1. C HAPTER 3: E XAMINING R ELATIONSHIPS

2. 3.2: C ORRELATION Measures the direction and strength of a linear relationship between two variables. Usually written as r. Video explaining how r is calculated Fortunately, most of the time we will use our calculators! 2

3. E XAMPLE 1 – FINDING CORRELATION BY HAND AbsencesGrade 1 92 4 93 2 90 10 45 15 36 6 79 1 93 2 95 9 44 The following data represents the number of absences for 9 different students and their overall grade in the course. Find the correlation.

4. -.94.72-.68 -.33.76-.25 -.73.63-.46.9 -1.17-1.053 1.92 -1.53-2.94.08.2.016 -.94.76-.71 -.73.84-.61.69 -1.21-.83

5. I MPORTANT FACTS ABOUT CORRELATION : 1. Makes no distinction between explanatory and response variables It doesn’t matter which variable is called x and which is called y 2. Requires that both variables be quantitative For example, the correlation between the incomes of a group of people and what city they live in cannot be calculated because city is a categorical variable. 3. Because r uses standardized values of the observations, it does not change when we change the units of measurement of x, y, or both r has no unit of measurement; it is just a number. 4. Positive r indicates positive association and negative r indicates negative association. 5

6. I MPORTANT F ACTS ABOUT CORRELATION : 5. r is always a number between -1 and 1 Values near 0 indicate a very weak linear relationship The strength increases as r moves toward -1 or 1. 6. Measures the strength of only a linear relationship Does not describe curved relationships 7. r is not a resistant measurement Use r with caution when there are outliers Note: r is not a complete description of two- variable data Need to use the means and standard deviations of BOTH x and y along with the correlation when describing the data. 6

7. Correlation measures how closely related the data is to a linear approximation. The slope of the correlation gives the sign of the value. 7 Correlation Charts

8. M AKE A S CATTERPLOT Use 2 nd Y= Turn plot 1 on The first type of graph is a scatterplot Xlist = L 1 Ylist = L 2 Press the zoom key then number 9 8

9. F IND THE C ORRELATION First, make sure the diagnostics are turned on: Press 2 nd 0 Brings up catalog Find DiagnosticOn and press enter twice Press the STAT key Scroll over to CALC Use either option 4 or 8 9

10. E XAMPLE 2 – U SING THE CALCULATOR Using the data from example 1, find the correlation using your calculator. STAT/CALC/LinReg r = -.946

11. S ECTION 3.2 COMPLETE Homework: p.142-146 #’s 24 (do part a by hand and for part b use lists to find r in your calc), 25, 26, 28, 34, 36, & 37