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Ch 14: Correlation and Regression, The relationship between two variables…
Ch 14: Correlation and Regression
Definitions & Conceptions
Formulas & Calculations
The Pearson correlation coefficient symbol is r.
The range of Pearson r is - 1.00 to +1.00
Hypothesis Testing & Interpretation
Applications & Uses
The relationship between two variables is measured by correlation
Correlations
Strength
Direction
Positive correlations show that variables rise in tandem
Negative correlations show that one variable rises while the other falls
There is no linear relations when the correlation is 0
Tightly clustered points = strong relationships
Widely dispersed = weak relationships
One variable is predicted from another using regression
Covariance is the basis for Pearson r
The coefficient of determination (r²) represents the percentage of shared variation
Joint variation between variables is measured by covariance
Y = bX + a is the regression equation
The slope (b) shows how much Y changes for every unit increase in X
A correlation's statistical significance can be determined through hypothesis testing
Correlation degrees of freedom are equivalent to n - 2
Correlation does not imply causation.
Spurious correlations can be produced by third variables
One participants's pair of scores is represented by each point on a scatterplot
Relationships between variables are shown graphically in scatterplots
X --> predictor variable
Y --> Criterion variable
Research in a behavioral science, forecasting, and prediction all make use of regression