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== Session 1:  Linear regression ==
'''May 29 2008'''

This session will cover the basics of linear regression. See below for a [#Topics list of topics]. Please make sure to do the readings, and post any terminology you'd like to be clarified or other questions you have below. You can also suggest further topics, but keep in mind that Session2 also covers aspects of linear regression modeling, specifically typical issues that come up during the modeling. The goal of this first session is to go through the basic steps of building a linear regression model and understanding the output of it. Session 2 is on validating how good this model is. 

We've also posted some [#assignments assignments] below that you should hand in by Friday, so that we can post them on this wiki page. There is only one way to learn how to use the methods we will talk about and that is to apply them yourself to a data set that you understand. The tutorial is intended to get you to the level where you can do that.

=== Materials ===

 * attachment:attention-r-data.csv
 * attachment:attention-procedure.ppt
 * attachment:attention-r-commands.R
 * attachment:case-influence.ppt

 * for the kidiq data from G&H
  * attachment:kidiq.dta
  * attachment:contrast-coding.R
  * attachment:contrast-coding2.R

=== Reading ===
|| G&H07 || Chapter 3 (pp. 29-49) || Linear regression:  the basics ||
|| Baa08 || Section 4.3.2 (pp. 91 - 105) || Functional relations:  linear regression ||
|| || Sections 6 - 6.2.1 (pp. 181-198) || Regression Modeling (Introduction and Ordinary Least Squares Regression) ||
|| || Section 6.6 (pp. 258-259) || General considerations ||

=== Notes on the readings ===
If you'd like to follow along, the dataset used in the G&H07 reading can be found here:  [http://www.stat.columbia.edu/~gelman/arm/examples/child.iq/].  To use the file, you will need to load the "foreign" package, then use the read.dta() function.  Eg:
    `library("foreign")` [[BR]]
    `kidiq <- read.dta(file="kidiq.dta")`

=== Additional terminology ===
Feel free to add terms you want clarified in class:
 
 *  
 *

=== Questions ===
 * Q: On page 181, Baayen refers to one of the models, done via `lm()`, as a covariance model.  Why is this considered a model of covariance rather than a regression?
 * A: This refers to the fact that 'lm()' or any regression model allows the inclusion of continuous predictors (unlike ANOVA, aov() in R, but like ANCOVA - analysis of covariance). The idea is that, for a linear model, where the outcome is a continuous variable, a continuous predictor co-varies (to whatever extent) with the continuous outcome.

 * Q: When doing a regression with a categorical variable (as Baayen does on page 182), is there an easy way to see which level is coded as 1 and which as 0? 
 * A: By default R codes the dependent variable so that the the outcome is the level that is 2nd in terms of alpha-numerically order.

[[Anchor(assignments)]]
=== Assignments ===
Please upload your solutions by Friday 3:30pm.

|| G&H07 || Section 3.9 (pp. 50-51) || Exercises 3 and 5 ||
|| Baa08 || Section 4.7 (p. 126) || Exercises 3 and 7* ||
*  (for Exercise 7, Baayen treats linear regression using {{{lm}}} or {{{ols}}} as the same as analysis of covariance (see section 4.4.1 (pp. 117-119))).

 * attachment:APS-hw1.R
 * attachment:BenVanDurme-hw1.R
 * attachment:TingQian-hw1.R


== Suggested topics ==
If you have any material that you would like to cover that isn't included in the list below, please make note of it here.


[[Anchor(Topics)]]
== Topics ==

=== Interacting with R and R files ===
 * Quick recap: Formulating your research questions; Hypothesis testing; a "model"
       Dependence on assumptions[[BR]]
       Dependence on sample[[BR]]
       Dependence on available outcome and input measures[[BR]]
       Goal: [[BR]]
             Find generalizations that hold beyond the sample[[BR]]
             Predicting and outcome based on a set of predictors[[BR]]
            
 * Understanding your data set, predictors, and outcome, available information
       {{{str(), summary(), names()}}}[[BR]]
 * Understanding the distributions of your variables
       {{{plot(), points(), lines(), barplot()}}}[[BR]]
       {{{xtabs(), table(), prop.table()}}}[[BR]]
       {{{hist(), histogram(), densityplot()}}}[[BR]]
 * Understanding dependencies between your variables
       {{{pairs(), cor(), abline(), loess()}}}[[BR]]

 * The Linear Model (LM)
       Geometric interpretation[[BR]]
       Ordinary least squares (and how they are "optimal" for the purpose of predicting an outcome Y)[[BR]]
 * Building a linear model (for data analysis)
       {{{lm(), ols()}}}[[BR]]
       Structure and class of these objects
             {{{coef(), display(), summary()}}}[[BR]]
             {{{fitted(), resid()}}}[[BR]]
       Standard output 
 * Interpreting the output of a linear model
       What hypotheses are we testing?[[BR]]
       What are coefficients and how to read them?[[BR]]
             {{{anova(), drop()}}}[[BR]]
       Coding?[[BR]]
             {{{contrasts()}}}[[BR]]
       Transformations and other non-linearities[[BR]]
             {{{log(), sqrt()}}}[[BR]]
             {{{rcs(), pol()}}}[[BR]]
 * Using a model to predict unseen data
       {{{predict()}}}[[BR]]
 * Understanding the influence of individual cases, identifying outliers
       {{{boxplot()}}}[[BR]]
       {{{lm.influence()}}}[[BR]]