Topic 07 - Topic 7 Other Regression Issues Reading Some...

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Topic 7 – Other Regression Issues Reading: Some parts of Chapters 11 and 15
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Overview Confounding (Chapter 11) Interaction (Chapter 11) Using Polynomial Terms (Chapter 15)
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Regression: Primary Goals We usually are focused on one of the following goals: Predicting the response variable based on a set of predictors Quantifying the relationship between the predictors and the response In the latter case (interpretation), both confounding and interaction are concerns.
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What is “Confounding”? We start with an example. Suppose in the SBP example we consider the relationship of SBP to…’ Smoking Status alone Smoking Status along with age Our interest is in determining whether smoking raises blood pressure.
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SBP Example Continued
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Confounding of Age Without age, we wouldn’t be able to see a difference in the smoking groups. In fact the groups are different, but we cannot see it unless we account for age (a covariate ). Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 140.80000 3.66147 38.45 <.0001 SMK 1 7.02353 5.02350 1.40 0.1723
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Confounding of Age (2) After adjusting for age, the two smoking groups are clearly different! Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 48.04960 11.12956 4.32 0.0002 AGE 1 1.70916 0.20176 8.47 <.0001 SMK 1 10.29439 2.76811 3.72 0.0009
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Estimates Without adjusting for age, estimated increase in SBP for smokers is 7, but with a standard error of 5. After adjusting for age, we see that the estimated increase is 10.3 and (more importantly) the SE is only 2.8 The effect of smoking is confounded with age – if we don’t first adjust for age we cannot won’t see accurately the effect of smoking.
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This note was uploaded on 02/20/2012 for the course STAT 502 taught by Professor Staff during the Fall '08 term at Purdue.

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Topic 07 - Topic 7 Other Regression Issues Reading Some...

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