Outline


Below is a rough, tentative outline of topics covered.  Sometimes, topics will be introduced simultaneously, or we will make only passing reference.  This is meant more as a study guide than a schedule.  The outline gets more vague further down the page, and our progress will depend on great part on the interests and background of the class.

1. univariate (1 week)

    a) sample distributions (descriptions)
        histograms, dot-plots, boxplots, stem and leaf
        measures of center, spread
        the average when used for prediction (least squares)
    b) samples as instances of populations
        pdfs
        means,  conditional means
        confidence intervals
        hypothesis test review
        assessing normality
               
2. bivariate (1 week)
    a) bivariate sample
        boxplots,  scatterplot
        mean function and variance function
        lowess, smoothers
        LS regression
       
    b) population
        bivariate distributions & bivariate normal
        correlation (correlation in normal populaiton)
        Regression in bivariate normal population

3. Simple Linear Regression (2 weeks)
    a)  The model 
    b) estimating parameters, slope interecept variance
    c) properties of estimators
    d) estimating population means and predition
    f) diagnostics
        i) residual plots
        ii) r-squared
    g) transformations

4. Multiple Regression formalities
    a) Matrix review , multivariate normal review
    b) The model
    c) Estimating Coefficients
    d) Inference
   
5. Multiple Regression in practice
    a) Interpreting coefficients, causality and confounding and interactions
    b) assessing the model
    d) relating to simple regression: added variable plots, partial correlation
    e) model selection, stepwise regression and pitfalls

6.  Diagnostics
    a) Leverage, influence, cross-validation, etc.

7.  Principal Components  Regression

8.  Multi-level models