Statistics: Scatter Plots and Lines of Fit

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Lesson 5-7

• Statistics Scatter Plots and Lines of Fit

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Transparency 7
Click the mouse button or press the Space Bar to
display the answers.
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Transparency 7a
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Objectives

• Interpret points on a scatter plot
• Write equations for lines of fit

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Vocabulary

• Scatter plot Two sets of data plotted as
  ordered pairs in a coordinate plane
• Positive correlation in a scatter plot, as x
  increases, y increases
• line of fit a line that describes the trend of
  the data in a scatter plot
• Best-fit line The line that most closely
  approximates the data in a scatter plot
• Linear interpolation The use of a linear
  equation to predict values that are inside of the
  data range
• Negative correlation in a scatter plot, as x
  increases, y decreases

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x-y Coordinate Plane
Quadrants
Point Plotting
I
II
up 7
left 4
right 5
III
IV
down 8
(x, y) (-4, 7) (5, -8) x left or
right y up or down
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Example 1a
Determine whether the graph shows a positive
correlation, a negative correlation, no
correlation. If there is a positive or negative
correlation, describe it.
The graph shows average personal income for U.S.
citizens.
Answer The graph shows a positive correlation.
With each year, the average personal income rose.
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Example 1b
Determine whether the graph shows a positive
correlation, 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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Example 2a
The table shows the world population growing at a
rapid rate.
Year Population (millions)
1650 500
1850 1000
1930 2000
1975 4000
1998 5900
Draw a scatter plot and determine what
relationship exists, if any, in the data and draw
a line of fit.
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Example 2a cont
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.
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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Example 2b
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.
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Example 2b cont
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
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Example 3
Use the prediction equation y 33.1x 60,235
where x is the year and y is the population (in
millions), to predict the world population in
2010.
Answer 6,296,000,000
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Summary Homework

• Summary
• If y increases as x increases, then there is a
  positive correlation between x and y
• If y decreases as x increases, then there is a
  negative correlation between x and y
• If there is no relation between x and y, then
  there is no correlation between x and y
• A line of fit describes the trend of data
• You can use the equation of a line of the fit to
  make predictions about the data
• Homework
• N/A