Chapter 4.4, Problem 3CYU

a.

To determine

If the graph shows a positive, negative or no correlation by drawing a graph of scatter plot.

Explanation of Solution

Given information:

The table shows the median age of females when they were first married.

Year	Age
2001	25.1
2002	25.3
2003	25.3
2004	25.3
2005	25.5
2006	25.9
2007	26
2008	26.2
2009	26.5
2010	26.7
2011	26.9

Calculations:

Here the graph of year versus age is drawn.

  

Here the graph shows a positive correlation. In the graph of positive correlation, as the X-parameter increases, the Y-parameter also increases. Here in this graph the age is shown in X-axis and year is shown in Y-axis. So as the year increases the age also increases. So the graph shows a positive correlation.

b.

To determine

A line of fit for the scatter plot.

Explanation of Solution

Given information:

The table shows the median age of females when they were first married.

Year	Age
2001	25.1
2002	25.3
2003	25.3
2004	25.3
2005	25.5
2006	25.9
2007	26
2008	26.2
2009	26.5
2010	26.7
2011	26.9

Calculations:

Here the graph of year versus age is drawn.

  

Here the graph shows a positive correlation. In the graph of positive correlation, as the X-parameter increases, the Y-parameter also increases. Here in this graph the age is shown in X-axis and year is shown in Y-axis. So as the year increases the age also increases. So the graph shows a positive correlation. Here line of fit for the scatter plot is drawn.

c.

To determine

An equation in slope intercept form for the line in fit.

Explanation of Solution

Given information:

The table shows the median age of females when they were first married.

Year	Age
2001	25.1
2002	25.3
2003	25.3
2004	25.3
2005	25.5
2006	25.9
2007	26
2008	26.2
2009	26.5
2010	26.7
2011	26.9

Calculations:

Here the graph of year versus age is drawn.

  

Here the graph shows a positive correlation. In the graph of positive correlation, as the X-parameter increases, the Y-parameter also increases. Here in this graph the age is shown in X-axis and year is shown in Y-axis. So as the year increases the age also increases. So the graph shows a positive correlation. Here line of fit for the scatter plot is drawn.

Equation of the line of line in fit is,

  $\begin{array}{l}\mathrm{Y}=\mathrm{m}\mathrm{x}+\mathrm{c}\\ \mathrm{m}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}=\frac{26.9-25.1}{2011-2001}=\frac{1.8}{10}=0.18\\ \mathrm{N}\mathrm{o}\mathrm{w},\\ \mathrm{y}-{\mathrm{y}}_1=\mathrm{m}(\mathrm{x}-{\mathrm{x}}_1)\\ \mathrm{y}-25.1=0.18(\mathrm{x}-2001)\\ \mathrm{y}=0.18\mathrm{x}-335.08\end{array}$

So the equation is $\mathrm{y}=0.18\mathrm{x}-335.08$ .

d.

To determine

The median age of females when they are first married in the year $2026$

Explanation of Solution

Given information:

The table shows the median age of females when they were first married.

Year	Age
2001	25.1
2002	25.3
2003	25.3
2004	25.3
2005	25.5
2006	25.9
2007	26
2008	26.2
2009	26.5
2010	26.7
2011	26.9

Calculations:

Here the graph of year versus age is drawn.

  

Here the graph shows a positive correlation. Here line of fit for the scatter plot is drawn.

Equation of the line of line in fit is,

  $\begin{array}{l}\mathrm{Y}=\mathrm{m}\mathrm{x}+\mathrm{c}\\ \mathrm{m}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}=\frac{26.9-25.1}{2011-2001}=\frac{1.8}{10}=0.18\\ \mathrm{N}\mathrm{o}\mathrm{w},\\ \mathrm{y}-{\mathrm{y}}_1=\mathrm{m}(\mathrm{x}-{\mathrm{x}}_1)\\ \mathrm{y}-25.1=0.18(\mathrm{x}-2001)\\ \mathrm{y}=0.18\mathrm{x}-335.08\end{array}$

So the equation is $\mathrm{y}=0.18\mathrm{x}-335.08$ .

Now to get the age of females in year $2026$ we have take $\mathrm{x}=2026$ in the equation and find the value of y.

Thus,

  $\begin{array}{l}\mathrm{y}=0.18\mathrm{x}-335.08\\ \mathrm{y}=0.18(2026)-335.08\\ \mathrm{y}=364.68-335.08\\ \mathrm{y}=29.60\end{array}$

Thus the median age of females when they are first married in the year $2026$ is $29.60\mathrm{y}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{s}.$