1. Scatter Plots, Correlation and Linear Regression

2. Correlation Coefficient (r) The correlation coefficient is an indication of how well a model fits a particular set of data. It ranges from -1 to 1

3. Correlation Coefficient: As the coefficient approaches -1: Strong Negative relationship As the coefficient approaches 1: Strong positive relationship As the coefficient approaches 0: No relationship

4. Guess the Correlation Coefficient: Close to -1, -.5, 0,.5, 1

5. TI 30x Line of Best Fit steps: 2 nd DATA choose 2-VAR DATA (enter data and use down arrow) STAT VAR Arrow over to find a = This is the slope b = This is the y-intercept r = This is the correlation coefficient The equation of the line is y = ax + b. Just plug in a and b! To predict use a(predict #) + b. Estimated method

6. Find the correlation coefficient: Use your calculator handout to help you! r = ___________

7. Linear Regression (Line of Best Fit) A statistical approach for determining the relationship between x and y variables. We placed a trend line in the data before, but now we will use the actual data to determine the equation of the line.

8. TI 30x Line of Best Fit steps: 2 nd DATA choose 2-VAR DATA (enter data and use down arrow) STAT VAR Arrow over to find a = This is the slope b = This is the y-intercept r = This is the correlation coefficient The equation of the line is y = ax + b. Just plug in a and b! To predict use a(predict #) + b. Estimated method

9. Let’s write some Equations: XY 11 24 36 48 Equation:__________________________ Correlation Coefficient:____________ XY 2.34.9 3.34.2 3.73.9 4.23.5 Equation:__________________________ Correlation Coefficient:____________

10. Write the linear regression model for the data: The table shows the enrollment of a pre-school from 1980-2000. Plot the points on a scatterplot, write the model, and then graph it. Year (x)Enroll (y) 198014 198520 199022 199528 200037 Equation:__________________________ Correlation Coefficient:____________

11. Write the linear regression model for the data: The data table below shows the water temperature at various depths in an ocean: Water Depth (x) 5018 7515 10012 1507 2001 Equation:__________________________ Correlation Coefficient:____________

12. Write the linear regression model for the data: The number of newly reported crime cases in New York is shown in the table below: Year (x) New Cases (y) 1999440 2000457 2001369 2002351 Equation:__________________________ Correlation Coefficient:____________