1. Chapter 14 Inference for Regression
AP Statistics
14.1 – Inference about the Model
14.2 – Predictions and Conditions

2. Two Quantitative Variables
Plot and Interpret
Explanatory Variable and Response Variable
FSDD
Numerical Summary
Correlation (r) – describes strength and direction
Mathematical Model
LSRL for predicting

3. Conditions for Regression Inference
For any fixed value of x, the response y varies according to a Normal distribution
Repeated responses y are Independent of each other
Parameters of Interest:
The standard deviation of y (call it ) is the same for all values of x. The value of is unknown  t-procedures!
Degrees of Freedom: n – 2

4. Conditions for Regression Inference (Cont’d)
Look at residuals:
residual = Actual – Predicted
The true relationship is linear
Response varies Normally about the True regression line
To estimate , use standard error about the line (s)

5. Inference Unknown parameters:
a and b are unbiased estimators of the least squares regression line for the true intercept and slope , respectively
There are n residuals, one for each data point. The residuals from a LSRL always have mean zero. This simplifies their standard error.

6. Standard Error about the Line
Two variables gives: n – 2 df (not n – 1)
Call the sample standard deviation (s) a standard error to emphasize that it is estimated from data
Calculator will calculate s! Thank you TI!

7. t-procedures (n - 2 df) CI’s for the regression slope
standard error of the LSRL slope b is:
Testing hypothesis of No linear relationship
x does not predict y  r = 0

8. What is the equation of the LSRL?
Estimate the parameters
In your opinion, is the LSRL an appropriate model for the data? Would you be willing to predict a students height, if you knew that his arm span is 76 inches?

11. Construct a 95% CI for mean
increase in IQ for each additional
peak in crying

13. Scatter Plot and LSRL? Perform a Test of Significance

17. Checking the Regression Conditions
All observations are Independent
There is a true LINEAR relationship
The Standard Deviation of the response variable (y) about the true line is the Same everywhere
The response (y) varies Normally about the true regression line
* Verifying Conditions uses the Residuals!