Chapter 1.3, Problem 22E

To determine

To find: An equation of the line of best fit for given data using linear regression feature on a graphing calculator, and then to find and interpret the correlation coefficient.

Answer to Problem 22E

Equation of the line of best fit is $y=-1.04x+5.68$ , $r$ is $-0.93$ , points lie around a negative slope.

Explanation of Solution

Given information: Relevant graph with marked data points.

Calculation:

After examining the graph it can be ascertained that the points are $(1,5),(2,3),(2,4),(3,2),$

  $(3,3),(4,1)and(5,1)$ ,

Using the linear regression feature of a graphing utility,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= -1}\text{.0394736842105263}\\ \text{ b= 5}\text{.684210526315789}\\ {\text{ r}}^2\text{= 0}\text{.8736002239641658}\\ \text{ r= -0}\text{.9346658354535945}\end{array}$

Rounding the values (if needed) and substituting in the standard form,

Equation is $y=-1.04x+5.68$

Graph:

  

Interpretation:

Correlation coefficient $(r)$ is $-0.93$ , as $r$ is inclined towards $-1$ , points lie around a negative slope.

Thus, equation of the line of best fit is $y=-1.04x+5.68$ , $r$ is $-0.93$ , points lie around a negative slope.