example 7-1a determine whether the graph shows a positive correlation, a negative correlation, no...
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![Page 1: Example 7-1a Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation,](https://reader036.vdocuments.site/reader036/viewer/2022062423/5697bf721a28abf838c7eaf9/html5/thumbnails/1.jpg)
Determine whether thegraph shows a positivecorrelation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.
The graph shows average personal income forU.S. citizens.
Answer: The graph shows a positive correlation. With each year, the average personal income rose.
![Page 2: Example 7-1a Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation,](https://reader036.vdocuments.site/reader036/viewer/2022062423/5697bf721a28abf838c7eaf9/html5/thumbnails/2.jpg)
Determine whether thegraph shows a positivecorrelation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.
The graph shows the average students per computer in U.S. public schools.
Answer: The graph shows a negative correlation. With each year, more computers are in the schools, making the students per computer rate smaller.
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Determine whether each graph shows a positivecorrelation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.
a. The graph shows thenumber of mail-order prescriptions.
Answer: Positive correlation; with each year, the number of mail-order prescriptions has increased.
![Page 4: Example 7-1a Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation,](https://reader036.vdocuments.site/reader036/viewer/2022062423/5697bf721a28abf838c7eaf9/html5/thumbnails/4.jpg)
Determine whether each graph shows a positivecorrelation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.
Answer: no correlation
b. The graph shows thepercentage of voterparticipation in Presidential Elections.
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The table shows the world population growing at a rapid rate.
Year Population (millions)1650 500
1850 1000
1930 2000
1975 4000
1998 5900
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Draw a scatter plotand determine whatrelationship exists, if any, in the data.
Let the independentvariable x be the yearand let the dependentvariable y be thepopulation (in millions).
The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables.
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Draw a line of fit for the scatter plot.
No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot.
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Write the slope-intercept form of an equation for equation for the line of fit.
The line of fit shown passes through the data points (1850, 1000) and (1998, 5900).
Step 1 Find the slope.
Slope formula
Letand
Simplify.
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Step 2 Use m = 33.1 and either the point-slope form or the slope-intercept form to write the equation.You can use either data point. We chose (1850, 1000).
Point-slope form Slope-intercept form
Answer: The equation of the line is .
![Page 10: Example 7-1a Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation,](https://reader036.vdocuments.site/reader036/viewer/2022062423/5697bf721a28abf838c7eaf9/html5/thumbnails/10.jpg)
Check Check your result by substituting (1998, 5900) into
Line of fitequation
Subtract.
The solution checks.
Replace x with 1998 and y with 5900.
Multiply.
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The table shows the number of bachelor’s degrees received since 1988.
Years Since 1988 2 4 6 8 10
Bachelor’s Degrees Received (thousands)
1051 1136 1169 1165 1184
Source: National Center for Education Statistics
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a. Draw a scatter plot and determine what relationship exists, if any, in the data.
Answer: The scatter plot seems to indicate that as the number of years increase, the number of bachelor’s degrees received increases. There is a positive correlation between the two variables.
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b. Draw a line of best fit for the scatter plot.
c. Write the slope-intercept form of an equation for the line of fit.
Answer: Using (4, 1137) and (10, 1184),
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Use the prediction equationwhere x is the year and y is the population (in millions), to predict the world population in 2010.
Original equation
Replace x with 2010.
Simplify.
Answer: 6,296,000,000
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Use the equation where x is the years since 1988 and y is the number of bachelor’s degrees (in thousands), to predict the number of bachelor’s degrees that will be received in 2005.
Answer: 1,204,000