Chapter 4.5, Problem 29E

a.

To determine

To predict: The total number of people who reported earthquake after $9and15$ minutes of its happening.

Answer to Problem 29E

  $2864$ people reported after $\text{9 minutes}$ .

  $5150$ people reported after $\text{15 minutes}$ .

Explanation of Solution

Given information: Table of data values from exercise $17$ .

Calculation:

Using a graphing calculator to find an equation of line of best fit, results are,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= 381}\text{.07142857142856}\\ \text{ b= -565}\text{.7142857142857}\\ {\text{ r}}^2\text{= 0}\text{.9778615503013061}\\ \text{ r= 0}\text{.9888688236067037}\end{array}$

As $y=ax+b$, Equation is $y=381.07x-565.71$ .

Putting $x=9$ in above stated equation,

  $\begin{array}{l}y=381.07(9)-565.71\\ y\approx 2864\end{array}$

Thus, $2864$ people reported after $\text{9 minutes}$ .

Putting $x=15$ in above stated equation,

  $\begin{array}{l}y=381.07(15)-565.71\\ y\approx 5150\end{array}$

Thus, $5150$ people reported after $\text{15 minutes}$ .

b.

To determine

To predict: The total number of people who reported earthquake after $9and15$ minutes of its happening.

Answer to Problem 29E

The model is fairly accurate for the values not far removed from the known range, but for values far removed from the known range e,g. $15$ the model’s accuracy is very low and thus model becomes unreliable.

Explanation of Solution

Given information: Table of data values from exercise $17$ . Extrapolations of part $a$ .

Calculation:

After $\text{9 minutes}$ ,

Value derived from model: $\text{2864}$

Actual Value: $\text{2750}$

Difference: $2864-2750=114$

After $\text{15 minutes}$ ,

Value derived from model: $5150$

Actual Value: $3200$

Difference: $5150-3200=1950$

The model gave a close rough estimate of the amount of people of reported after $\text{9 minutes}$ but for the amount of people who reported after $\text{15 minutes}$ estimate greatly varies with respect to the actual value.

Thus, the model is fairly accurate for the values not far removed from the known range, but for values far removed from the known range e,g. $15$ the model’s accuracy is very low and thus model becomes unreliable.