Workshop Statistics: Discovery with Data, Second Edition

Topic 11: Least Squares Regression II

Activity 11-1: Gestation and Longevity

(a) gestation = 21.7 + 13.1 * longevity

(b) For each addition year of the animal's longevity, its gestation period is longer by 13.1 days.
(c) 44%
(d)
        It seems as though the predictions are generally closer when the longevity is very small.
(e) The elephant (residual = 98.23) is an outlier in both longeviy and gestation.  There are 6 other animals with larger positive value residuals, and 6 other animals with larger negative value residuals.  So no, the elephant, while being extreme in longevity and gestation, does not have the largest residual.
(f) The giraffe's gestation period is much longer than expected for an animal with its longevity (residual = 272)
(g) regression line: gestation = 9 + 13.6 * longevity;  r2 = .501
(h) no
(i) regression line: gestation = 45 + 11.1 * longevity;  r2 = .269
(j) elephant
(k) regression line: gestation = 110 + 5.26 * longevity;  r2 = .092
Thus, the regression line is not resistant to outliers, especially points that are extreme in the horizontal direction.

Activity 11-2: Residual Plots

(a) (b) (c) Plots 1 and 4 summarize the relationship in the data about as well as possible.  The points fall roughly evenly about the least squares regression line.  Plots 2 and 3 would best be described by some type of curve.
(d) The scatterplots where the lines summarize the data about as well as possible do not correspond to the highest values of r2.  More points fall closer to the line in the other two plots, although they aren't best modeled by a linear fit.
 

Activity 11-3: Televisions and Life Expectancy (cont.)

(a)
        This relationship does not appear to be linear, but rather curved.
(c) life exp = 80.6 - 13.3 * log(per TV)
(d) .850
(e) 67.3
(f) 54;  difference = 13.3, the slope coefficient
(g)
        This scatterplot reveals no clear pattern.
(h) The linear regression model is a better fit with the transformed data than with the original data.