1. Unit 2.2 Linear Regression
“If you’re not the lead dog
the view’s the same.”
-Coach Ivey
What does this quote mean?

2. Unit 2.2 Linear Regression

3. Unit 2.2 Linear Regression
Line of Best Fit
A line that best approximates ALL the data in a scatterplot

4. Unit 2.2 Linear Regression
Domain Range
x values y values

5. Unit 2.2 Linear Regression
Interpolation Extrapolation
To predict y-values from given x-values To predict y-values outside the given set of bivariate data

6. Unit 2.2 Linear Regression
Correlation Coefficient “r”
A number between -1 & 1 used to indicate how close data is to a line of best fit -1 < r < 1

7. Unit 2.2 Linear Regression
Strong Correlation r > 0.7 r < -0.7 Weak Correlation r < 0.3 r > -0.3

8. Unit 2.2 Linear Regression
Steps to find Linear Regression of Data Points
Step 1: Plot the data on a Coordinate Plane Step 2: Draw a “Line of Best Fit” through your data. Step 3: Use 2 of the best fitting data points to determine your slope Step 4: Use a 3rd different data point near your best fit line to determine y-intercept

9. Example 1
Find the equation of the linear regression line for Rachael’s scatterplot in Example 1 from Lesson 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)

10. Unit 2.2 Linear Regression
Step 1
Step 1: Plot the data on a Coordinate Plane *Make sure you use a proper x-y scale The more accurate your plot the more accurate your linear equation

11. Unit 2.2 Linear Regression
Step 2
Step 2: Draw a “Line of Best Fit” through your data. You have to “eyeball” this and try to get the same # of data points on each side of your Line of Best Fit

12. Unit 2.2 Linear Regression
Step 3
Step 3: Use 2 of the best fitting data points to determine your slope Slope = Rise = y = (y2 – y1) = m Run x (x2 – x1) Linear Equation is … y = mx + b where m = slope

13. Unit 2.2 Linear Regression
Step 4
Now that you have slope … Step 4: Use a 3rd different data point near your best fit line to determine y-intercept y = mx + b if you know m all you need is one point to find b

14. CHECK YOUR UNDERSTANDING
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.

15. Example 2
Interpret the slope as a rate for Rachael’s linear regression line. Use the equation from Example 1.

16. CHECK YOUR UNDERSTANDING
Approximately how many more water bottles will Rachael sell if the temperature increases 2 degrees?

17. 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?

18. CHECK YOUR UNDERSTANDING
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.

19. EXAMPLE 4
Find the correlation coefficient to the nearest hundredth for the linear regression for Rachael’s data. Interpret the correlation coefficient.

20. CHECK YOUR UNDERSTANDING
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.

21. EXTEND YOUR UNDERSTANDING
Carlos entered data into his calculator and found a correlation coefficient of Interpret this correlation coefficient.

22. Example 1
Find the equation of the linear regression line for Rachael’s scatterplot in Example 1 from Lesson 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)

23. CHECK YOUR UNDERSTANDING
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.

24. Example 2
Interpret the slope as a rate for Rachael’s linear regression line. Use the equation from Example 1.

25. CHECK YOUR UNDERSTANDING
Approximately how many more water bottles will Rachael sell if the temperature increases 2 degrees?

26. 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?

27. CHECK YOUR UNDERSTANDING
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.

28. EXAMPLE 4
Find the correlation coefficient to the nearest hundredth for the linear regression for Rachael’s data. Interpret the correlation coefficient.

29. CHECK YOUR UNDERSTANDING
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.

30. EXTEND YOUR UNDERSTANDING
Carlos entered data into his calculator and found a correlation coefficient of Interpret this correlation coefficient.