DO NOW

Get a graphing calculator Graph the line: y = -5x + 6 Use the table to find the value of y, when x = 25 View graph using “zoom 6”

UNIT 1: LINEAR REGRESSIONDay 2: Scatter Plots

LINEAR REGRESSION DAY 2 OBJECTIVES

Students will be able to: Create mathematical models on the graphing

calculator Describe use correlation coefficients to describe

correlations Use mathematical models to make interpolations and

extrapolations

UNIT1: LINEAR REGRESSION BMHS Enrollment Data

Year Zero = 2000

Year 2001 2002 2003 2004 2005 2006 2007 2008

Enrollment 1243 1267 1410 1420 1493 1547 1661 1708

0 1000 20000

200

400

600

800

1000

1200

1400

1600

1800

0 1 2 3 4 5 6 7 8 9 100

200400600800

10001200140016001800

UNIT 2 - LINEAR REGRESSION

Enter Data into graphing Calculator Use table to see what the prediction is Determine if the prediction is accurate

UNIT - LINEAR REGRESSION

What is r2?

POOR FIT 50/50 FIT PERFECT FIT

The model will make an accurate prediction

0% of the time

The model will make an accurate prediction

50% of the time

The model will make an accurate prediction

100% of the time

Known as the coefficient of determination. It is a number between 0 and 1 that describes how well the model “fits” the data.

r 2= 0 r 2= 0.5 r2 = 1

UNIT 1 - LINEAR REGRESSION

r r2

Name Coefficient of Correlation Coefficient of Determination

What does it

do?

Describes the relationship between data

Describes how well a model fits data

Values

-1 1 0 1

-1: Negative Correlation (x increases and y

decreases)

0: The model does not fit the data and will not make an

accurate prediction

0: No Correlation(No relationship between

data)

0.5: The model somewhat fits the data, the prediction

will be 50% accurate

1: Positive Correlation (x and y both increase)

1: The model fits the data perfectly and the prediction

will be 100% accurate

What is the difference between r and r-squared?

UNIT 1 - LINEAR REGRESSION

Closure: Why do we need to use a zero year when finding

a mathematical model?

How do you know if a model will make an accurate prediction about the future?

What is the difference between r and r-squared?

UNIT 1 - LINEAR REGRESSION

Did you meet today’s objectives? Create mathematical models on the graphing

calculator Describe use correlation coefficients to describe

correlations Use mathematical models to make interpolations

and extrapolations

Look in section 2.4 for extra help!

Homework: pg. 81 (12- 14) Quiz on Monday!