Download Finding the Line of BEST Fit

Scatter Plots
Learn to create and
interpret scatter plots and
find the line of best fit.
A scatter plot shows
relationships between two
sets of data.
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).
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
ruler’s edge over the graph and adjust it until it
looks closest to all the points.
Positive
correlation;
both data sets
increase
together.
No correlation Negative
correlation;
as one data set
increases, the
other decreases.
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.
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.
Practice Problem…
The Olympic Games Discus Throw
Year
1908
1912
1920
1924
1928
1932
1936
1948
1952
1956
1960
1964
1968
1972
1976
1980
1984
1988
1992
1996
Winning throw
134.2
145.1
146.6
151.4
155.2
162.4
165.6
173.2
180.5
184.9
194.2
200.1
212.5
211.4
221.5
218.7
218.5
225.8
213.7
227.7
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.
Step 1 & 2: Place your ruler on the
page and draw a line where it touches
the most points on the graph.
Olympic Games Discus Throw
250
Distance of Throw
200
150
100
50
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
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
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 + b
225.8 = 8/7(88) + b
• 225.8 = 704/7 + b
• 225.8 = ≈100.6 + b
-100.6 -100.6
• 125.2 = b
Step 5: Write in
slope-intercept form.
• Substitute each value into y = mx + b.
• The equation of the line of best fit is:
y = 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.