1. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 1 2-2 LINEAR REGRESSION Be able to fit a regression line to a scatterplot. Find and interpret correlation coefficients. Make predictions based on lines of best fit. OBJECTIVES

2. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Warm-UpWarm-Up Find the slope and y-intercept of the graphs of each line. y = 8x – 70 2y = 8x – 70 2y + 8x = 70 Slide 2

3. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 3 line of best fit, linear regression line, & least squares line - single line that best fits the scattered points domain - first elements range - second elements interpolation - predict corresponding y-values given an x- value within the domain extrapolation - predict corresponding y-values outside of the domain correlation coefficient - r, is a number between –1 and 1 inclusive that is used to judge how closely the line fits the data strong correlation - absolute value > 0.75 weak correlation - absolute value < 0.3 moderate correlation - Any other correlation Key Terms

4. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Skills and Strategies Enter data points into excel having a separate column for x and y. Highlight data. Click Insert tab and then Scatter in the Charts group. Under Chart Tools, Layout, select Trend line and then More Trend line Options. Make sure linear is selected and Display Equation on Chart (at the bottom) is checked. Slide 4

5. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 5 Example 1 Find the equation of the linear regression line for Rachael’s scatterplot in Example 1 from Lesson 2-1. Round the slope and y -intercept to the nearest hundredth. The points are given below. (65, 102), (71, 133), (79, 144), (80, 161), (86, 191), (86, 207), (91, 235), (95, 237), (100, 243)

6. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 6 Find the equation of the linear regression line of the scatterplot defined by these points: (1, 56), (2, 45), (4, 20), (3, 30), and (5, 9). Round the slope and y -intercept to the nearest hundredth. CHECK YOUR UNDERSTANDING

7. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 7 Example 2 Interpret the slope as a rate for Rachael’s linear regression line. Use the equation from Example 1.

8. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 8 Approximately how many more water bottles will Rachael sell if the temperature increases 2 degrees? CHECK YOUR UNDERSTANDING

9. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 9 EXAMPLE 3 Rachael is stocking her concession stand for a day in which the temperature is expected to reach 106 degrees Fahrenheit. How many water bottles should she pack?

10. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 10 How many water bottles should Rachael pack if the temperature forecasted were 83 degrees? Is this an example of interpolation or extrapolation? Round to the nearest integer. CHECK YOUR UNDERSTANDING

11. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 11 EXAMPLE 4 Find the correlation coefficient to the nearest hundredth for the linear regression for Rachael’s data. Interpret the correlation coefficient.

12. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 12 Find the correlation coefficient to the thousandth for the linear regression for the data in Check Your Understanding for Example 1. Interpret the correlation coefficient. CHECK YOUR UNDERSTANDING

13. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. Slide 13 Carlos entered data into his calculator and found a correlation coefficient of -0.28. Interpret this correlation coefficient. EXTEND YOUR UNDERSTANDING

14. Financial Algebra © 2011 Cengage Learning. All Rights Reserved. ApplicationsApplications Pages 73 – 74, #2 – 10 even Slide 14