Inference for Regression Slope a.k.a., “the end” AP Statistics Chapter 27

c2 goodness-of-fit test c2 test of homogeneity c2 test of independence ??? 1 row or column (1 sample) 2-way table (2+ samples) 2-way table (1 sample)

c2 goodness-of-fit test t-test and t-interval for regression slope c2 goodness-of-fit test c2 test of homogeneity c2 test of independence 1 row or column (1 sample) 2-way table (2+ samples) 2-way table (1 sample)

What would a scatterplot look like if there is NO ASSOCIATION??? If there is no association, we say that the slope is “zero”

An Example: Body Fat and Waist Size

Assumptions/Conditions for regression inference Does the data appear to be linear? Do we have a random sample? This helps to check the independence assumption Does the plot thicken? The plot should NOT thicken. Nearly Normal Condition Histogram of residuals should be unimodal and roughly symmetric, without outliers Degrees of freedom: df = n – 2

If all assumptions are true, the IDEALIZED regression model would look like this: We can depict our distribution like this:

Regression Inference Define 1 (“true mean change in y for each unit increase in x”) t-test for regression slope Ho: 1 = 0 Ha: 1 ≠ 0 and continue as we would with any other t-test. obs – exp st. dev Confidence interval for 1 (regression slope) statistic ±crit. value × st. err

(examples on computer printout worksheet) 27 Worksheet - Computer Printout Regression T-Test Practice

Homework #27 Group Quiz next time (Ch. 26 – 27)