Check it out! 4.3.3: Distinguishing Between Correlation and Causation http://walch.com/wu/CAU4L3S3Guitar 4.3.3: Distinguishing Between Correlation and Causation

The owner of a guitar store asks customers how many hours a week they practice. He also tracks how much the customers spend. The relationship is shown in the scatter plot on the next slide. Use the scatter plot to answer the question that follows. Common Core Georgia Performance Standard: MCC9–12.S.ID.9 4.3.3: Distinguishing Between Correlation and Causation

Purchase amount in dollars ($) Practice hours per week Is there a linear correlation between x and y? Explain. Purchase amount in dollars ($) Practice hours per week 4.3.3: Distinguishing Between Correlation and Causation

The data to the right represents the number of minutes guitarists practice per day and the number of mistakes they make during a performance. Use the data in the table to complete the remaining problems. x y 4 35 7 26 3 37 6 32 29 8 28 9 1 40 33 38 10 22 4.3.3: Distinguishing Between Correlation and Causation

Create a scatter plot of the data set. Find the correlation coefficient, r, of the data. Is there a linear relationship between x and y? 4.3.3: Distinguishing Between Correlation and Causation

Is there a linear correlation between x and y? Explain. The shape of a linear graph is a straight line. The data seems to follow a straight line, and it appears that there is a linear correlation between x and y. 4.3.3: Distinguishing Between Correlation and Causation

Mistakes made during a performance Minutes spent practicing per day Create a scatter plot of the data set. Mistakes made during a performance Minutes spent practicing per day 4.3.3: Distinguishing Between Correlation and Causation

Find the correlation coefficient, r, of the data Find the correlation coefficient, r, of the data. Is there a linear relationship between x and y? Use a graphing calculator to find r. Follow the steps on the next few slides. 4.3.3: Distinguishing Between Correlation and Causation

On a TI-83/84: Step 1: The calculator must first be set up to find correlations. Press [2nd], then [CATALOG] (the “0” key). Scroll down and select DiagnosticOn, then press [ENTER]. (This step only needs to be completed once; the calculator will stay in this mode until changed in this menu.) Step 2: To calculate the correlation coefficient, first enter the data into a list. Press [2nd], then L1 (the “1” key). Scroll to enter data sets. Press [2nd], then L2 (the “2” key). Enter the second event in L2. 4.3.3: Distinguishing Between Correlation and Causation

Step 3: Now calculate the correlation coefficient Step 3: Now calculate the correlation coefficient. Press [STAT], then select CALC at the top of the screen. Scroll down to 8:LinReg(a+bx), and press [ENTER]. Step 4: The r value (the correlation coefficient) is displayed along with the equation. 4.3.3: Distinguishing Between Correlation and Causation

Step 4: Press the [menu] key. On a TI-Nspire: Step 1: Go to the lists and spreadsheet page. The icon looks like a table. Step 2: Enter the data into the first column underneath the shaded row, pressing [enter] after each data value. Step 3: Use the nav pad to arrow up to the first row below the shaded row and then arrow over to the right so that you are in the second column. Enter the data values, pressing [enter] after each data value. Step 4: Press the [menu] key. 4.3.3: Distinguishing Between Correlation and Causation

Step 5: Arrow down to 4: Statistics and press the center click key. Step 6: Press the center click key again to select 1: Stat Calculations. Step 7: Choose 3: Linear Regression (mx+b). Step 8: At the X List field, press [clear] and then type in “a[]”. To type “[]”, press the [ctrl] key and then the [(] key. Step 9: Press [tab] to go the Y List field and type in “b[]”. 4.3.3: Distinguishing Between Correlation and Causation

Step 11: Press [tab] to “OK” and press the center click key. Step 10: Press [tab] to go the Results field and check that results are listed in “c[]”. If not, change them. Step 11: Press [tab] to “OK” and press the center click key. Step 12: Arrow down until you see the “r” and look to the right. The number to the right is the correlation coefficient, r. Using a calculator, r = –0.97. The correlation coefficient is very close to –1, so there is a strong negative linear correlation between x and y. Connection to the Lesson In this lesson, students will examine linear correlations between data. This warm-up will remind students how to identify linear correlations graphically and by using the correlation coefficient, r. Students will differentiate between linear correlations and causations. 4.3.3: Distinguishing Between Correlation and Causation