Chapter 1.7, Problem 32E

a.

To determine

To calculate:

Equation and correlation coefficient for given graphs.

Answer to Problem 32E

Correlation coefficients that represents the graph $\left(iii\right)$ is $0.973$ , graph $\left(ii\right)$ is $0.624$ , and the graph $\left(i\right)$ is $-0.986$ .

Explanation of Solution

Given information:

  

  $\begin{array}{l}y=0.68x+2.7\\ y=0.41x+2.7\\ y=-0.62x+10.0\\ r=0.973\\ r=-0.986\\ r=0.624\end{array}$

Calculation:

Consider the first equation,

  $y=0.68x+2.7$

Now plot a scatter plot for the equation $y=0.68x+2.7$ ,

  

From the above graph it is observed that the it is same as the graph in option $\left(iii\right)$

Thus, equation $y=0.68x+2.7$ represents the graph $\left(iii\right)$

Also, slope of the equation $y=0.68x+2.7$ is most positive, thus the correlation coefficients that represents the graph $\left(iii\right)$ is $0.973$ .

Now, consider the second equation,

  $y=0.41x+2.7$

Now plot a scatter plot for the equation $y=0.41x+2.7$ ,

  

From the above graph it is observed that the it is same as the graph in option $\left(ii\right)$

Thus, equation $y=0.41x+2.7$ represents the graph $\left(ii\right)$

Also, slope of the equation $y=0.41x+2.7$ is second most positive, thus the correlation coefficients that represents the graph $\left(ii\right)$ is $0.624$ .

Now, consider the third equation,

  $y=-0.62x+10.0$

Now plot a scatter plot for the equation $y=-0.62x+10.0$ ,

  

From the above graph it is observed that it is same as the graph in option $\left(i\right)$

Thus, equation $y=-0.62x+10.0$ represents the graph $\left(i\right)$

Also, slope of the equation $y=-0.62x+10.0$ is negative, thus the correlation coefficients that represents the graph $\left(i\right)$ is $-0.986$

b.

To determine

To calculate:

Model that best fit for its data according to correlation coefficient.

Answer to Problem 32E

Model equation $y=-0.62x+10.0$ fits the data well.

Explanation of Solution

Given information:

  

  $\begin{array}{l}y=0.68x+2.7\\ y=0.41x+2.7\\ y=-0.62x+10.0\\ r=0.973\\ r=-0.986\\ r=0.624\end{array}$

Calculation:

According to the correlation coefficient, model number $3$ fits the data well which represents $y=-0.62x+10.0$ equation as it has closet $\left|r\right|\le 1$