Correlation: Bivariate Data and Scatter Plot
- 1. CORRELATION: Bivariate Data And Scatter Plot SUBJECT: STATISTICS AND PROBABILITY TEACHER: ALMA MAE C. PUTONG
- 3. DIVIDE THE PHRASES INTO TWO GROUPS . EXPLAIN THE GROUP YOU CREATED. Mean age of Grade 11 students No. of absences and grades in 1st quarter Average height of varsity players Weight and Pulse Rate of women above 50 yrs. Old Weight of SHS students Age and height of varsity players Grades in 1st quarter Math score and Physics score of SHS students
- 4. Univariate Bivariate Mean age of Grade 11 students Weight and Pulse Rate of women above 50 yrs. old Average height of varsity players Math score and Physics score of SHS students Weight of SHS students No. of absences and grades in 1st quarter Grades in 1st quarter Age and height of varsity players
- 5. Consists of the values of two variables that are obtained from the same population of interest. Bivariate Data Three combinations of variable types: 1. Both variables are qualitative (attribute). 2. One variable is qualitative (attribute) and the other is quantitative (numerical). 3. Both variables are quantitative (both numerical).
- 6. What to do with the two variables?
- 7. The primary purpose of bivariate data is to compare the two sets of data or to find a relationship between the two variables.
- 8. • Is caffeine related to heart damage? • Is there a relationship between a person’s age and his or her blood pressure? • Is the number of hours a student studies related to the student’s score on a particular exam? • Is the birth weight of a certain animal related to its life span?
- 9. TWO QUANTITATIVE VARIABLES: EXPRESSED AS ORDERED PAIRS: (X, Y) X: INPUT VARIABLE, INDEPENDENT VARIABLE (EXPLANATORY). Y: OUTPUT VARIABLE, DEPENDENT VARIABLE(RESPONSE).
- 10. GROUP ACTIVITY Using a tape measure, measure the length of the arm span and height of all the members of the group in centimeters. Tabulate the result. Student Length of the arm span (x) (cm) Height (y) (cm) 1 2 3 4 5
- 11. INSTRUCTIONS: 1.Construct a graph out of the data you collected. Present it on a scatterplot using geogebra application. 2.Describe the direction where the points are going?
- 12. Scatter Plot • A scatter plot is a picture of the relationship between two quantitative variables. If a linear relationship exists between two variables the scatter plot will exist as a swarm of points stretched out in a generally consistent manner.
- 13. SCATTERPLOT
- 15. INTERPRETATION: • If the data show an uphill pattern as you move from left to right, this indicates a positive relationship between X and Y. As the X-values increase (move right), the Y-values tend to increase (move up). • If the data show a downhill pattern as you move from left to right, this indicates a negative relationship between X and Y. As the X-values increase (move right) the Y-values tend to decrease (move down). • If the data don’t seem to resemble any kind of pattern (even a vague one), then no relationship exists between X and Y.
- 16. WHAT SHOULD YOU LOOK FOR IN A SCATTERPLOT? Direction – which way are the points going? positive, negative, neither. Strength – how much scatter is there in the plot? Weak, moderate, strong
- 17. REMEMB ER scatterplot only suggests a linear relationship between the two sets of values. It does not suggest that one variable causes the change of the other variable.
- 18. For example, a doctor observes that people who take vitamin C each day seem to have fewer colds. Does this mean vitamin C prevents colds? Not necessarily. It could be that people who are more health conscious take vitamin C each day, but they also eat healthier, are not overweight, exercise every day, and wash their hands more often. If this doctor really wants to know if it’s the vitamin C that’s doing it, she needs a well- designed experiment that rules out these other factors.
- 19. APPLICAT ION Given the variable y ( response), what could be the variable x (explanatory) 1. Number of cars 2. Number of tardiness among students 3. Ice cream sales
- 20. CORRELATION COEFFICIENT (r) The correlation coefficient (r) gives us a numerical measurement of the strength of the linear relationship between the explanatory and response variables. Where n is the number of pairs.
- 21. RANGE DESCRIPTIVE EQUIVALENT -1.00 Perfect Negative Correlation (-0.60) – (-0.99) Strong Negative Correlation (-0.30) – (-0.59) Moderate Negative Correlation (-0.10) – (-0.29) Weak Negative Correlation 0.00 No Correlation 0.10 – 0.29 Weak Positive Correlation 0.30 – 0.59 Moderate Positive Correlation 0.60 – 0.99 Strong Positive Correlation 1.00 Perfect Positive Correlation
- 22. A group of students conducted an experiment to see if the height of seedlings has a relationship with its number of leaves. They planted several seedlings and measured the height after a certain number of weeks. The number of leaves was also counted. Below is a table of the height of seedlings and the number of leaves they have. Construct a scatter plot of the results and compute the correlation coefficient of these two variables. Height of Seedlings (mm) 8 13 10 9 12 7 15 11 6 14 Number of leaves 2 4 2 2 3 1 4 3 1 3
- 23. In a graphing paper, make a scatter plot of the given table showing the results of a study made about the height (cm) and their shoe sizes. Height of Students (cm) 164 160 159 149 162 166 151 154 160 146 158 161 157 162 150 Shoe Sizes 9 7.5 9.5 6 8 10 6.5 7 8 6 7 9 8 8.5 6
- 24. CONSTRUCT A SCATTER PLOT THAT CORRESPONDS TO THE FOLLOWING DATA THEN INTERPRET YOUR GRAPH. Weight in kg (x) 72 45 60 55 70 75 42 51 49 88 Pulse Rate in bpm (y) 67 80 55 105 88 110 55 65 100 65
- 25. THE FOLLOWING TABLE SHOWS DATA THAT DESCRIBE THE TEST SCORES OF STUDENTS IN MATHEMATICS IN RELATION TO THEIR TEST SCORES IN PHYSICS. COMPUTE THE CORRELATION COEFFICIENT OF THESE TWO VARIABLES. Math score (x) 64 90 56 85 93 95 73 78 66 98 89 74 55 60 Physic s score (y) 70 85 60 70 88 98 60 80 75 95 84 69 40 45
- 26. “ A relationship with God is the most important relationship you can have. Trust Him and everything will always turn out fine”. - www.dailyinspirationalquotes.in