Section 11.2 Day 5
Page 770, E16
Page 770, E16 Randomness: We can not tell whether or not this is a random sample of private well users.
Page 770, E16 Linearity: The scatterplot shows a trend that appears to be linear, but there is an outlier.
Page 770, E16 Uniform residuals: The variation in residuals appear constant except for one outlier.
Page 770, E16 Normality: Except for one outlier, the residuals appear to be slightly skewed right.
Page 770, E16
Page 770, E16 Based on conditions, what should we do?
Page 770, E16 Based on conditions, what should we do? Proceed with construction of the interval but be cautious in our interpretation.
Page 770, E16 (9.9027, 16.0685)
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 9.9027 and 16.0680. As it stands, our confidence should not be quite so high because of the outliers.
Page 770, E16 (ii)
Page 770, E16 Randomness: We can not tell whether or not this is a random sample of private well users.
Page 770, E16 Linearity: The scatterplot shows a trend that appears to be linear, but there is an outlier.
Page 770, E16 Uniform residuals: The variation in residuals appear constant except for an outlier.
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.
Page 770, E16 Based on conditions, what should we do? Proceed with construction of the interval but be cautious in our interpretation.
Page 770, E16 (ii)
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 0.04719 and 0.07657. As it stands, your confidence is not quite so high because of the outliers and because the sample was not random.
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.
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.
Questions?