Chapter 1.7, Problem 31E

a.

To determine

To graph: the data on the scatter plot.

Answer to Problem 31E

  

Explanation of Solution

Given information:

The table of values given is as follows:

Workers 16 years and older	Percent of workers using public transportation
3183088	53.4
1629096	10.5
1181677	29.7
772957	6.5
640577	28.7
560913	4.2
500566	6.7
473966	3.3
400932	3.5
395551	4.9
382309	33.5
362777	3.3
325054	10.7
312958	2.7
307679	22.0

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 31E

  $y=-0.000079x+46.41$

Explanation of Solution

Given information:

The table of values given is as follows:

Workers 16 years and older	Percent of workers using public transportation
3183088	53.4
1629096	10.5
1181677	29.7
772957	6.5
640577	28.7
560913	4.2
500566	6.7
473966	3.3
400932	3.5
395551	4.9
382309	33.5
362777	3.3
325054	10.7
312958	2.7
307679	22.0

Calculation:

Let’s select any two ordered pair like $\left(307679,22.0\right)$ and $\left(500566,6.7\right)$ . Plug in the values in the slope equation and solve m as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{6.7-22.0}{500566-307679}\\ =\frac{-15.3}{192887}\\ =-0.00007932804479701353\end{array}$

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

  $\begin{array}{c}y=mx+b\\ 22.0=\left(-0.00007932804479701353\right)307679+b\\ 22.0=-24.407573495100+b\\ b=22.0+24.407573495100\\ =46.41\end{array}$

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

  $\begin{array}{l}y=mx+b\\ y=-0.000079x+46.41\end{array}$

Thus, the line equation is $y=-0.000079x+46.41$ .

c.

To determine

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

Answer to Problem 31E

  $\begin{array}{c} y=4.5535172668186+\left(1.358669136733{\rm E}-5\right)x\\ r=0.68354065326125\end{array}$

Explanation of Solution

Given information:

The table of values given is as follows:

Workers 16 years and older	Percent of workers using public transportation
3183088	53.4
1629096	10.5
1181677	29.7
772957	6.5
640577	28.7
560913	4.2
500566	6.7
473966	3.3
400932	3.5
395551	4.9
382309	33.5
362777	3.3
325054	10.7
312958	2.7
307679	22.0

Calculation:

The graph for the above equation is as follows:

  

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

  $y=4.5535172668186+\left(1.358669136733{\rm E}-5\right)x$

Using the graphing calculator, the correlation coefficient comes out to be, $r=0.68354065326125$

d.

To determine

To find: the percentage of worker using public transports in Baltimore, Maryland and explain whether the prediction is reliable.

Answer to Problem 31E

  $\approx 8.7$

Prediction is not reliable.

Explanation of Solution

Given information:

The table of values given is as follows:

Workers 16 years and older	Percent of workers using public transportation
3183088	53.4
1629096	10.5
1181677	29.7
772957	6.5
640577	28.7
560913	4.2
500566	6.7
473966	3.3
400932	3.5
395551	4.9
382309	33.5
362777	3.3
325054	10.7
312958	2.7
307679	22.0

  $\begin{array}{c} y=4.5535172668186+\left(1.358669136733{\rm E}-5\right)x\\ r=0.68354065326125\end{array}$

Calculation:

The equation of regression line shows strong relationship because $0.75\le r\le 1$ .

Plugging $x=307679$ into the regression formula and evaluate y as follows:

  $\begin{array}{c} y=4.5535172668186+\left(1.358669136733{\rm E}-5\right)x\\ y=4.5535172668186+\left(1.358669136733{\rm E}-5\right)\left(307679\right)\\ =4.5535172668186+4.1803396132087\\ = 8.733856880027328\\ \approx 8.7\end{array}$

Since the actual value of Baltimore is listed as 22.0, the prediction from the equation for the regression line is not very reliable.