least squares criterion linear regression multiple linear regression prediction interval regression line residual simple linear regression slope standard error of the estimate Y-intercept Y prime | the standard deviation of the residual scores, a measure of error in regression. prediction errors are squared and the best-fitting regression line is the one that has the smallest sum of squared errors. the difference between an actual score and a predicted score; the size of the error in prediction. the spot where the regression line would pass through the Y-axis. prediction in which Y′ is predicted from a single predictor variable. the best-fitting straight line for predicting Y from X. a range around Y′ within which there is some certainty that a case’s real value of Y falls. the tilt of the line; rise over run; how much up or down change in Y is predicted for each 1-unit change in X. prediction in which multiple predictor variables are combined to predict an outcome variable. a predictor variable is used to predict a case’s score on another variable and the prediction equation takes the form of a straight line. the value of Y predicted from X by a regression equation; Y′. |
In the DIY of Chapter 13, you calculated the correlation between foot size and height. Now, take that same correlation coefficient and generate the regression equation to predict height from foot size. When you have arrived at the equation, use it to calculate Y′ for the students on whom the equation was based. For each of the cases, calculate residual scores. Do they sum to zero? Now, find the standard deviation of the residual scores. Then, use Equation 14.4 to calculate the standard error of the estimate. Is that the same value you calculated for the standard deviation?
Want more fun? Select 10 new cases and use the regression equation to calculate Y′ scores for them. Will the regression equation be as accurate for them as it was for the original group? Investigate this by calculating residual scores and finding their standard deviation. Is it larger or smaller than the first standard deviation? Why?