Chapter 1.3, Problem 21E

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 21E

Equation of the line of best fit is $y=-0.45x+4.26$ , $r$ is $-0.668$ , 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 $(1,4),(2,3),(3,2),(3,4),$

  $(4,2),(4,3)and(5,2)$ ,

Using the linear regression feature of the graphing utility,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= -0}\text{.4473684210526316}\\ \text{ b= 4}\text{.2631578947368425}\\ {\text{ r}}^2\text{= 0}\text{.4473684210526316}\\ \text{ r= -0}\text{.6688560540599386}\end{array}$

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

Equation is $y=-0.45x+4.26$

Graph:

  

Interpretation:

Correlation coefficient $(r)$ is $-0.668$ , as $r$ is inclined towards $-1$ , points lie around a negative slope.

Thus, equation of the line of best fit is $y=-0.45x+4.26$ , $r$ is $-0.668$ , points lie around a negative slope.