5. Regression

Cloud of points, axes, independent and dependent variables, point of averages
SD line, regression line, regression estimate: SD line versus regression line, and their slopes
Computation of regression estimates for a dependent variable, given the value of the independent variable --- how to figure out what is required in a given situation, and how to compute it.

Residuals, prediction errors

Residual = observed value minus predicted value
Rms error = SD of residuals: a measure of the likely size of the residuals
---Measures how well the line fits the cloud of points
Computing the rms error
Figuring the normal approximation in 'vertical strips'

When to use or not use a regression estimate

YES: a football shaped scatterplot
NO: Outliers, non-linear relationships, heteroscedasticity.
NO: Extrapolation beyond the values or population. Interventions.

6. Chance variation and Sampling distributions

Chance variation
The Law of Averages
Box models
Probability Histograms
Expected Values and Standard Errors for counts and sums
Normal approximation for probability histograms of counts and sums
Sampling from large populations: relating to box models.
Expected Values and Standard Errors for sample percents and sample averages

7. Statistical Inference

Confidence intervals for population averages.
Interpreting confidence intervals.
Hypotheses: tests of hypotheses -- decision making
The null hypothesis (and the alternative***)
The P-value (we do 2-sided, book does 1-sided -- you can do either).
z-test for value of a population average**
The SE of a difference
z-test for the difference of averages**.

**: Because the ``percent chance of chance errors in percents" gets just too messy, the final exam will NOT
include any example of tests or confidence intervals for proportions or percents (Homework 9 does have 1 such example).
For the final exam: variables will be inches, $$, pounds, years, .... (something with real units) NOT percents.
***: Don't worry about the ``alternative hypothesis''