Learn moreLearn moreApplied Statistics Handbook

Table of Contents

 


 

Simple Linear Regression

Linear regression involves predicting the score for a dependent variable (Y) based on the score of an independent variable (X). Data are tabulated for two variables X and Y. If a linear relationship exists between the variables, it is appropriate to use linear regression to base predictions of the Y variable from values of the X variable.  See multiple regression for assumptions.

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

      where

= predicted score

b = slope of a regression line (regression coefficient)

x = individual score from the X distribution

a = Y intercept (regression constant)

    where

= mean of variable X

 = mean of variable Y

 


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

 

Determine the Standard Error of the Estimate

Higher 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 (tcv)from the t-distribution

Example


Google

 


Copyright 2015, AcaStat Software. All Rights Reserved.