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

2. 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)

3. 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)

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

5. An Example: Body Fat and Waist Size

6. 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

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

8. 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

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

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