Bivariate Correlation & Regression
1. Direction of relationship (+ or -)
2. Form of relationship (linear is most common)
3. Degree of relationship (measured by the numerical value of the correlation. A value of 1.00 indicates a perfect relationship and a value of zero indicates no relationship)
Conceptually, Pearson correlation coefficient computes
Regression--the statistical technique used to find the best-fitting straight line (i.e., the regression line) for a set of data.
where the value of "b" is the slope and the value of "a" is the y-intercept
Caution when interpreting predicted values from regression equations:
1) The predicted value is not perfect. Three will be some error between predicted Y values and the actual data...As absolute value of the correlation coefficient gets closer to zero, the magnitude of the error will increase.
The standard error of estimate (SEE) provides a measure of how accurately the regression equation predicts the Y values. For example, SEE of 2.16 would tell us that the standard or average distance between the actual data points and the regression line is 2.16 units. There will be, on average, 2.16 units of discrepancy between our predicted values we obtain using the regression equation and the actual values in the data.
2) The regression equation should not be used to make predictions for X values that fall outside of the range of values covered by the sample data.
coefficient of determination
Indicates the size or strength of the relationship between x and y. Measures the proportion of y variability that is associated with the x variable.
categories for r2 (same as for t-test or ANOVA)
.01 for small
.09 for medium
.25 or larger for a large correlation
In regression r2 also provides a measure of the accuracy of the prediction using the regression equation. Because r2 measures the predicted portion of variability in the Y scores, we can use the expression (1 - r2) to measure the unpredicted portion or residual variability.