## Reviewing for the Math 2200 Final

This informal document is intended to help you study, and inform you of additional resources that are available. I don't guarantee that it is complete -- please inform me if you feel something important is missing.

Make sure you know in what circumstances you apply each test!

### Material since the last exam

• Chi-squared
• Independence/homogeneity test
• Requirements: counts, independent/random sample, E>=5 in each cell
• Residuals
• Regressions: hypothesis testing and confidence intervals
• Population vs sample regression line
• Requirements: same as Chapters 7-10, + nearly normal residuals
• Linear regression t-test -> standard error for residuals
• Confidence intervals and standard errors for:
• Beta1 (population regression line slope)
• The (population) prediction at a specific x value
• An individual y value at a specific x value
• Know how to calculate invT on your TI!
• ANOVA
• Tests null hypothesis: means of all groups are equal
• Requirements: random/independent data, nearly normal, equal variance
• The F distribution and its two dfs
• On TI/interpreting R output
• ANOVA model and residuals -- "treatment effect"
• Multifactor ANOVA
• Need to interpret output from R only
• Requirements: as per single-factor, with respect to each categorical variable
• Multiple treatment effect
• Interaction plots
• Interaction terms in ANOVA
• Multiple regression
• Need to interpret output from R only
• Requirements: to add a term, should have similar conditions to single regression on the residuals
• Several hypothesis tests
• That some Betai is nonzero
• That a particular Betai is nonzero
• Finding a good model: add terms one-by-one
• Indicator variables
• Indicator variable changes intercept for a group inside your sample
• Indicator variable interaction term changes intercept
• Using for outliers
• Indicator variables for categorical variables with more than 2 levels
• Stepwise regression
• Two methods
• Advantages and disadvantages

### Main ideas from the class

• How to randomize
• Sampling
• Experiments
• Probability and distributions
• Hypotheses tests, confidence intervals, and their relation
• Several types of data, with a test (or several tests) for each
• Proportions
• Comparing 2 proportions
• Quantitative variable means -- t-test
• Quantitative variable median -- sign test
• Comparing means of quantitative variable over 2 samples
• Independent samples -- 2 sample t-test, Wilcoxon, Tukey
• Paired data -- paired t-test (also: paired sign test for median)
• Comparing multiple proportions -> counts -- chi-squared
• Comparing means of multiple samples -- ANOVA
• Two quantitative variables on one sample -- regression
• Multiple quantitative and categorical variables on one sample -- multiple regression with indicator variables

### Finding practice problems

First: you should do the suggested problems from the schedule! More than half of the exam will be taken directly from the suggested problems, so working these is the best thing you can do to study.

Next: you may want to look at the old exams. Do this less because they're such good practice problems, and more to get a sense of what a multiple-choice statistics exam might look like, or at least has looked in the past.

If you still want more, then:
If you're using the book, it has a lot of problems in it that were not assigned, and almost all of them are appropriate and worthwhile to think about.
If you're using MyStatLab, then there is a link at left from the main page: "STUDY PLAN". This will take you to additional practice problems. As usual, MyStatLab will tell you if you've done them correctly.
(Please note that you can also browse the textbook online in MyStatLab by following the "Chapter Contents" link from the main page, and look at the problems in the textbook, etc.)

### Getting help

I will (personally) be holding a review session at a time and place TBA. Come with thoughtful questions, or come to listen to the thoughtful questions of your peers.
I'll be around my office M-Th of this week during the hours 12 - 3 PM. I'm also willing to make appointments for other times. I believe that Akshay also has some availability.