1. Scatterplots and Linear Regressions Unit 8

2. Warm – up!! As you walk in, please pick up your calculator and begin working on your warm – up! 1. Look at the scatter plot to the right. What is the correlation? 2. What is the slope? 3. Describe the data. 4. Write an equation that describes an initial value of 85 and a rate of 34.

3. What is a Scatter Plot? Trend Line: A line drawn near the points in a scatter plot. ** Can help show positive, negative, or no correlation.**

4. Line of Best Fit: The trend line that shows the relationship between two sets of data most accurately. In order to find the Line of Best Fit, you are going to use Linear Regression.

5. Using Linear Regression to find the Line of Best Fit To find the equation for the Line of Best Fit, Grab your CALCULATOR and turn it on. Steps to press in your calculator. Step 1: Turn on your Diagnostic. Once you turn this on for the first time, you do not have to continue doing this step. Press 2 nd Press 0 Scroll down to Diagnostic On Press ENTER twice *Note: Your screen must say Done. Step 2: Enter your data into L1 and L2. Press STAT Press ENTER Type your data into L1 and L2

6. Using Linear Regression to find the Line of Best Fit Step 3: After you have entered your data into L1 and L2, go back to your main screen. Press 2nd Press MODE Step 4: Find the equation for the Line of Best Fit. Press STAT  to CALC  Press 4 (LinReg(ax+b)) Press VARS Over to Y-VARS Press ENTER three times Line of Best Fit: Describe the Correlation:

7. Your Screen Should Look Like This: Slope Y – intercept Correlation Coefficient *Note: If r² and r don’t show up, you need to go back and turn on your Diagnostic! On the calculator screen, notice that there is a variable called r → this represents the correlation coefficient, which tells how closely the line of best fit models the data.

8. Describing the Correlation Describing the correlation If r is a negative number, it has a Negative correlation. If r is 0, it has No correlation. If r is a positive number, it has a Positive correlation. The closer r is to 1 or –1, the Stronger the correlation is. In other words, the data gathers more closely around the line of best fit. A strong correlation ranges from 0.8 to 1.0 OR -1.0 to -0.8 A moderate correlation ranges from 0.6 to 0.8 OR -0.8 to -0.6 A weak correlation ranges from 0 to 0.6 OR -0.6 to 0

9. Example 1: Find the Line of Best Fit, Describe the Correlation, and find the correlation coefficient. XY 15 23 32 42 51 Line of Best Fit: Positive, Negative, or No Correlation: R =

10. Example 2: Find the Line of Best Fit, Describe the Correlation, and find the correlation coefficient. XY -35 1 6 02 05 10 Line of Best Fit: Positive, Negative, or No Correlation: R =

11. You Try!! Find the Line of Best Fit, Describe the Correlation, and find the correlation coefficient. XY 127 229 334 443 545 650 Line of Best Fit: Positive, Negative, or No Correlation: R =

13. Practice!!