Scatter PlotsScatter Plots

Vocabulary

scatter plot

correlation

line of best fit

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Course 3

4-7 Scatter Plots

Course 3

4-7 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.

Additional Example 1: Making a Scatter Plot of a Data Set

Course 3

4-7 Scatter Plots

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

Course 3

4-7 Scatter Plots

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.

Course 3

4-7 Scatter Plots

Positive correlation; both data sets increase together.

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

No correlation; as one data set increases, the other decreases.

Additional Example 2A: Identifying the Correlation of Data

Course 3

4-7 Scatter Plots

A. The size of a jar of baby food and the number of jars of baby food a baby will eat.

Negative correlation: The more food in each jar, the fewer number of jars of baby food a baby will eat.

Do the data sets have a positive, a negative, or no correlation?.

Do the data sets have a positive, a negative, or no correlation?.

Additional Example 2B: Identifying the Correlation of Data

Course 3

4-7 Scatter Plots

B. The speed of a runner and the number of races she wins.

Positive correlation: The faster the runner, the more races she will win.

Do the data sets have a positive, a negative, or no correlation?.

Additional Example 2C: Identifying the Correlation of Data

Course 3

4-7 Scatter Plots

C. The size of a person and the number of fingers he has

No correlation: A person generally has ten fingers regardless of their size.

Try This: Example 2A

Course 3

4-7 Scatter Plots

A. The size of a car or truck and the number of miles per gallon of gasoline it can travel.

Negative correlation: The larger the car or truck, the fewer miles per gallon of gasoline it can travel.

Do the data sets have a positive, a negative, or no correlation?.

Do the data sets have a positive, a negative, or no correlation?.

Course 3

4-7 Scatter Plots

C. The number of telephones using the same phone number and the number of calls you receive.

No correlation: No matter how many telephones you have using the same telephone number, the number of telephone calls received will be the same.

Try This: Example 2C

Use the data to predict how much a worker will earn in tips in 10 hours.

Additional Example 3: Using a Scatter plot to Make Predictions

Course 3

4-7 Scatter Plots

According to the graph, a worker will earn approximately $24 in tips in 10 hours.

Use the data to predict how many circuit boards a worker will assemble in 10 hours.

Try This: Example 3

Course 3

4-7 Scatter Plots

According to the graph, a worker will assemble approximately 10 circuit boards in 10 hours.

141210 8 6 4 2

2 4 6 8 10 12 14

Hou

rs

Circuit Board Assemblies

Scatter PlotScatter Plot

• A scatter plot is a graph of a collection of ordered pairs (x,y).

• The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

Positive CorrelationPositive Correlation

• If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION.

• This means that both are going up, and they are related.

Positive CorrelationPositive Correlation

• If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation.

Negative CorrelationNegative Correlation

• If the x-coordinates and the y-coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION.

• This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

Negative CorrelationNegative Correlation

• If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation.

No CorrelationNo Correlation

• If there seems to be no pattern, and the points looked scattered, then it is no correlation.

• This means the two are not related.

No CorrelationNo Correlation

• If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

ScatterplotsWhich scatterplots below show a linear trend?

a) c) e)

b) d) f)

NegativeCorrelation

PositiveCorrelation

ConstantCorrelation

Year

Sport Utility Vehicles(SUVs) Sales in U.S.

Sales (in Millions)

19911992

199319941995

1996

19971998

1999

0.91.1

1.41.61.7

2.1

2.42.7

3.2

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Vehicle S

ales (Millions)

5

4

3

2

1

Objective - To plot data points in the coordinate plane and interpret scatter

plots.

1991 1993 1995 1997 1999 1992 1994 1996 1998 2000

x

y

Year

Vehicle S

ales (Millions)

5

4

3

2

1

Trend is increasing.

Scatterplot - a coordinate graph of data points.

Trend appears linear.

Positive correlation.

Year SUV Sales

Predict the sales in 2001.

Describe the relationship between time spent onhomework and time spent watching TV.

Time Watching TV

Tim

e on

Hom

ewor

k

30 90 150 210 60 120 180 240

240

210

180

150

120

90

60

30

Trend is decreasing.

Trend appears linear.

Negative correlation.

Time on TV Time on HW

Line of Best Fit• A line of best fit is a line that best represents the

data on a scatter plot.• A line of best fit may also be called a trend line

since it shows us the trend of the data

– The line may pass through some of the points, none of the points, or all of the points.

– The purpose of the line of best fit is to show the overall trend or pattern in the data and to allow the reader to make predictions about future trends in the data.

Use the data to create a scatter plot1.  Prepare a scatter plot of the data on graph paper.

Fat Grams and Calories in Food

0

100

200

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400

500

600

700

0 5 10 15 20 25 30 35 40

Total Fat Grams

To

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2.  Using a straight edge, position it so that the plotted points are as close to the line as possible.DRAW A LINE.

3.  Find two points that you think will be on the "best-fit" line. 

Perhaps you chose the points (9, 260) and (30, 530). 

Different people may choose different points.  All of them are "correct“.

5. This equation can now be used to predict information that was not plotted in the scatter plot.  For example, you can use the equation to find the total calories based upon 22 grams of fat.

If you have 22 grams of fat in your food, the it will also be about 427.141 calories.

Fat Grams and Calories in Food

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35 40

Total Fat Grams

To

tal C

alo

rie

s4. Write the equation of the line.