Chapter 1.3, Problem 20E

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 20E

Equation of the line of best fit is $y=0.88x+1.69$ , $r$ is $0.8846$ , points lie around a positive 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 $(1,2),(1,3),(2,3),(2,4),$

  $(3,4),(3,5)and(4,5)$ ,

Using the linear regression feature of the graphing utility,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= 0}\text{.8846153846153846}\\ \text{ b= 1}\text{.6923076923076923}\\ {\text{ r}}^2\text{= 0}\text{.7825443786982248}\\ \text{ r= 0}\text{.8846153846153846}\end{array}$

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

Equation is $y=0.88x+1.69$

Graph:

  

Interpretation:

Correlation coefficient $(r)$ is $0.8846$ , as $r$ is inclined towards $1$ , points lie around a positive slope.

Thus, equation of the line of best fit is $y=0.88x+1.69$ , $r$ is $0.8846$ , points lie around a positive slope.