Session 2: Outline
                          
                          
Review of KKMN Sections 5-4 to 5-8
==================================

5.4 Assumptions

   - see my notes

5.5 Estimates of slope/intercept

5.6 Residual variation

   - MSE = average squared "error"
   
   - Root Mean Squared Error = MSE
   
     = square root of average squared error
	 
     = "average" error  (roughly!)
	 
     = "average" residual

5.7 Inferences re slope/intercept

    - 2 ingredients
	
      - standard error of parameter estimate
	  
      - t-deviate (with n-2 degrees of freedom)
	  
          - why n-2 df?  
		  
		    See my notes on 5.6 "why do we divide by n-2?"

    - Factors affecting the standard errors
	
      - see "Factors affecting reliability of slope/intercept
	         estimates" in "Inferences re S. L. R." in my notes
			 on M&M ch 2/9


5.8.1 Inferences re: slope 

    - cf diagrams on page 56 of KKMN



New: KKMN Sections 5.9 & 5.10
=============================

5.9 The REGRESSION LINE as object

    - Meaning of "true" line
	
      - a line of mu(Y|X)'s!!
	  
      - estimate of line
	  
      - "centered" version

    - Estimate of mu(Y|value X0 of X)
	
      - X0 not necessarily in dataset
	  
      - Ingredients
	  
        - SE of mu_hat (Y|X0) formula 5.12 p. 57
		
        - t deviate
		
           - note: SE larger the further X0 is from Xbar.
		   
           - Why?

    - (Not mentioned in KKMN) 
	
	CI's are for mu(Y) at a specific X0 value not for 
	entire line (see Neter).


5.9 "Prediction" of a new Y value at X=X0

    - best (point) estimate is estimate of mu(Y|X0)

    - BUT... 
	
	    Y is an INDIVIDUAL value!
	
	    it is not influenced by n used to estimate mu(Y|X0)
		
        Y will vary around true mu(Y|X0) according to the SD
		of INDIVIDUAL Y's at X=X0
		
  - SO...
  
      Uncertainty concerning Y is amalgam of
	  
      - SD of INDIVIDUALS
	  
      - uncertainty in estimate of mu(Y|X0)
	   
	  and is (llmost) independent of n used to estimate mu(Y|X0)

     
	 ==> "Prediction Bands"


NB Difference between 5.8 and 5.9
---------------------------------

   CI's for             AVERAGE    value
   
   Prediction bands for INDIVIDUAL value.


   Examples: Alcohol and Eye Movement
   
             Noninvasive prediction
			 (see Appropriate use of prediction bands
			  letter to NEJM ... on web page under chapter 5)
			  
			  
   
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


Chapter 6 of KKMN
=================

Highlights only

    - r <==> b (slope)
	
	
    - r is range-dependent
	
	
    - Method Comparisons
	
	DONT use r (see article on Method Agreement by Bland and Altman


			  
   
 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
 
 - Further Steps in computing

    - Getting existing data into SAS