Chapter 10, Problem 29E

(a)

To determine

To find: the re-expression to create a suitable model.

Explanation of Solution

Given:

Age	Years left
10	60.3
20	50.7
30	41.8
40	32.9
50	24.8
60	17.9
70	12.1
80	7.9
90	5
100	3

Calculation:

Re-expressing the data. Taking the root of year left

Age	Years left	$\sqrt{yearleft}$
10	60.3	7.765307463
20	50.7	7.120393248
30	41.8	6.46529195
40	32.9	5.73585216
50	24.8	4.979959839
60	17.9	4.23083916
70	12.1	3.478505426
80	7.9	2.810693865
90	5	2.236067977
100	3	1.732050808

Graph:

Scatter Plot:

  

Data analysis

Data > Data analysis > Regression

Step 1. Enter data in excel spreadsheet

Step 2. Click on Data > Data analysis > Regression.

Step 3. Select input Y and X range

Step 4. Click Ok

This is the obtained output

  

By seeing the scatter plot, it looks that there is strong linear data between age and root of year left. And the regression equation is

  $\sqrt{yearleft}=-0.0693\left(Age\right)+8.465$

And the

R-squared value is 0.998 which represents that 99.8 percent of the variability in the root of number of year left is estimated for the model.

(b)

To determine

To Explain: the prediction of the lifespan of the 18-year-old black man.

Answer to Problem 29E

52.09

Explanation of Solution

Given:

Year = 18

Calculation:

  $\begin{array}{c}\sqrt{yearleft}=-0.0693\left(Age\right)+8.465\\ =-0.0693\left(18\right)+8.465\\ =-1.2474+8.465\\ =7.2176\\ yearleft={7.2176}^2\\ =52.09\end{array}$

(c)

To determine

To Explain: the satisfaction of the relation between years left and age.

Explanation of Solution

Given:

Age	Years left
10	60.3
20	50.7
30	41.8
40	32.9
50	24.8
60	17.9
70	12.1
80	7.9
90	5
100	3

Graph:

  

By seeing the residual plot, it represents the model is not fit the data well, therefore, this is not satisfying this model.