Session 3: Outline
                          
                          
KKMN Chapter 7 (The Analysis of Variance Table)
===============================================

Preamble

   - is this chapter central/essential in understanding
     and interpreting regression results?
     
       main use is in testing a "block" of variables
       in a multiple regression...
     
       otherwise, can get by with CI's and tests
       based on t-distribution  
     
   
7.1 Preview

   - see my notes re "classical" anova 
   

7.2 The Anova Table for regression

   - same structure whether one or many X's
   
   - equation 7.1 page 105 is the key, and the origin
     of the term "anova" itself 
     
     ("partitioning" of variance)
     
       - In notes, I give the algebraic proof, but Fig 7.1 is
         enough for our purposes
     
   - basis for the F test not that well explained;
     
     see simulation using Excel. 


   
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KKMN Chapter 8 (Multiple Regression Analysis ... General ) 
==========================================================

Preamble / Motivation / ...
---------------------------

   - Easy to carry out (just click!)   
   - Easy to be "glib" about what it accomplishes 
   - BUT ... WHY use it ??? HOW to explain to father-in-law?
    
        
   If interested in independent contributions of each of 
   several variables...
     
      are there situations where one can assess them one at a time
      
        i.e. assess a particular X while ignoring the others ...      
             assess a different  X while ignoring the others ... ?
   
      or does one always have to assess them simultaneously ? 
   
   
   
      If interested in contribution of ONE particular variable...
     
      are there situations where one can assess it while ignoring
      the others ... ?
  
      or does one always have consider the other X's as well ? 
      

   Answers ... Illustrated by examples
   
     - birthweight as function of gestational age and gender
     
     - weight in relation to age and height
     
     - BREAST MILK AND SUBSEQUENT INTELLIGENCE QUOTIENT 
       IN CHILDREN BORN PRETERM

     - increase in heating costs after adding a room to a house
     
     - decrease in longevity if greater amount of sexual activity
   
   
Multiple regression Equation
----------------------------

   - meaning / how to say in words
   
   - geometrically
   
   - as a sequence of simple linear regressions
   
   - (in case of 2 X's) as contour map
   
   - assumptions re fitting / inferences
   

Multiple Correlation Coefficient

   - a helpful way to look at least squares estimate (scalar)
   

Models as "approximations
------------------------- 

   - model misspecification as a source of "errors"
   
    (e.g. estimating the area of a rectangle)
    

Models for interpolation / smoothing
------------------------------------

   - "borrowing strength" (e.g. outcome of prostate cancer)
    
    
     
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 - Further Steps in computing

    - Getting existing ASCII data into SAS via SAS Editor