Chapter 3.2, Problem 56E

(a)

To determine

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

Answer to Problem 56E

  

Explanation of Solution

Calculation:

The figure shows a random scatter of points in a horizontal band centered at zero. Most of the residuals are between $-100$ and $+200$ . For these individuals, the predicted metabolic rate from the least squares line is within 200 of their actual metabolic rate, in calories burned per 24 hrs. Prediction error of 200 is relatively large compared with the actual metabolic; line does not fit the data accurately.

  

Conclusion:

Therefore, the residual plot is drawn.

Prediction error of 200 is relatively large compared with the actual metabolic; line does not fit the data accurately.

(b)

To determine

To find: the point which has the largest residual

Answer to Problem 56E

The point $\left(42,1418\right)$ has the largest residual

Explanation of Solution

Calculation:

The below table shows the values of predicted Y and residuals

Mass (kg) (X)	Metabolic rate (cal/24hrs) (Y)	Predicted Y (Y)	Residuals (Y-Y)
36.1	995	1068.503	$\begin{array}{l}-73.5026\hfill \end{array}$
54.6	1425	1512.985	$-87.9848$
48.5	1396	1366.426	$\begin{array}{l}29.57417\hfill \end{array}$
42	1418	1210.256	$\begin{array}{l}207.7436\hfill \end{array}$
50.6	1502	1416.881	$\begin{array}{l}85.11943\hfill \end{array}$
42	1256	1210.256	$\begin{array}{l}45.7436\hfill \end{array}$
40.3	1189	1169.412	$\begin{array}{l}19.58792\hfill \end{array}$
33.1	913	996.4244	$\begin{array}{l}-83.4244\hfill \end{array}$
42.4	1124	1219.867	$\begin{array}{l}-95.8668\hfill \end{array}$
34.5	1052	1030.061	$\begin{array}{l}21.9391\hfill \end{array}$
51.1	1347	1428.894	$\begin{array}{l}-81.8936\hfill \end{array}$
41.2	1204	1191.036	$\begin{array}{l}12.96446\hfill \end{array}$

From the table, the point $\left(42,1418\right)$ has the largest residual. Since this point deviate greatly from a line, it is an outlier.

Conclusion:

Therefore, the point $\left(42,1418\right)$ has the largest residual