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 53E
Solution

a.

The scatter plot when x=0 represents 1980 and x=1 represents 1981.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 53E , additional homework tip 1

Given:

The table shows world population in millions,

    YearPopulation (millions)
    19804453
    19905285
    20006085
    20106972
    20137130

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 53E , additional homework tip 2

b.

The linear equation that gives the population y , in terms of the years x using the year 1980 and 2010.

  y=84x+4453

Given:

The table shows world population in millions,

    YearPopulation (millions)
    19804453
    19905285
    20006085
    20106972
    20137130

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=84 and x1,y1=0,4453 into the point-slope form of the line and simplify further as shown below

  y−y1=mx−x1y−4453=84x−0y=84x+4453

Thus, the linear equation for world population is y=84x+4453 .

The graph of the equation y=84x+4453 is shown on the scatter plot of the data below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 53E , additional homework tip 3

c.

The midyear world population in 2020 using the graph.

  7813 million

Given:

The linear equation for world population is y=84x+4453 .

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=40 and locate the intersection point with the line as shown below

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter P.4, Problem 53E , additional homework tip 4

Thus, the midyear world population in 2020 is 7813 million .

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Chapter P.4, Problem 52E
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Chapter P.4, Problem 54E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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