1. Section 11.2
Day 5

2. Page 770, E16

3. Page 770, E16
Randomness: We can not tell whether or not this is a random sample of private well users.

4. Page 770, E16 Linearity: The scatterplot shows a trend that
appears to be linear, but there is an outlier.

5. Page 770, E16
Uniform residuals: The variation in residuals appear constant except for one outlier.

6. Page 770, E16
Normality: Except for one outlier, the residuals appear to be slightly skewed right.

7. Page 770, E16

8. Page 770, E16
Based on conditions, what should we do?

9. Page 770, E16 Based on conditions, what should we do?
Proceed with construction of the interval but be cautious in our interpretation.

10. Page 770, E16
(9.9027, )

11. Page 770, E16
Had all conditions been met, I would be 95% confident that the slope of the true linear relationship between arsenic level in toenails and arsenic level in the well water is between and
As it stands, our confidence should not be quite so high because of the outliers.

12. Page 770, E16 (ii)

13. Page 770, E16
Randomness: We can not tell whether or not this is a random sample of private well users.

14. Page 770, E16 Linearity: The scatterplot shows a trend that
appears to be linear, but there is an outlier.

15. Page 770, E16
Uniform residuals: The variation in residuals appear constant except for an outlier.

16. Page 770, E16 Normality: Except for one outlier, there is
no reason to suspect that the residuals
could not have come from a normal
distribution.

17. Page 770, E16 Based on conditions, what should we do?
Proceed with construction of the interval but be cautious in our interpretation.

18. Page 770, E16 (ii)

19. Page 770, E16 (ii) Had all conditions been met, we would be 95%
confident that the slope of the true linear
relationship between arsenic level in well water
and arsenic level in the person’s toenails is
between and
As it stands, your confidence is not quite so high
because of the outliers and because the sample
was not random.

20. Page 770, E16 (ii) b. When you reverse the roles of arsenic level in
well water and arsenic level in toenails, the entire
regression line changes. The unit of the slope
changes from ppm in toenails per ppm in well
water to ppm in well water per ppm in toenails.
The sizes of the residuals change too because
they are measured from a different line and from a
different direction. Note: The two slopes are not
reciprocals of one another.

21. Page 770, E16 (ii) c. When the point (0.137, 2.252) is removed,
both intervals get wider. That point is an outlier
in the explanatory variable in both cases above,
which means it pulls the regression line close
to it. This will reduce the standard error of the
estimated slope. Removing this point, then,
increases the standard error and widens the
interval.

22. Questions?