Exercise 1.7

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.

        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

Recall in the last problem set that you obtained an eyeball fit of this data. Use your fitted line (don't calculate!) to obtain the predicted value for each value of x. Then by subraction $(Y - \hat{Y})$ obtain the residuals.

(a)

Plot the residuals versus the fitted values. Comment on the plot.

(b)

Obtain a stem leaf plot of the residuals.

(c)

Obtain the 5 basic descriptive statistics for the residuals. Are there any outliers?

2.

Recall that you obtained the LS fit for the above data in the last problem set. Calculate the LS residual for Case 9 ( x = 22, y = 64 ).

3.

Recall that you obtained the Wilcoxon fit for the above data in the last problem set. Calculate the Wilcoxon residual for Case 9 ( x = 22, y = 64 ). From which of the 3 fits, LS, Wilcoxon or eyeball, would you spot the outlier more readily? Why?