Chapter 5.9, Problem 11AYU

(a)

To determine

To find: The scatter diagram of the given data by the use of age as the independent variable and total cholesterol as the dependent variable.

Answer to Problem 11AYU

The required plot is shown in Figure 1

Explanation of Solution

Given:

The given table is shown in table 1

Table 1

Age(x)	Total Cholesterol (y)
27	189
40	205
50	215
60	210
70	210
80	194

Calculation:

Consider the cholesterol as the dependent variable then the scatter plot for the function is shown in Figure 1

  

Figure 1

(b)

To determine

To find: The exponential model from the given data.

Answer to Problem 11AYU

The open curve on one side represents that it is a quadratic function with polynomial of degree 2.

Explanation of Solution

From the graph shown in Figure 1, graph seems to increasing and decreasing function and the open curve on one side represents that it is a quadratic function with polynomial of degree 2.

(c)

To determine

To find: The expression for the best fit model.

Answer to Problem 11AYU

The required model is $y=-0.031x^2+3.44x+118.25$ .

Explanation of Solution

From the scatter plot shown in Figure 1, the best fit model is,

  $y=-0.031x^2+3.44x+118.25$

(d)

To determine

To find: The scatter plot for the best fit model.

Answer to Problem 11AYU

The best fit model is shown in Figure 2

Explanation of Solution

Consider the best fit model is,

  $y=-0.031x^2+3.44x+118.25$

The required plot is shown in Figure 2

  

Figure 2

(e)

To determine

To find: The cholesterol of a 35 year old male.

Answer to Problem 11AYU

Thecholesterol is $200.675$ .

Explanation of Solution

Consider the best fit model is,

  $y=-0.031x^2+3.44x+118.25$

Then,

  $\begin{array}{c}y=-0.031{\left(35\right)}^2+3.44\left(35\right)+118.25\\ =200.675\end{array}$