1. Inference for Regression
CHAPTER 15
Inference for Regression

2. Regression Inference
USUALLY ABOUT TRUE SLOPE OF A LINEAR RELATIONSHIP.
The mean response has a straight-line relationship with x.
UNKNOWN PARAMETERS
For intercept and slope

3. CONDITIONS! Observations are independent. True relationship is LINEAR.
Standard deviation of the response about the true line is the same everywhere.
Response varies Normally about the true regression line

4. Observations are Independent
Observations on different individuals will often be independent.
Repeated observations on the same individual would violate this condition.

5. True Relationship is Linear
We cannot observe the true regression line but we can look at the sample’s relationship.
Check the scatterplot to see if a linear relationship is present.
ALSO CHECK THE RESIDUAL PLOT!

6. Standard Deviation of the response about the true line is the same everywhere
Check the RESIDUAL PLOT.
Make sure the spread about the axis is roughly the same everywhere.

7. Response varies Normally about the true regression line.
Check the RESIDUALS! Make sure they follow a normal distribution. Make a histogram to see shape. You can also check the NPP!
(Inference for regression is not very sensitive to a minor lack of Normality. Watch out for influential points)

8. CHECKING the RESIDUALS
Remember the calculator can find the residuals for you!! (and make the residual plot)
Enter your data points
Run LinReg(a+bx)
STAT PLOT
For residual plot – scatterplot
xlist = L1 , ylist=RESID
For histogram – RESID as your xlist

9. Confidence Interval for the True Slope
Standard Error of the least-squares slope
USUALLY GIVEN!

10. df = n-2

11. Hypothesis Test! H0 : There is no true linear relationship  = 0
(This would also test a null hypothesis of there being no correlation between the two variables. Testing about correlation requires our observations to be from a random sample)

12. T-TEST!!

13. SEb