Chapter 4.5, Problem 17E

a.

To determine

To write:An equation of line of best fit for given data and to further graph the points and plot the line.

Answer to Problem 17E

Equation of line of best fit is $\text{y= 381x - 565}\text{.71}$ .

Explanation of Solution

Given Information: Data values of minutes, $x$ and number of people, $y$ is given.

Calculation:

Entering the data and using the linear regression feature in the graphing calculator,

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

As $y=ax+b$ ,

thus, equation of line of best fit is $\text{y= 381x - 565}\text{.71}$ .

Graph:

  

b.

To determine

To identify:The correlation coefficient and to further interpret it.

Answer to Problem 17E

  $r$ is $0.988$ .

Data values have strong positive correlation.

Explanation of Solution

Given information:Graphing calculator display from the previous part.

Interpretation:

From the graphing calculator display in the previous part, it can be inferred that correlation coefficient $r$ is $0.988$ . Value of r is near $1$ , this implies that data values have strong positive correlation and the points lie around a positive slope.

c.

To determine

To interpret:The slope and $y-\mathrm{int}ercept$ of the line of best fit.

Answer to Problem 17E

Slope is positive and is 381.

Line of best fit crosses the $y-axis$ at $\text{- 565}\text{.71}$ , however, in this case it has no significance.

Explanation of Solution

Given Information:Graphing calculator display from previous part.

Interpretation:

From the graphing calculator display shown in part $(a)$ , it can be inferred that slope $a$ is $\text{381}$ , this implies that slope is positive and its high magnitude indicates that it is very steep. ( $y$ increases sharply w.r.t. to $x$ when moved along $x-axis$ ).

It interprets that number of reports might increase by 381 per minute after the earthquake ended.

  $y-\mathrm{int}ercept(b)$ is $\text{- 565}\text{.71}$ , this means that line of best fit crosses the $y-axis$ at $\text{- 565}\text{.71}$ . However, since number of people cannot be negative, $\therefore$ it has no significance in this case.