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Correlation and Regression

Correlation and Regression. Correlation and linear regression: Not the same, but are related Linear regression: line that best predicts Y from X Correlation: quantifies how X and Y vary together. Correlation and Regression. Use correlation when both X and Y are measured

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Correlation and Regression

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  1. Correlation and Regression Correlation and linear regression: Not the same, but are related Linear regression: line that best predicts Y from X Correlation: quantifies how X and Y vary together

  2. Correlation and Regression Use correlation when both X and Y are measured Use linear regression when one of the variables is controlled

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  7. Correlation and Regression Linear regression If two variables are linearly related it is possible to develop a simple equation to predict one variable from the other The outcome variable (dependent variable) is designated the Y variable, and the predictor variable (independent variable) is designated the X variable

  8. Correlation and Regression • Assumptions • Values of the independent variable (X) are fixed and/or measured without error • For each observed value of X, there is a normally distributed population of Y values. • Variances of populations of Y values lie on a straight line • Errors in Y are additive • All values of Y are independents of all other values of Y

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  20. Correlation and Regression EXAMPLE

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  26. Correlation and Regression r is an estimate of the population 

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  39. Correlation and Regression EXAMPLE

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  42. Y Correlation and Regression

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  47. Correlation and Regression And beyond……. • Can compare two (or more) straight-line regression equations • Can do multiple linear regression (more than one variable)

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