Chapter 1.6, Problem 9E

a.

To determine

To graph: the data on the scatter plot.

Answer to Problem 9E

  

Explanation of Solution

Given information:

The table of values given is as follows:

Acorn size in cm3 (x)	Range in 100 km2 (y)
0.3	233
0.9	7985
1.1	10161
2.0	17042
3.4	7900
4.8	3978
8.1	28389
10.5	7646
17.1	?

Calculation:

The graph for the given data is shown below.

  

b.

To determine

To find: best fit line using two ordered pairs.

Answer to Problem 9E

  $y=3609.74x-849.92$

Explanation of Solution

Given information:

The table of values given is as follows:

Acorn size in cm3 (x)	Range in 100 km2 (y)
0.3	233
0.9	7985
1.1	10161
2.0	17042
3.4	7900
4.8	3978
8.1	28389
10.5	7646
17.1	?

Calculation:

Let’s select any two ordered pair like $\left(0.3,233\right)$ and $\left(8.1,28389\right)$ . Plug in the values in the slope equation and solve m as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{28389-233}{8.1-0.3}\\ =\frac{28156}{7.8}\\ =3609.74\end{array}$

Now, plug the value of m and any one point coordinate into the slope intercept equation and evaluate b as follows:

  $\begin{array}{c}y=mx+b\\ 233=\left(3609.74\right)\left(0.3\right)+b\\ 233=\text{1082}\text{.922}+b\\ b=233-\text{1082}\text{.922}\\ =-849.92\end{array}$

Now, plug the values of m and b in the slope intercept formula as follows:

  $\begin{array}{l}y=mx+b\\ y=3609.74x-849.92\end{array}$

Thus, the line equation is $y=3609.74x-849.92$ .

c.

To determine

To find: the equation for regression line and correlation value using the graphing calculator.

Answer to Problem 9E

  $\begin{array}{c} y=6973.1416998759+885.81563990331x\\ r=0.37562233185356\end{array}$

Explanation of Solution

Given information:

The table of values given is as follows:

Acorn size in cm3 (x)	Range in 100 km2 (y)
0.3	233
0.9	7985
1.1	10161
2.0	17042
3.4	7900
4.8	3978
8.1	28389
10.5	7646
17.1	?

Calculation:

The graph for the above equation is as follows:

  

Using the graphing calculator, the regression line equation is as follows:

  $y=6973.1416998759+885.81563990331x$

Using the graphing calculator, the correlation coefficient comes out to be, $r=0.37562233185356$

d.

To determine

To find: the missing value if regression line equation has strong or moderate relationship, and explains whether the prediction is reliable.

Answer to Problem 9E

  $\approx 22121$

Prediction is unreliable.

Explanation of Solution

Given information:

The table of values given is as follows:

Acorn size in cm3 (x)	Range in 100 km2 (y)
0.3	233
0.9	7985
1.1	10161
2.0	17042
3.4	7900
4.8	3978
8.1	28389
10.5	7646
17.1	?

  $\begin{array}{c} y=6973.1416998759+885.81563990331x\\ r=0.37562233185356\end{array}$

Calculation:

Plugging $x=17.1$ into the regression formula and evaluate y as follows:

  $\begin{array}{c} y=6973.1416998759+885.81563990331x\\ =6973.1416998759+885.81563990331\left(17.1\right)\\ =6973.1416998759+\text{15147}\text{.4474423466}\\ =22120.589142222503\\ \approx 22121\end{array}$

The equation of regression line shows weak relationship because $0<r\le 0.5$ . So, the predicted value is unreliable.