PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
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Chapter P.4, Problem 54E
Solution

a.

The scatter plot of given data.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 54E , additional homework tip 1

Given:

The table shows world population in millions,

    Time (Years)U.S. Exports (billions of dollars)
    2005211.9
    2010249.3
    2012292.7
    2013300.8
    2014312.8
    2015280.6

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

The scatter plot of the given data is shown below:

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 54E , additional homework tip 2

b.

The linear equation that gives the U.S Exports y , in terms of the years x using the year 2005 and 2015.

  y=6.87x−2005+211.9

Given:

The table shows world population in millions,

    Time (Years)U.S. Exports (billions of dollars)
    2005211.9
    2010249.3
    2012292.7
    2013300.8
    2014312.8
    2015280.6

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to find the linear equation, first find the slope of the line using the points 0,4453 and 30,6972 as shown below

  m=y2−y1x2−x1=6972−445330−0=251930≈84

Now, substitute m=6.87 and x1,y1=2005,211.9 into the point-slope form of the line and simplify further as shown below

  y−y1=mx−x1y−211.9=6.87x−2005y=6.87x−2005+211.9

Thus, the linear equation for world population is y=6.87x−2005+211.9 .

The graph of the equation y=6.87x−2005+211.9 is shown on the scatter plot of the data below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 54E , additional homework tip 3

c.

The U.S. export in 2020 using the equation.

  $314.95 billion

Given:

The linear equation for U.S. export is y=6.87x−2005+211.9 .

Concept Used:

  • The slope-intercept form of a line is y=mx+b, where m is the slope of the line and b is the y -intercept of the line.
  • Slope of the line passing through the points x1,y1 and x2,y2 is given by m=y2−y1x2−x1
  • The slope of a line is defined as rise over run

Calculation:

In order to predict the world population in 2020, draw a vertical line at x=2020 and locate the intersection point with the line as shown below

  y=6.87x−2005+211.9y=6.872020−2005+211.9y=6.8715+211.9y=314.95

Thus, the U.S. export to Canada in 2020 is $314.95 billion .

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Chapter P.4, Problem 53E
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Chapter P.4, Problem 55E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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