1. Influential Points By Noelle Hodge

2. Does the age at which a child begins to talk predict later score on a test of mental ability? A study of the development of young children recorded the age in month at which each of the 21 children spoke their first word and Gesell Adaptive Score, the result of an aptitude test taken much later. The data appears below. Child123456789101112131415161718192021 Age152610915201811820791011 101242171110 Score957183911028793100104941138384 1021001055712186100 Enter data into calculator, List 1 and List 2

3. Calculate the LSRL for the data. Sketch a scatter plot with the LSRL

4. Sketch a residual plot of the data..

5. Is there a point that seems like an outlier in the y-direction? Circle it. Which child is it? Child 19

6. Is there a point that seems like an outlier in the x-direction? Circle it. Which Child is it? Child 18

7. Remove the point you chose for the outlier in the y-direction. Sketch the scatter plot with the LSRL

8. Sketch the residual plot of the data..

9. What is different from this LSRL and the plots, than from the original?. With point removed:Original:

10. Insert this data point back into your data. STAT -> edit 2 nd -> DEL (Insert) -> (enter 17) Curser over to y column -> 2 nd -> DEL (Insert) -> (enter 121)

11. Remove the point you chose for the outlier in the x-direction. Sketch the scatter plot with the LSRL

12. Sketch the residual plot of the data..

13. What is different from this LSRL and the plots than from the original?. With point removed:Original:

14. Influential points

15. Influential Points Unusual points in a regression often tell us more about the data and the model than any other points. Whenever you have influential points, you should fit the linear model to the other points alone and then compare the two regression models to understand how they differ.

16. Just Checking: For each of the three scatter plots, tell whether the point indicated is a HIGH LEVERAGE POINT, would have a LARGE RESIDUAL, or IS INFLUENTIAL. 12 10 8 6 4 2 4 6 8 x y 25 20 15 10 5 0 5 15 20 x y 10 0 -10 -20 0 510 15 20 x y Not high leverage, not influential, large residual High Leverage, not influential, small residual High Leverage, influential, not large residual