1. Inference for Regression
Chapter 27

2. Linear Regression
A model that describes the relationship between two variables.
Line of best fit
Use the TI to determine
________
Correlation, r
Describes the strength of our line of best fit
r<0 indicates…
r>0 indicates…
r = 0 indicates…
Used to make predictions,

3. Seeing the Data
Scatter plots
Line of Best Fit

4. What is inference for regression?
In the sample data there may be a correlation that can be represented by a line of best fit.
Inference for regression
Does our data suggest that there is a correlation …
“data or sample”

5. Conditions/Assumptions
Straight Enough
Independence
Does the Plot Thicken?
Normal

6. Straight Enough Condition
Does the plot look _____?
Be careful about drawing a line…

7. Independence Randomization? Is the sample Representative?
Does the plot of the _____ against x show a clumping or pattern?
___________
Clumping can indicate …

8. Time
If the data are measured over time, plot the residuals against time to check for evidence of patterns that might suggest they are not independent.

9. Does the Plot Thicken?
Is the variability of y fairly consistent for all values of x?
Check Scatter Plot
Make sure …

10. Scatter Plot Predicaments
________
______
_______

11. Normal Is the histogram of the residuals nearly normal?
_______
We assume the errors around the idealized (population) regression line

12. The Test Lets remember what we are testing:
Does our data suggest that there is a correlation in the ________?

13. Regression Slope T-Test
Hypotheses:
Ho :
H1 :
there is a linear relationship between ______ and ______.
_______ increases with _______
_______decreases with _______
State the Model and Test:
________
We will use a regression slope t-test.
Run the test
Draw the Conclusion

14. Example
Does a person’s cholesterol level tend to increase with age? Data collected in Framingham, MA, from 294 adults aged produced the regression analysis shown. Assuming that the data satisfy the condition for inference, examine the association between age and cholesterol level.
Dependent variable is: Cholesterol
Variable Coefficient SE(Coeff) t-ratio P-value
Intercept <
Age
*for a two tailed test*
State an appropriate hypothesis for the slope.
Test your hypothesis and state your conclusion.
The Test:
Ho :
H1 :
Assumptions:
State the Model:
Conclusion:

15. Example #2
In March 2002, Consumer Reports reviewed several models of inkjet printers. Shown are the speed of the printer (in pages per minute) and the cost per page printed. Is there evidence of an association between speed and cost? Test an appropriate hypothesis and state your conclusion.
Speed (ppm)
4.6
5.5
4.5
3.8
3.7
4.7
4.0
3.1
1.9
2.2
1.8
2.0
Cost (c/p)
12.0
8.5
6.2
3.4
2.6
5.8
6.1
9.4
14.9
4.3
14.8
4.4