Warm-Up #13 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.

Lesson 6.8 Linear Trends in Scatter Plots

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

little or no correlation Positive correlation Negative correlation little or no correlation

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

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.

Strength of Correlation

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

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

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

EXAMPLE 3 SOLUTION 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.

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.

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.

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.

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.

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.

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 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x 1999 3.2 Year

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. 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x Year

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.

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. 30 90 150 210 60 120 180 240 Time Watching TV

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 30 90 150 210 60 120 180 240 Negative correlation. Time Watching TV