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.
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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.