Chapter 1, Problem 66RE

a.

To determine

To find: a linear regression equation for the data and superimpose its graph on a scatter plot of the data.

Answer to Problem 66RE

  $y=72.695x+\mathrm{721.941.}$

Explanation of Solution

Given information: The table shows the number of doctoral degrees earned by Hispanic students for several years. Let $x=0$ represent 1990, $x=1$ represent 1991, and so forth.

Year	Number of Degrees
1990	780
2000	1305
2005	1824
2006	1882
2007	2035

Calculation:

Let $x=0$ represent 1990, $x=1$ represent 1991, and so forth, then the above table can be written as

Year	Number of Degrees
0	780
10	1305
15	1824
16	1882
17	2035

Using linear regression calculator on the above data, the linear regression model is:

  $y=72.695x+\mathrm{721.941.}$

The graph of the linear model $y=72.695x+\mathrm{721.941.}$ using graphing utility is shown below.

  

b.

To determine

To predict: predict the number of doctoral degrees earned by Hispanic Americans in 2009 using the regression equation in part (a).

Answer to Problem 66RE

Explanation of Solution

Given information: $y=72.695x+\mathrm{721.941.}$

Calculation:

  $\begin{array}{c}y=72.695x+\mathrm{721.941.}\\ \text{For}2009,t=19\\ y(19)=72.695\times 19+721.941\\ =2103.146\\ \approx 2103\text{degrees}\text{.}\end{array}$

c.

To determine

To find: the slope of the regression line and what does the slope represent.

Answer to Problem 66RE

The slope of 72.695 represents the number of degrees earned by Hispanic Americans is increasing by about 72.695 degrees per year.

Explanation of Solution

Given information: $y=72.695x+\mathrm{721.941.}$

Calculation:

The linear regression is $y=72.695x+\mathrm{721.941.}$ which has a slope of 72.695. Since the units for y are degrees and the units for x are years, the slope has units of degrees per year.

The slope of 72.695 represents the number of degrees earned by Hispanic Americans is increasing by about 72.695 degrees per year.