• June 8th: Overview & Review

We covered many things: Using Z and t charts; Central Limit Theorem and Sampling Distributions; Confidence Intervals; Hypothesis Testing. PLEASE READ 8.1 and 8.2.

• June 8th Lab 1: Minitab lookups, confidence intervals, normality testing, hypothesis testing
• June 9th: Comparing Two Population Means

We cover two sample comparisons using large samples, small samples, pooled variances, unpooled variances.

Work these: 8.2, 8.3, 8.5, 8.8, 8.9, 8.11, 8.13, 8.15

CATCH UP on Sampling Distributions

• June 10th: Paired Differences by Design

We learn how to detect when an experiment should be seen as paired and when it should be seen as independent. We learn the impact of pairing.

Pair/Ind sample

A large set of experiments to practice with

Solutions

Work these problems: 8.26, 8.29, 8.31, 8.34, 8.35

• June 10th Lab 2: Two sample mean fully worked.
• June 11th: two sample proportion inference.

Sampling Distribution Properties of two-sample proportions

Practice Exam 1

Solutions to practice exam

Example of an AP exam

Solutions with perfectly worded solutions

For 8.4 work: 8.43, 8.44, 8.46, 8.47, 8.54

• June 12th: Two sample variance, Experimental Design

Key facts about testing variance and experimental design

For 8.6 work: 8.73, 8.74, 8.77, 8.78, 8.81

Practice for detecting observed vs designed experiments

For 9.1 work: 9.1 through 9.8, 9.13

• Jun 15th Review: Work these, concentrate on letting the problem guide you through the flow chart.
• 8.31
• 8.8
• 8.82
• 8.30
• 9.8
• 8.45
• 8.101
• 8.57
• 8.51
• What does the central limit theorem tell us?
• 8.99
• 8.15
• 9.13
• 8.111
• 8.35
• 8.90
• 8.18
• 8.78
• 8.120
• 8.14
• June 16th ANOVA day 1:

Variance between groups vs variance within groups.

Signal to noise concept

ANOVA sample problem

Let's build out a chart on the board, work 9.17, 9.19 together.

Practice with: 9.20, 9.25, 9.18, 9.26, 9.33, 9.29

A JAVA applet where you can play with ANOVA SSE vs SST

• June 17th Multiple Comparisons:

Appropriate charts from book

Overall error rates vs individual.

Practice: 9.35-9.39, 9.43, 9.45, 9.46

Rats revisited

• June 18th and June 22nd Two way Anova:

Practice: 9.64 - 9.70, 9.73

Interaction handout

Bakery handout

Golf Handout

Theme Tune Problem

Work 9.105 completely and grade the write-up

• June 23rd Block Designs and ANOVA

Charts and insights from book

Example of block design benefits

Randomized block design is the many treatment version of paired difference.

Work these: 9.50-9.53, 9.59

Practice high level ANOVA ideas with these: 9.82-9.85, 9.91, 9.96, 9.102, 9.104

Practice Test on ANOVA

• June 24th Goodness of Fit

Reference charts

This is the many-bucket version of the binomial experiment. We call it goodness of fit because it is a test of how well a proposed distribution matches the distribution in a sample.

We'll talk out the details and practice with Skittles.

Problems to work: 10.1-10.5, 10.8, 10.9, 10.18

• June 25th Contingency Tables

Detailed Notes

This is the two-factor multinomial experiment. The goal is to see if the proportions of one factor stay the same for all levels of some other factor. If not then there is an interaction. You hear these in headlines all the time, for instance: men that drink green tea are half as likely to get prostate cancer.

The sampling distribution is a Chi-squared, built just like the goodness of fit test, but with degrees of freedom (r-1)(c-1) and the expected values for each square being a perfectly independent prediction. That is, take the proportion for each row and column and multiple those by n.

I brought in a handout to work through.

Then we'll work these problems: 10.19-10.23, 10.25, 10.26, 10.33

• June 26th: Test 2 Review
Flow charts on page 550 and page 588
• 9.99
• 10.38
• 9.105
• 10.48
• 9.39
• Explain the charts in figure 9.23
• 9.88
• 9.41
• 10.45
• 9.50
• 10.40
• 10.44
• 9.49
• 10.32
• 9.14
• 9.107
• 9.46
• 10.22
• 9.59
• 9.28
• 9.102
• 9.95
• June 30th: Simple Linear Regression 1

Key concepts for SLR

Sample Linear Regression Problem

This is the first time we get to take quantitative input and quantitative output. For a continuous range of independent/predictor values we want to make a best guess for an output. This is very useful, but it only applies inside the range of values we have observed. We'll get some statistical analysis cranking tomorrow.

