1. Warm-Up #26
Write increase or decrease to complete the sentence regarding expectations for the situation.
The more one studies, their grades will _____.
The more a person diets, their weight will ______,
The longer one diets, the amount of weight loss will ______.
The more a person exercises, their muscle mass will _____.
The more a person exercises, their fat mass will ______.
The more a person jumps rope, their heart rate will _____.
The more a class talks, the teacher’s patience will _____.
The more a person reads, their vocabulary will _____.
This is called correlation.

2. Lesson 6.8 Linear Trends in Scatter Plots

3. Scatter plots provide a convenient way to determine whether a ___________ exists between two variables.
correlation
positive
A __________ correlation occurs when both variables increase.
negative
A ___________ correlation occurs when one variable increases and the other variable decreases.
If the data points are randomly scattered there is _______ or no correlation.
little

4. little or no correlation
Positive correlation
Negative correlation
little or no correlation

5. The scatter plots of data relate characteristics of children from
Example 1:
The scatter plots of data relate characteristics of children from
0 to 18 years old.
Match each scatter plot with the appropriate variables studied.
1. age and height
2. age and eye color
3. age and time needed to run a certain distance 2 1 3
no correlation between age and eye color
as your age increases your height also increases
as your age increases the time will decrease

6. Scatter Plot: Dots representing data placed on coordinate grid.
Line of Best Fit: Trend Line – Goes through the center of the scatter plot. You can study the line to see how the data behaves. You may have a basis predict what the data might be for values not given.

7. Strength of Correlation

8. Use the line of best fit to predict how many tornadoes may be reported in the United States in 2015 if the trend continues.
1200
1000
800
600
If the trend continues we predict that there will be 1200 tornadoes reported in 2015.
400
200
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015

9. If the data points are close to the line of best fit, it is said to have a ___________correlation.
strong
strong positive
weak positive
strong negative
weak negative

10. BIRD POPULATIONS
The table shows the number of active woodpecker clusters in a part of the De Soto National Forest in Mississippi. Determine the correlation between the year and the number of Active clusters.
Year
1992
1993
1994
1995
1996
1997
1998
1999
2000
Active clusters 22 24 27 34 40 42 45 51

11. EXAMPLE 3
SOLUTION
Make a scatter plot of the data. Let x represent the number of years since Let y represent the number of active clusters Since the dots are generally going up and to the right, we say this is a positive correlation.

12. Describe the correlation of the data graphed in the scatter plot.
The scatter plot shows a positive correlation between hours of studying and test scores. This means that as the hours of studying increased, the test scores tended to increase.

13. EXAMPLE 1
Describe the correlation of data
The scatter plot shows a negative correlation between hours of television watched and test scores. that as the hours of television This means that as the hours of television watched
Increased, the test scores tended to decrease.

14. EXAMPLE 2
Swimming Speeds
The table shows the lengths (in centimeters) and swimming speeds (in centimeters per second) of six fish.
a. Make a scatter plot of the data.
b. Describe the correlation of the data.

15. EXAMPLE 2
a. Treat the data as ordered pairs. Let x represent the fish length (in centimeters),and let y represent the speed (in centimeters per second). Plot the ordered pairs as points in a coordinate plane.
SOLUTION
b. The scatter plot shows a positive correlation,
which means that longer fish tend to swim faster.

16. GUIDED PRACTICE
Make a scatter plot of the data in the table. Describe the correlation of the data.
ANSWER
The scatter plot shows a positive correlation.

17. Objective - To plot data points in the coordinate plane and interpret scatter plots.y
Sport Utility Vehicles
(SUVs) Sales in U.S. 5 4 3 2 1
Year
Sales (in Millions)
1991
0.9
1992
1.1
Vehicle Sales (Millions)
1993
1.4
1994
1.6
1995
1.7
1996
2.1
1997
2.4
1998
2.7 x
1999
3.2
Year

18. Scatterplot - a coordinate graph of data points.y
Trend appears linear. 5 4 3 2 1
Trend is increasing.
Vehicle Sales (Millions)
Positive correlation.
Predict the sales in 2001. x
Year

19. Plot the data on the graph such that homework time
is on the y-axis and TV time is on the x-axis..
Time Spent
Watching TV
Time Spent
on Homework
Student
Sam
30 min.
180 min.
Jon
45 min.
150 min.
Lara
120 min.
90 min.
Darren
240 min.
30 min.
Megan
90 min.
90 min.
Pia
150 min.
90 min.
Crystal
180 min.
90 min.

20. Plot the data on the graph such that homework time
is on the y-axis and TV time is on the x-axis. TV
Homework
240
210
180
150
120 90 60 30
30 min.
180 min.
45 min.
150 min.
120 min.
90 min.
Homework
Time on
240 min.
30 min.
90 min.
120 min.
150 min.
120 min.
180 min.
90 min.
Time Watching TV

21. Describe the relationship between time spent on
homework and time spent watching TV.
Trend appears linear.
240
210
180
150
120 90 60 30
Trend is decreasing.
Homework
Time on
Negative correlation.
Time Watching TV