Chapter 1.3, Problem 23E

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 23E

Equation of the line of best fit is $y=0.61x+0.097$ , $r$ is $0.946$ , 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 $(1,1),(2,1),(3,2),(4,2),$

  $(4,3),(5,3)and(6,4)$ ,

Using the linear regression feature of the graphing utility,

  $\begin{array}{l}\text{LinReg}\\ \text{ y=ax+b}\\ \text{ a= 0}\text{.6129032258064516}\\ \text{ b= 0}\text{.09677419354838714}\\ {\text{ r}}^2\text{= 0}\text{.8957816377171217}\\ \text{ r= 0}\text{.9464574146347641}\end{array}$

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

Equation is $y=0.61x+0.097$

Graph:

  

Interpretation:

Correlation coefficient $(r)$ is $0.946$ , as $r$ is inclined towards $1$ , points lie around a positive slope.

Thus, equation of the line of best fit is $y=0.61x+0.097$ , $r$ is $0.946$ , points lie around a positive slope.