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Correlation and Regression Analysis

Correlation and Regression Analysis. Some correlation questions. Questions: Objectives : . Correlation. Strength of the association between two variables Interval and ratio level variables – Rank-order variables – Categorical Variables –

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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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