Chapter 3.2, Problem 55E

(a)

To determine

To make: a residual plot and describe how the line fits the data.

Answer to Problem 55E

  

Explanation of Solution

Calculation:

The below figure shows the residual plot for the given data:

  

The above figure shows a residual plot with an unstructured (random) scatter of points in a horizontal band centered at zero. Most of the residuals are between $-5$ and $+5$ . For these individuals, the predicted new adults from the least squares line are within 5 of their actual new adults that join colony. Prediction error of 5 is relatively large compared with the actual adult joins; line does not fit the data accurately.

Conclusion:

Thus, the residual plot is plotted.

(b)

To determine

To find: the point which has the largest residual

Answer to Problem 55E

The point $\left(66,6\right)$ has the largest residual

Explanation of Solution

Calculation:

The below table shows values of predicted Y and residuals

Percent return (X)	New adults (Y)	Predicted Y (Y)	Residuals(Y-Y)
74	5	9.43656125	$\begin{array}{l}-4.43656125\hfill \end{array}$
66	6	11.86874481	$\begin{array}{l}-5.868744811\hfill \end{array}$
81	8	7.308400634	$\begin{array}{l}0.691599366\hfill \end{array}$
52	11	16.12506604	$\begin{array}{l}-5.125066043\hfill \end{array}$
73	12	9.740584195	$\begin{array}{l}2.259415805\hfill \end{array}$
62	15	13.08483659	$\begin{array}{l}1.915163409\hfill \end{array}$
52	16	16.12506604	$\begin{array}{l}-0.125066043\hfill \end{array}$
45	17	18.25322666	$\begin{array}{l}-1.253226659\hfill \end{array}$
62	18	13.08483659	$\begin{array}{l}4.915163409\hfill \end{array}$
46	18	17.94920371	$\begin{array}{l}0.050796287\hfill \end{array}$
60	19	13.69288248	$\begin{array}{l}5.307117518\hfill \end{array}$
46	20	17.94920371	$\begin{array}{l}2.050796287\hfill \end{array}$
38	20	20.38138727	$\begin{array}{l}-0.381387275\hfill \end{array}$

From the table,the point $\left(66,6\right)$ has the largest residual. Since this point deviate greatly from a line, it is an outlier.

Conclusion:

Therefore, the point $\left(66,6\right)$ has the largest residual