Chapter 4.5, Problem 13E

To determine

To find: An equation of the line of best fit for the given data and to further identify and interpret the correlation coefficient.

Answer to Problem 13E

  $\text{Line of best fit is y= 1}\text{.38x + 15}\text{.68}$ .

  $\text{Correlation Coefficient (r)= 0}\text{.99}$ .

Explanation of Solution

Given information: Graphing calculator should be used to work on given data.

Calculation:

After entering the data in the graphing calculator, values are calculated as follows,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= 1}\text{.3785714285714286}\\ \text{ b= 15}\text{.678571428571429}\\ {\text{ r}}^2\text{= 0}\text{.9973047506001835}\\ \text{ r= 0}\text{.9986514660281551}\end{array}$

As $y=ax+b$ ,

Rounding and substituting the values in slope-intercept form,

  $\text{Line of best fit is y= 1}\text{.38x + 15}\text{.68}$ .

Interpretation:

From the results outputted by graphing calculator,

  $\text{Correlation Coefficient (r)= 0}\text{.99}$

As $r$ is near about $\text{1}$ , $\therefore$ there is a strong positive correlation between data values and points lie around a positive slope.