1. Linear Models and scatter plots SECTION 1.7

2. An effective way to see a relationship in data is to display the information as a __________________. It shows how two variables relate to each other by showing how closely the data points _______ to a line. The following table presents information on tornado occurrences. Make a scatter plot for the table. Year 1950195519601965197019751980198519901995 # of Tornadoes 20159361689765491986668411331234 scatter plot fit

3. Year 1950195519601965197019751980198519901995 # of Tornadoes 20159361689765491986668411331234 1950195519601965197019751980199019851995 200 400 600 800 1000 1200 Do you notice a trend?

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

5. Positive correlation Negative correlation little or no correlation

6. 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 no correlation between age and eye color as your age increases your height also increases as your age increases the time will decrease 213

7. Sometimes points on a scatter plot are represented by a trend line or a _______________________. 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. line of best fit Example 2: Find the line of best fit for the scatter plot you made on the first page. To fit the line to the points, choose your line so that it best matches the overall trend. The line does not have to pass through any of the points.

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. 1950195519601965197019751980199019851995 200 400 600 800 1000 1200 2000200520102015 If the trend continues we predict that there will be 1200 tornadoes reported in 2015.

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

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 199219931994199519961997199819992000 Active clusters 222427 3440424551

11. SOLUTION EXAMPLE 3 Make a scatter plot of the data. Let x represent the number of years since 1990. 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. Swimming Speeds EXAMPLE 2 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 b. The scatter plot shows a positive correlation, which means that longer fish tend to swim faster. SOLUTION 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.

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.