a. Answer y = 72.695 x + 721.941. Explanation 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 = 72.695 x + 721.941. The graph of the linear model y = 72.695 x + 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 Explanation Given information: y = 72.695 x + 721.941. Calculation: y = 72.695 x + 721.941. For 2009 , t = 19 y ( 19 ) = 72.695 × 19 + 721.941 = 2103.146 ≈ 2103 degrees . c. To determine To find: the slope of the regression line and what does the slope represent. Answer The slope of 72.695 represents the number of degrees earned by Hispanic Americans is increasing by about 72.695 degrees per year. Explanation Given information: y = 72.695 x + 721.941. Calculation: The linear regression is y = 72.695 x + 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.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 1, Problem 66RE

To determine

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

Expert Solution

Answer to Problem 66RE

y=72.695x+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+721.941.

The graph of the linear model y=72.695x+721.941. using graphing utility is shown below.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1, Problem 66RE

To determine

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

Expert Solution

Answer to Problem 66RE

Explanation of Solution

Given information: y=72.695x+721.941.

Calculation:

y=72.695x+721.941.For 2009,t=19y(19)=72.695×19+721.941=2103.146≈2103 degrees.

To determine

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

Expert Solution

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+721.941.

Calculation:

The linear regression is y=72.695x+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.

Chapter 1, Problem 65RE

Chapter 1, Problem 67RE

Chapter 1 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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