WarmupWrite increase or decrease to complete the sentence regarding expectations for the situation.1.The more one studies, their grades will _____.

2.The more a person diets, their weight will ______,

3.The longer one diets, the amount of weight loss will ______.

4.The more a person exercises, their muscle mass will _____.

5.The more a person exercises, their fat mass will ______.

6.The more a person jumps rope, their heart rate will _____.

7.The more a class talks, the teacher’s patience will _____.

8.The more a person reads, their vocabulary will _____.

This is called correlation.

Lesson 12Scatter Plots and Lines of Best Fit

Objectives:

Determine whether displayed data has positive, negative, or no correlation.

Draw a line of best fit to show the trend in data.

Scatter Plot: Dots representing data placed on coordinate grid.

Line of Best Fit: Trend Line – Goes through the center of the scatter plot. (Line of Best Fit Interactive – scroll to 2nd coordinate plane)

Positive Correlation: Group of dots go up and right (Line of best fit shows increasing values.)

Negative Correlation: Group of dots go down and right (Line of best fit shows increasing values.)

No Correlation: Points are scattered and no pattern can be determined.

CorrelationFrom birth to your current age, what happened to your height as you grew older?

When dieting, does a person expect their weight to go up or down?

From birth to your current age, what has happened to your weight?

When working out frequently, does one expect their amount of body fat to increase or decrease?

YouTube Video – What is Correlation?Youtube Video on Correlation

Strength of Correlation

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 27 34 40 42 45 51

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.

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.

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.

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.

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.