Chapter 14, Problem 10T

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In the last half of the twentieth century the U.S. population grew more diverse both racially and ethnically, with persons of Hispanic origin representing one of the fastest growing segments. The table gives the percent of the U.S. civilian non-institutional population of Hispanic origin for selected years from 1980 and projected to 2050.(a) Find the linear regression line for these data. Use x = 0 to represent 1980.(b) How well does the regression line fit the data?(c) Using the linear regression equation, predict the percent of the U.S. civilian non-institutional population of Hispanic origin in 2025. Year Percent 1980 5.7 1990 8.4 2000 10.7 2010 13.0 2015 14.1 2020 15.3 2030 17.8 2040 20.3 2050 22.8 Source: U.S. Bureau of the Census

(a)

To determine

To calculate: The linear regression line for the data given in the table.

 Year Percent 1980 5.7 1990 8.4 2000 10.7 2010 13.0 2015 14.1 2020 15.3 2030 17.8 2040 20.3 2050 22.8
Explanation

Given Information:

The table gives the percent of the U.S. civilian non-institutional population of the Hispanic origin for selected years from 1980 and projected to 2050.

 Year Percent 1980 5.7 1990 8.4 2000 10.7 2010 13.0 2015 14.1 2020 15.3 2030 17.8 2040 20.3 2050 22.8

Formula used:

According to linear regression equation, the equation of the line that is the best fit for the given data points (x1,y1),(x2,y2),â€¦,(xn,yn) is y^=a+bx, where b=âˆ‘i=1nxiâˆ‘i=1nyiâˆ’nâˆ‘i=1nxiyi(âˆ‘i=1nxi)2âˆ’nâˆ‘i=1nxi2, and a=âˆ‘i=1nyiâˆ’bâˆ‘i=1nxin.

Calculation:

Consider the table,

 Year Percent 1980 5.7 1990 8.4 2000 10.7 2010 13.0 2015 14.1 2020 15.3 2030 17.8 2040 20.3 2050 22.8

Let xi denote the years past 1980 for 1<i<9.

That is, x1=0,x2=10,x3=20,x4=30, x5=35,x6=40,x7=50,x8=60,

x9=70.

Let yi denote the population for 1<i<9.

That is, y1=5.7,y2=8.4,y3=10.7,y4=13.0, y5=14.1,y6=15.3,y7=17.8,y8=20.3,

y9=22.8

(b)

To determine

The explanation how the regression line fits the data in the table that gives the percent of the U.S. civilian non-institutional population of the Hispanic origin for selected years from 1980 and projected to 2050.

 Year Percent 1980 5.7 1990 8.4 2000 10.7 2010 13.0 2015 14.1 2020 15.3 2030 17.8 2040 20.3 2050 22.8

(c)

To determine

To calculate: The percent of the U.S. civilian non institutional population of Hispanic origin in 2025 using the reported linear regression equation for the table that gives the percent of the U.S. civilian non-institutional population of the Hispanic origin for selected years from 1980 and projected to 2050.

 Year Percent 1980 5.7 1990 8.4 2000 10.7 2010 13.0 2015 14.1 2020 15.3 2030 17.8 2040 20.3 2050 22.8

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