PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT

1. Calculate the Pearson Product Moment Correlation Coefficient
2. Solve problems involving correlation analysis.

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1. PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT

2. Learning Competencies The learner will be able to: Calculate the Pearson Product Moment Correlation Coefficient; and Solve problems involving correlation analysis.

3. In the previous lesson on scatter plots, the degree or strength of relationship between the two variables was not numerically measured . The strength of relationship was only estimated and described visually based on the dots plotted on the xy coordinate plane. The Pearson Product Moment Correlation Coefficient , denoted by r, measures the strength of the linear relationship .

4. Where n= number of paired values = sum of x-values = sum of y-values = sum of the products of paired values of x and y = sum of squared x-values = sum of squared y-values   FORMULA

5. Value of r Strength of Correlation Perfect positive correlation Strong positive correlation Moderately positive correlation Weak positive correlation Negligible positive correlation No correlation Negligible negative correlation Weak negative correlation Moderately negative correlation Strong negative correlation Perfect negative correlation Value of r Strength of Correlation Perfect positive correlation Strong positive correlation Moderately positive correlation Weak positive correlation Negligible positive correlation No correlation Negligible negative correlation Weak negative correlation Moderately negative correlation Strong negative correlation Perfect negative correlation INTERPRETATION

6. The table below shows the time in hours (x) spent by six Grade 11 students in studying their lessons and their scores (y) on a test . Solve for the Pearson Product Moment Correlation Coefficient r. Solution x 1 2 3 4 5 6 y 5 15 10 15 30 35 x y xy 1 5 5 1 25 2 10 20 4 100 3 15 45 9 225 4 15 60 16 225 5 25 125 25 625 6 35 210 36 1225 x y xy 1 5 5 1 25 2 10 20 4 100 3 15 45 9 225 4 15 60 16 225 5 25 125 25 625 6 35 210 36 1225 Example 1

7. The value r=0.962 is between In the table of interpretation of r. It indicates that there is a strong positive correlation between the time in hours spent in studying and the scores on a test.   Solving r

8. Scatter Plot

9. The table below shows the time in hours (x) spent by six Grade 11 students in playing computer games and the scores these students got on a math test (y ). Solve for the Pearson Product Moment Correlation Coefficient r. Solution x 1 2 3 4 5 6 y 30 25 25 10 15 5 x y xy 1 30 30 1 900 2 25 50 4 625 3 25 75 9 625 4 10 40 16 100 5 15 75 25 225 6 5 30 36 25 x y xy 1 30 30 1 900 2 25 50 4 625 3 25 75 9 625 4 10 40 16 100 5 15 75 25 225 6 5 30 36 25 Example 2

10. The value is between In the table of interpretation of r. It indicates that there is a strong negative correlation between the time spent in playing computer games and the scores on a test.   Solving r

11. Scatter Plot

12. The table below shows the number of selfies (x) posted online of students and the scores (y) they obtained from a Science test. Solve for the Pearson Product Moment Correlation Coefficient r. Solution x 1 2 3 4 5 6 y 25 5 20 40 25 9 x y xy 1 25 25 1 625 2 5 10 4 25 3 20 60 9 400 4 40 160 16 1600 5 25 125 25 625 6 9 54 36 81 x y xy 1 25 25 1 625 2 5 10 4 25 3 20 60 9 400 4 40 160 16 1600 5 25 125 25 625 6 9 54 36 81 Example 3

13. The value . It indicates that there is no correlation between the number of selfies posted online and the scores obtained from a Science test.   Solving r

14. Scatter Plot

15. The table below shows the number of composition notebooks and the corresponding costs. The cost per composition notebook is Php 25. Solve for the Pearson Product Moment Correlation Coefficient r. Solution x 1 2 3 4 5 6 y 25 50 75 100 125 150 x y xy 1 25 25 1 625 2 50 100 4 2500 3 75 225 9 5625 4 100 400 16 10000 5 125 625 25 15625 6 150 900 36 22500 x y xy 1 25 25 1 625 2 50 100 4 2500 3 75 225 9 5625 4 100 400 16 10000 5 125 625 25 15625 6 150 900 36 22500 Example 4

16. The value . It indicates that there is a perfect positive correlation between the two variables.   Solving r

17. Scatter Plot

18. Norman and Beth traveled from City A to City B. They traveled at a constant rate of 40 kilometers per hour. The distance between City A and City B is 280 kilometers. Beth decided to write on a piece of paper the distance they travel after 1 hour, 2 hours, 3 hours, and so on until they reached City B. These are shown on the following Table. Solve for the Pearson Product Moment Correlation Coefficient r. Solution x 1 2 3 4 5 6 7 y 240 200 160 120 80 40 x y xy 1 240 240 1 57600 2 200 400 4 40000 3 160 480 9 25600 4 120 480 16 14400 5 80 400 25 6400 6 40 240 36 1600 7 49 x y xy 1 240 240 1 57600 2 200 400 4 40000 3 160 480 9 25600 4 120 480 16 14400 5 80 400 25 6400 6 40 240 36 1600 7 49 Example 5

19. The value . It indicates that there is a perfect negative correlation between the two variables.   Solving r

20. Scatter Plot

21. Shown on the table below are bivariate data. Solve for the Pearson Product Moment Correlation Coefficient r. Solution x 4 2 8 10 12 14 6 16 y 10 5 25 10 15 20 5 10 x y xy 4 10 40 16 100 2 5 10 4 25 8 25 200 64 625 10 10 100 100 100 12 15 180 144 225 14 20 280 196 400 6 5 30 36 25 16 10 160 256 100 x y xy 4 10 40 16 100 2 5 10 4 25 8 25 200 64 625 10 10 100 100 100 12 15 180 144 225 14 20 280 196 400 6 5 30 36 25 16 10 160 256 100 Example 6

22. The value is between Hence, there is a weak positive correlation between the two variables.   Solving r

23. Scatter Plot

24. Listed below are the heights in centimeters and weights in kilograms of six teachers. Solve for the Pearson Product Moment Correlation Coefficient r. Solution Teacher A B C D E F Height (cm) 160 162 167 158 167 170 Weight (kg) 50 59 63 52 65 68 Teacher x y xy A 160 50 8000 25600 2500 B 162 59 9558 26244 3481 C 167 63 10521 27889 3969 D 158 52 8216 24964 2704 E 167 65 10855 27889 4225 F 170 68 11560 28900 4624 Teacher x y xy A 160 50 8000 25600 2500 B 162 59 9558 26244 3481 C 167 63 10521 27889 3969 D 158 52 8216 24964 2704 E 167 65 10855 27889 4225 F 170 68 11560 28900 4624 Example 7

25. The value is between It indicates a strong positive correlation between the height and weight of the six teachers.   Solving r

26. Scatter Plot