Correlation and Regression Correlation and linear regression Not
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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 Use linear regression when one of the variables is controlled
Correlation and Regression
Correlation and Regression
Correlation and Regression
Correlation and Regression
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
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
Correlation and Regression
Correlation and Regression
Correlation and Regression
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Correlation and Regression E LE P M XA
Correlation and Regression E LE P M XA
Correlation and Regression E LE P M XA
Correlation and Regression
Correlation and Regression
Correlation and Regression
Correlation and Regression r is an estimate of the population
Correlation and Regression E LE P M XA
Correlation and Regression E LE P M XA
Correlation and Regression
Correlation and Regression
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Correlation and Regression E LE P M XA
Correlation and Regression E E L P M XA
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Correlation and Regression And beyond……. • Can compare two (or more) straight-line regression equations • Can do multiple linear regression (more than one variable)