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Measures of Association, Correlation and Regression Analysis
- 2. Measures ofAssociation, Correlation and Regression Analysis Presented by: Hamza Yousaf M. Phil Education University of Kotli, Azad Jammu and Kashmir Prepared by Hamza Yousaf 2
- 3. Association In statistics the word ‘association’ is about any relationship between two variables, whether it’s linear or non-linear. Association is a statistical relationship between two variables. Two variables may be associated without a causal relationship. Prepared by Hamza Yousaf 3
- 4. Measures ofAssociation In statistics, any of various factors or coefficients used to quantify a relationship between two or more variables. Measures of Association in Research Refers to a wide variety of statistics that quantify the strength and direction of the relationship between exposure and outcome variables, enabling comparison between different groups. Prepared by Hamza Yousaf 4
- 5. Conti… Several statistical techniques for determining the strength of the association among dependent and independent variables are presented below. The choice of which technique to use is largely driven by the level of data being analyzed. Prepared by Hamza Yousaf 5
- 6. Level of Data Statistical Technique Test Statistic Ratio or Interval Pearson’s Regression/Correlatio n R, R2 Ordinal (Rank Order) Spearman’s Rank Order Correlation Rho ( Rho2 Nominal (Categorical) Chi-Square Cramer’s V Binary (1=Yes, 0=No) Chi-Square Phi () Binary (1=Yes, 0=No) Logistic Regression Nagelkerke’s Pseudo R2 Prepared by Hamza Yousaf 6
- 7. Correlation The method of correlation is developed by FRANCIS GALTON in 1885. Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). Prepared by Hamza Yousaf 7
- 8. Conti… In correlation, the relation between two factors can fluctuate from absolute to not at all. Types of Correlation 1. Positive Correlation 2. Negative Correlation 3. Non-Linear Correlation 4. No Correlation Prepared by Hamza Yousaf 8
- 9. Conti… • Positive Linear Correlation If two variables are moving in the same direction, i.e., as one increases, another also increases, or as one decreases, another also decreases. For example, the gravitational force increases as the mass of the object increases Negative Linear Correlation If the changes in the two variables are in the opposite direction, i.e., if one variable increases the other decreases. Height above sea level and temperature. Prepared by Hamza Yousaf 9
- 10. Conti… • Non-liner Correlation Known as curvilinear correlation. For Example, bakery’s daily output of bread and number of bakers. • No Correlation The absence of any relationship between the two variables leads to zero or no correlation. For example, the grades obtained by students in examinations and their height. Prepared by Hamza Yousaf 10
- 11. Correlation Estimation There are different ways of estimating the correlation between two random variables. Here we discuss three ways. • Scatter Diagram • Pearson’s Correlation Coefficient • Spearman’s Rank Correlation Coefficient Prepared by Hamza Yousaf 11
- 13. Pearson’s Coefficient Correlation Scale Prepared by Hamza Yousaf 13 Spearman’s Rank Correlation Coefficient
- 14. RegressionAnalysis • Regression analysis is a set of statistical methods used for the estimation of relationships between a dependent variable and one or more independent variables. • It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them. Prepared by Hamza Yousaf 14
- 15. Conti… • Regression analysis is a way to find trends in data. For example, you might guess that there’s a connection between how much you eat and how much you weigh; regression analysis can help you quantify that equation. • Prediction about your data Prepared by Hamza Yousaf 15
- 16. Types of RegressionAnalysis 1. Simple Linear Regression The relationship between a dependent variable and a single independent variable is described using a basic linear regression methodology. 2. Multiple Linear Regression It is a statistical process that uses multiple explanatory factors to predict the outcome of a response variable. Prepared by Hamza Yousaf 16
- 18. Conti… Polynomial Regression Analysis It allows you to consider non-linear relations between variables and reach conclusions that can be estimated with high accuracy. Prepared by Hamza Yousaf 18
- 19. Application of RegressionAnalysis 5 applications of regression analysis are following: 1. Forecasting 2. CAPM (Capital Asset Pricing Model) 3. Comparing with Competition 4. Identifying Problems 5. Reliable Source Prepared by Hamza Yousaf 19