1. D O N OW 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”

2. U NIT 1: L INEAR R EGRESSION Day 2: Scatter Plots

3. L INEAR R EGRESSION D AY 2 O BJECTIVES 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

4. U NIT 1: L INEAR R EGRESSION BMHS Enrollment Data Year Zero = 2000 Year 20012002200320042005200620072008 Enrollment 12431267141014201493154716611708

5. U NIT 2 - L INEAR REGRESSION Enter Data into graphing Calculator Use table to see what the prediction is Determine if the prediction is accurate

6. U NIT - L INEAR R EGRESSION What is r 2 ? POOR FIT50/50 FITPERFECT 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 = 0r 2 = 0.5r 2 = 1

7. U NIT 1 - L INEAR R EGRESSION rr2r2 NameCoefficient of CorrelationCoefficient of Determination What does it do? Describes the relationship between data Describes how well a model fits data Values -1  10  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?

8. U NIT 1 - L INEAR 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?

9. U NIT 1 - L INEAR R EGRESSION 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!