Our best guess prediction will be a least-squares fit of our data plus an error term which will be an independent random variable centered around 0.

Practice line-math with these: 11.1-11.7

Practice least-squares with these: 11.10-11.12, 11.14-11.16

• July 1st: Simple Linear Regression 2

11.3: Standard Error and Valid Conditions

Problems to work: 11.27, 11.29, 11.32, 11.34

11.4: Testing the model and slope CI

Problems to work: 11.41c, 11.45, 11.46 (careful), 11.48

11.5: Coefficients of correlation and determination aka r and r^2

Problems to work: 11.59, 11.63, 11.64, 11.67

11.6: Making predictions from your model, with confidence

11.79, 11.81, 11.82

Practice situation to work through

• July 2nd: Intro to Multiple Regression, Wrap-up Linear Regresssion

Concepts for Multiple Regression

Multiple Regression example

Practice Exam1

Practice Exam2

3rd Practice Exam

4th Practice Exam

Some screenshots of a multiple regression for price prediction

• July 6th: Statistical Tests in Multiple Regression and Interaction Models

Main ideas for fitness of model testing

We want to do overall fitness testing of a multiple regression model. Make predictions with the model using CI and PI. Test individual coefficients (rarely and a priori). Check the four conditions on the error distribution.

Test ideas with: 12.1, 2, 4, 9, 11; 12.25, 28; Explain figures 12.35, 12.36, SIA12.10 vs SIA12.13

Basics of interaction

Learn how to think about the twisted plane created by interaction terms. Typically analyze at fixed values for all but one input, then think about how the picture changes.

Practice with 12.34, 35, 37, 39, 38, 44

• July 7th: Quadratic Models, Dummy Variables

If we want to model data that has curvilinear patterns then we can add higher-order terms. At the moment we'll just use quadratic terms. An x^2 will be the curvature term, with positive coefficients indicating concave up and negative concave down. The linear terms will just be shifts. For multiple inputs we should add interaction terms too.

Practice with 12.49-53, 55, 56

Dummy Basics

We can model using qualitative variable (bucket variables) in a regression too. To pull this off we create many variables that will be valued either 0 or 1 depending on the actual input. So if the bucket variable is music genre and it takes three values: "Rock", "Reggae", "Elevator" we might create two dummy variables to describe this one attribute. They would be x_1 is 1 when "Reggae" and 0 otherwise and x_2 is 1 when "Elevator" and 0 otherwise. The model would look like E(y) = b_0 + b_1 x_1 + b_2 x_2. Notice that when Rock is the input value x_1 and x_2 will be 0 so E(y) = b_0. Etc.

Practice with problems 12.66-69, 72, 76

Study session in Lerner Trading Lab (first floor of Purnell with the big ticker) Wednesday 2-4ish.

• July 8th: Mixing dummy and quantitative variables. Testing nested models.

Examples of mixed models

If we have a qualitative variable with k levels and we want to mix with linear models then we will need k different lines. To achieve this we'll have a base-line line and then for each dummy variable an adjustment line. Same will be true for a quadratic model / dummy variable mix. Let's do a dummy variable for gender (which has two levels), x1 = 1 if male 0 otherwise, and a qualitative variable x2 = age. If we are trying to predict salary from age and gender then we would have a model like: E(y) = b0 + b1*x2 + x1*(b2 + b3*x2 ) which expands to b0 + b1*x2 + b2*x1 + b3*x1*x2.

Let's practice with: 12.82-12.86, 12.87, 12.89, 12.94

Mechanics of nested models

Now that we've learned to model data with many inputs, interactions, and second order terms we might want to test which of two tests does the better job. It will ALWAYS be that adding terms to a model will reduce error. So in our nested test we compare the amount of error that is reduced for each extra term against the error in the complete model. One of the key skills will be recognizing which subset of the coefficients you are testing for importance.

Let's practice with: 12.97, 98, 99, 101, 103

An extra example with dummy variables

Study session in Lerner Trading Lab (first floor of Purnell with the big ticker) Today 2-4ish.

• July 9th: Final Review
• 10.45
• 9.102
• 9.96
• 12.94
• 11.95
• 8.102
• 12.165
• 10.42
• 9.97
• 12.58
• 12.162
• 9.88
• 11.98
• 8.105
• 12.40
• 11.101
• 12.11
• 12.97
• 8.106
• 8.91
• 9.87