Chapter 1.6, Problem 10E

a.

To determine

To graph: the data on the scatter plot.

Answer to Problem 10E

  

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Percentage of women in Professional Jobs (y)
1986	23.7
1990	26.2
1993	28.3
1994	28.7
1995	29.4
1996	30.3
1997	30.8
2002	37.1
2003	37.6
2008	?

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 10E

  $y=0.625x+1976.3125$

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Percentage of women in Professional Jobs (y)
1986	23.7
1990	26.2
1993	28.3
1994	28.7
1995	29.4
1996	30.3
1997	30.8
2002	37.1
2003	37.6
2008	?

Calculation:

Let’s select any two ordered pair like $\left(1993,28.3\right)$ and $\left(1997,30.8\right)$ . Plug in the values in the slope equation and solve m as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{30.8-28.3}{1997-1993}\\ =\frac{2.4}{4}\\ =0.625\end{array}$

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

  $\begin{array}{c}y=mx+b\\ 1993=\left(0.625\right)\left(28.3\right)+b\\ 1993=17.6875+b\\ b=1993-17.6875\\ =1976.3125\end{array}$

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

  $\begin{array}{l}y=mx+b\\ y=0.625x+1976.3125\end{array}$

Thus, the line equation is $y=0.625x+1976.3125$ .

c.

To determine

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

Answer to Problem 10E

  $\begin{array}{c} y=0.84131067961463x-1648.2749514622\\ r=0.98352925215696\end{array}$

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Percentage of women in Professional Jobs (y)
1986	23.7
1990	26.2
1993	28.3
1994	28.7
1995	29.4
1996	30.3
1997	30.8
2002	37.1
2003	37.6
2008	?

Calculation:

The graph for the above equation is as follows:

  

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

  $y=0.84131067961463x-1648.2749514622$

Using the graphing calculator, the correlation coefficient comes out to be, $r=0.98352925215696$

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 10E

  $\approx 41$

Prediction is unreliable.

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Percentage of women in Professional Jobs (y)
1986	23.7
1990	26.2
1993	28.3
1994	28.7
1995	29.4
1996	30.3
1997	30.8
2002	37.1
2003	37.6
2008	?

  $\begin{array}{c} y=0.84131067961463x-1648.2749514622\\ r=0.98352925215696\end{array}$

Calculation:

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

Plugging $x=2008$ into the regression formula and evaluate y as follows:

  $\begin{array}{c} y=0.84131067961463x-1648.2749514622\\ y=0.84131067961463\left(2008\right)-1648.2749514622\\ =\text{1689}\text{.34404666177}-1648.2749514622\\ = 41.07689320397708\\ \approx 41\end{array}$

If 100% or more than that hold professional job, then there will be no women working for minimum wages. Only men will be working doing low wages jobs. The another possibility is that less and less women will hold jobs over the years. Unemployment will skyrocket and the few women who still have jobs, have managerial or professional jobs.

But this still doesn't account for the fact that the percentage will be larger than 100 fairly quickly. The regression line is completely unreliable, so any predictions made from it are also unreliable.