1. Linear Regression To accompany Hawkes lesson 12.2 Original content by D.R.S.

2. Linear Regression

3. Living with Inconsistencies

4. Slope: Regression, Inference, and Model Building 12.2 Linear Regression HAWKES LEARNING SYSTEMS math courseware specialists y-Intercept: When calculating the slope, round your answers to three decimal places. When calculating the y-intercept, round your answers to three decimal places.

5. The Horses Example again Some horses were measured – Height (in hands?), Girth (inches), Length (inches), Weight (pounds) – Put these data values into your TI-84 lists L 1, L 2, L 3, L 4. Original data source and idea for this problem is “Elementary Statistics” by Johnson & Kuby, 10 th Edition, © Brooks-Cole-Thomson, Page 702.

6. Recall: “Is Girth related to Weight?”

7. Recall: “Is Girth significantly related to Weight?”

8. Recall: LinRegTTest inputs Here are the inputs: Xlist and Ylist – where you put the data – Shortcut: 2 ND 2 puts L 2 Freq: 1 (unless…)

9. LinRegTTest Outputs, first screen

10. LinRegTTest Outputs, second screen

11. Recall your inputs: The calculator deposited the complete equation into your Y 1. Press Y= to see it.

12. You can make predictions Data and equation

13. Beware of “out-of-bounds” usage of the equation Data and equation

14. Scatter Plot and Regression Line 2 ND STAT PLOT ZOOM 9:ZoomStat

15. Scatter Plot and Regression Line ZOOM 9:ZoomStat Note that the data points do fall close to the line. WINDOW (could be cleaned up manually)

16. TI-84 Inputs and Outputs for the Girth and Length question Inputs (Data already in lists) Outputs First screen Second screen

17. Recall: Girth and Length conclusions ConclusionsOutputs First screen Second screen

18. Recall: Girth and Length conclusions ConclusionsOutputs First screen Second screen

19. The Theory behind it. Bluman, Chapter 10 19 Best fit Best fit means that the sum of the squares of the vertical distance from each point to the line is at a minimum. (This slide is mostly from Bluman’s 5 th edition, © McGraw Hill)