (weeks) 2,300 65 4,400 56 750 156 3,000 65 4,300 100 4,000 17 2,600 134 1,500 7 6,000 16 9,000 16 10,500 108 5,300 22 10,000 121 10,000 3 17,000 4 19,000 4 5,400 39 27,000 2 7,000 143 28,000 3 9,400 56 31,000 8 32,000 26 26,000 4 35,000 22 21,000 3 100,000 1 79,000 30 100,000 1 100,000 4 52,000 5 100,000 43 100,000 65 AG-Positive, n = 17 AG-Negative, n = 16 Data are shown below for two groups of patients who died of acute myelogenous leukemia (AML). Patients were classified into the two groups according to the presence or absence of a morphologic characteristic of white cells. Patients termed “AG positive” were identified by the presence of Auer rods and/or significant granulature of the leukemic cells in the bone marrow at diagnosis. For the AG negative patients these factors were absent.
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White Blood count Survival Time White Blood Count Survival Time (WBC) (weeks) (WBC) (weeks) 2,300 65 4,400 56 750 156 3,000 65 4,300 100 4,000 17 2,600 134 1,500 7 6,000 16 9,000 16 10,500 108 5,300 22 10,000 121 10,000 3 17,000 4 19,000 4 5,400 39 27,000 2 7,000 143 28,000 3 9,400 56 31,000 8 32,000 26 26,000 4 35,000 22 21,000 3 100,000 1 79,000 30 100,000 1 100,000 4 52,000 5 100,000 43
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This note was uploaded on 11/21/2011 for the course PUBH 7405 taught by Professor Staff during the Fall '08 term at Minnesota.

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F15-IntroductoryMLR - PubH 7405: REGRESSION ANALYSIS...

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