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Correlation and Regression Analysis

This guide explores correlation and regression analysis, focusing on their significance in understanding relationships between variables. Key objectives include assessing the strength of association, distinguishing between various variable types, and identifying curvilinear correlations. It covers the essential tools of scatter diagrams for visualizing relationships and hypothesis testing for correlation coefficients. Regression analysis is detailed with a focus on simple and multiple regression, emphasizing prediction, control of outcomes, and statistical significance. Learn to differentiate correlation from causation and the implications for data interpretation.

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Correlation and Regression Analysis

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  1. Correlation and Regression Analysis

  2. Some correlation questions • Questions: • Objectives:

  3. Correlation • Strength of the association between two variables • Interval and ratio level variables – • Rank-order variables – • Categorical Variables – • Curvilinear correlation - e.g. marginal product costs per unit are not linearly related to units produced

  4. Scatter Diagram • Plot points Xi and Yi on a graph and examine the general shape • If the points generally slope upward to the right • If the points generally slope downward to the right If there is no pattern to the points • If the points lie in straight line

  5. Correlation • Test the null hypothesis • Research Hypothesis – • r lies between 1 and -1 • R tested for significance at the 10%, 5% or 1% level • R is independent of sample size and unit of measurement

  6. Correlation • Be aware of spurious correlation • Correlation does not imply causation

  7. Regression • Simple regression • Multiple regression • More than one DV • ANOVA

  8. Objectives of regression • Understand a relationship • Closer towards causality • Predict values of DV for various values of the IV • Control outcomes

  9. Regression • Test the null hypothesis • i.e. Predictor X is not significantly related to dependent variable Y • Research hypothesis – • i.e. Predictor X is positively / negatively related to dependent variable Y

  10. Regression • Y = a + bx OR Y = alpha + beta (x) • a = alpha = constant • b = beta = the coefficient of the independent / predictor variable

  11. Regression • Objective: Prediction / Control • Values of the constant and the slope. • Objective: Understanding relationships • Statistical significance at specified level

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