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

5.4 Scatter Plots

A scatter plot shows relationships between two sets of data.

Use the given data to make a scatter plot of the weight and height of each member of a basketball team.

Making a Scatter Plot of a Data Set

The points on the scatter plot are (71, 170), (68, 160), (70, 175), (73, 180), and (74, 190).

Example 1

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.

Negative correlation; as one data set increases, the other decreases.

No correlation

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 Winning throw1908 134.21912 145.11920 146.61924 151.41928 155.21932 162.41936 165.61948 173.21952 180.51956 184.91960 194.21964 200.11968 212.51972 211.41976 221.51980 218.71984 218.51988 225.81992 213.71996 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

0

50

100

150

200

250

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Year

Dist

ance

of T

hrow

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.