Exercise 1.6

1.

Let X be the length (cm) of a laboratory mouse and let Y be its weight (gm). Consider the data for X and Y given below. Obtain a scatterplot of the data and comment on the plot.

        X     Y
        16   32
        15   26
        20   40
        13   27
        15   30
        17   38
        16   34
        21   43
        22   64
        23   45
        24   46
        18   39

2.

For the data set in Problem #1, eyeball a linear fit obtaining an estimate of the slope and the intercept.

(a)

Plot your fit.

(b)

Use your plotted fit, to predict the weight of a mouse that is 20 cm long.

(c)

Use your predicition equation to predict the weight of a mouse that is 25 cm long.

(d)

What does the estimate of slope mean in terms of the problem?

(e)

What does the estimate of intercept mean in terms of the problem?

3.

Use the formulas given in class to determine the LS fit for the data given in Problem #1. (ANS: LS slope is: 2.405).

4.

Plot your fit.

5.

Compare the LS fit with your eyeball fit? Which is a better fit? Why?

6.

Use the LS predicition equation to predict the weight of a mouse that is 25 cm long.

7.

What does the estimate of slope mean in terms of the problem?

8.

Use the regression module to scatterplot the data and obtain the LS and Wilcoxon fits. Write the Wilcoxon fit down.

(a)

Plot the Wilcoxon fit on your plot in #1.

(b)

Compare the Wilcoxn and the LS. Which is a better fit? Why?

(c)

Use the Wilcoxon predicition equation to predict the weight of a mouse that is 25 cm long.

(d)

What does the estimate of slope mean in terms of the problem?

9.

The height weight data for the baseball players is given here. Obtain the scatterplot of this data and the LS and Wilcoxon fits.

2000-08-26