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.
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)= n2
Select
alpha
(generally based on .05 for a 2tailed test)
Obtain
the critical value (t_{cv})from the tdistribution
Example
