Learn to create and interpret scatter plots and find the line of best fit.

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5.4 Scatter Plots
Learn to create and interpret scatter plots and
find the line of best fit.
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A scatter plot shows relationships between two
sets of data.
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Example 1
Making a Scatter Plot of a Data Set
Use the given data to make a scatter plot of the
weight and height of each member of a basketball
team.
The points on the scatter plot are (71, 170),
(68, 160), (70, 175), (73, 180), and (74, 190).
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Correlation describes the type of relationship
between two data sets. The line of best fit is
the line that comes closest to all the points on
a scatter plot. One way to estimate the line of
best fit is to lay a rulers edge over the graph
and adjust it until it looks closest to all the
points.
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No correlation
Negative correlation as one data set increases,
the other decreases.
Positive correlation both data sets increase
together.
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Finding the Line of BEST Fit

• Usually there is no single line that passes
  through all the data point, so you try to find
  the line that best fits the data.
• Step 1 using a ruler, place it on the graph to
  find where the edge of the ruler touches the most
  points.
• Step 2 Draw in the line. Make sure it touches
  at least 2 points.

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Finding the Line of BEST Fit (continued)

• Step 3 Find the slope between two points
• Step 4 Substitute that into slope-intercept
  form of an equation and solve for b.
• Step 5 Write the equation of the line in
  slope-intercept form.

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Practice Problem The Olympic Games Discus Throw

• Year Winning throw
• 1908 134.2
• 1912 145.1
• 1920 146.6
• 1924 151.4
• 1928 155.2
• 1932 162.4
• 1936 165.6
• 1948 173.2
• 1952 180.5
• 1956 184.9
• 1960 194.2
• 1964 200.1
• 1968 212.5
• 1972 211.4
• 1976 221.5
• 1980 218.7
• 1984 218.5
• 1988 225.8

The Olympic games discus throws from 1908 to 1996
are shown on the table. Approximate the best -
fitting line for these throws let x represent the
year with x 8 corresponding to 1908. Let y
represent the winning throw.
View scatter plot on handout.
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Step 1 2 Place your ruler on the page and
draw a line where it touches the most points on
the graph.
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Step 3 Find the slope between 2 points on the
line.

• The line went right through the point at 1960 and
  1988.
• The ordered pairs for these points are (60,
  194.2) and (88, 225.8).
• m y2 y1 225.8 194.2 31.6 32
  8 x2 x1 88 60
  28 28 7
• m 8 7

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Step 4 Find the y-intercept.

• Substitute the slope and one point into the
  slope-intercept form of an equation.
• Slope 8/7 and point (88, 225.8)
• y mx b225.8 8/7(88) b
• 225.8 704/7 b
• 225.8 100.6 b-100.6 -100.6
• 125.2 b

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Step 5 Write in slope-intercept form.

• Substitute each value into y mx b.
• The equation of the line of best fit isy 8/7
  x 125.2
• When you solve these problems, you can get
  different answers for the line of best fit if you
  choose different points. But the equations
  should be close.