RESEARCH METHODS HANDBOOK

AcaStat statistical software includes this Handbook, a search-and-expand statistics glossary, and an affordable easy to use analytical tool.

Available on CD-ROM or instantly as a download.


Contents	Introduction	Descriptive	Hypothesis	Tables	Appendix

Simple Linear Regression

Linear regression involves predicting the score on a Y variable based on the score of an X variable.

Procedure

Determine the regression line with an equation of a straight line.

Use the equation to predict scores.

Determine the "standard error of the estimate" (Sxy) to evaluate the distribution of scores around the predicted Y score.

Determining the Regression Line Data are tabulated for two variables X and Y. The data are compared to determine a relationship between the variables with the use of Pearson's r. If a significant relationship exists between the variables, it is appropriate to use linear regression to base predictions of the Y variable on the relationship developed from the original data.

Equation for a straight line

= predicted score

b = slope of a regression line (regression coefficient)

x = individual score from the X distribution

a = Y intercept (regression constant)

= mean of variable X

= mean of variable Y

Use an X score to predict a Y score by using the completed equation for a straight line.

Determine the Standard Error of the Estimate Higher Syx values indicate less prediction accuracy.

Confidence Interval for the Predicted Score
Sometimes referred to as the conditional mean of Y given a specific score of X.

Determine critical value

Degrees of Freedom (df)= n-2
Select alpha (generally based on .05 for a 2-tailed test)

Obtain the critical value (t_cv) from the t-distribution

Use the Standard Error of the Estimate and the t_cvto create confidence interval

Example