Calculate and apply a linear regression equation for a Pearson correlation coefficient.
Linear regression predicts a value of Y, Y′, for X when there is a statistically significant relationship between X and Y. The prediction equation uses the slope and Y-intercept to generate a regression line, the best-fitting line that minimizes the errors between Y and Y′. Slope indicates how much change in Y is predicted for each 1-unit change in X, and the Y-intercept tells where the line passes through the Y-axis.
As r approaches zero, the regression line becomes horizontal and predicted Y values approach MY. When r = 0, then X doesn’t predict Y and the best prediction that can be made for Y′ is MY.
Measure uncertainty in regression predictions.
Error in prediction is the difference between the actual score, Y, and the predicted score, Y′.
The average amount of error is summarized in a statistic called the standard error of the estimate, which is the standard deviation of the residual scores.
Describe how multiple regression works.
Simple regression uses a single predictor variable to predict Y′; multiple regression uses two or more predictor variables. By combining the unique predictive ability of multiple predictor variables, multiple regression accounts for more variability in the outcome variable.