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Correlation and Its Types with Questions and Examples
The document explains correlation as a measure of the relationship between two or more variables, highlighting its strength through various types such as positive, negative, and no correlation. It details the correlation coefficient, especially Pearson's r, which quantifies this relationship on a scale from -1 to +1, along with methods for calculating it like scatter diagrams and rank correlation. Additionally, it discusses linear versus non-linear correlations and their graphical representations.
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Correlation and Its Types with Questions and Examples
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- 2. Correlation • It isa measure of Relationship. It is a measure of association between two or more variables. • It describe the strength of linear relationship between two variable. • Correlation involves various methods and techniques used for studying and measuring the relation between the variables.
- 3. Cont.… • The datacan be represented by the ordered pairs (x,y) where X is the independent variable and y is the Dependent Variable. • Correlation lie outside the range of -1 to 1
- 4. Examples of Correlation •Height and Weight of children • Hours Study and Marks • Nature and Degree
- 5. Types of Correlation •Positive Correlation and Negative Correlation • Linear Correlation and Non-Linear Correlation • Simple and Multiple Correlation
- 6. Positive Correlation • Ifboth the variables move in the same directions. We say that there is a Positive Correlation. When one variable increase, the other variable tends to increase as well. It Mean that direct Relationship. Example: • Study time and Grades
- 7. Negative Correlation • Avariable move in opposite direction we say that it’s a negative relationships. When one variable increases, the other variable tends to decrease. It mean indirect/inverse relation. Example: • More exercise, lower your body weight • TV Time increases, grade decrease • Price and Quantity Demands
- 8. No Correlation • Insome cases change in one variable is not related to change in other variable. In these case there is said to no correlation or zero correlation between the two variables. For Example: • There is no relationship between heights of students and grades Scored in Examination.
- 9. Positive Correlation NegativeCorrelation No Correlation
- 10. Linear Correlation The ratioof Change between two variables is uniform then there will be linear Correlation. The graph will be a straight line.
- 11. Nonlinear Correlation • TheAmount of Change between one variables does not bear a constant ratio to the amount of change in the other variables. The graph will be curve For Example: • The relationship between distance and the brightness of a light source can be inverse. As you move away, brightness decreases, but it may not decrease linearly.
- 12. Linear Correlation NonLinear Correlation Y -axis X- axis Y -axis X- axis
- 13. Simple and MultipleCorrelation Simple Correlation: • If only two variable are involved in a study then a Simple Correlation. Multiple Correlation: • If three or more then three variable are involved in a study then a Multiple Correlation.
- 14. Correlation Coefficient • Acorrelation coefficient is a numerical representation of the relationship between a pair of random variables. There are several different correlation coefficients, the most commonly used of which is the Pearson correlation coefficient. • Correlation Coefficient denoted by r. • r lie between + 1 to -1. • -1 ≤ r ≤ +1
- 15. -1 +1 r =0 Y-axis X-axis
- 17. Interpretation of CorrelationCoefficient (r) • The value of correlation coefficient ‘r’ ranges from -1 to +1 • If r = +1, then the correlation between the two variables is said to be perfect and positive • If r = -1, then the correlation between the two variables is said to be perfect and negative • If r = 0, then there exists no correlation between the variables
- 18. Properties of CorrelationCoefficient (r) • The correlation coefficient lies between -1 & +1 symbolically ( - 1≤ r ≥ 1 ) • The coefficient of correlation is the geometric mean of two regression coefficient.
- 19. Method of StudyingCorrelation Coefficient 1. Scatter diagram 2. Karl Pearson's coefficient of correlation 3. Spearman’s Rank correlation coefficient 4. Method of least squares
- 20. 1. Scatter Diagram •Scatter Diagram is a graph of observed plotted points where each points represents the values of X & Y as a coordinate. It portrays the relationship between these two variables graphically. • For example, a plot of weight vs. height will show a positive correlation: as height increases, weight also increases. • One variable is shown on X-axis and Horizontal axis and the other on the Y-axis and Vertical axis.
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- 22. 2. Karl PearsonCorrelation Coefficient • The Pearson correlation coefficient (r), also referred to as Pearson's r, is a value between -1 and +1 that describes the linear relationship between two random variables. • Pearson’s ‘r’ is the most common correlation coefficient. • Karl Pearson’s Coefficient of Correlation denoted by- r -1 ≤ r ≥ +1
- 23. Karl Pearson CorrelationCoefficient • r = 1: perfect positive correlation • r = -1: perfect negative correlation • r = 0: no correlation • The coefficient of correlation between the two variables x and y is symmetric. =
- 24. Formula of KarlPearson Method 𝑟= 𝑛∑𝑥𝑦−∑𝑥∑𝑦 √(𝑛∑𝑥2 −(∑𝑥) 2 )(𝑛∑𝑦2 −(∑𝑦) 2 )
- 25. X Y 1 3 22 3 1 4 3 5 4 Question • Find Correlation Coefficient?
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- 27. 1 3 19 3 2 2 4 4 4 3 1 9 1 3 4 3 16 9 12 5 4 25 16 20 15 13 55 39 42 Solution by Putting values in Formula
- 29. Then Correlation isWeak Positive.
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- 31. 3. Spearman’s Rankcorrelation coefficient • "Spearman's rank correlation coefficient is a statistical measure that assesses how well the ranks of two variables are related. It is used when the variables are ordinal (can be ranked) but not necessarily measured on a specific scale."
- 32. Formula of Rankcorrelation coefficient =
- 33. States Math's 1 2 24 3 3 4 1 5 7 6 5 7 8 8 10 9 6 10 9 Question Find Coefficientof rank correlation from the following of 10 students in statistics and Mathmatics?
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- 35. 1 2 -11 2 4 -2 4 3 3 0 0 4 1 3 9 5 7 -2 4 6 5 1 1 7 8 -1 1 8 10 -2 4 9 6 3 9 10 9 1 1
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