Statistic of the Week

Multiple Regression and Multivariate Analysis

7400.685.080 Research Methods in HE/FE - Inst: D. Witt

We talked about correlations, and you have been plotting the values of X and Y on graphs.
These SCATTERGRAMS (many plotted XY Coordinates) have a shape that suggests a "line", which is known as the REGRESSION LINE.

By using a calculation method known as the least squares estimation method, a statistician (or a computer) can estimate the Regression Line of any correlation.
It is a "regression" line because any two coordinates are \"regressed " back to the line itself.

You may also remember from Geometry class, than any line on a graph can be generated by an equation. The Regression line has an equation too, and it is this: y = a + bx
y is the predicted value of variable Y a is the intercept (where the line crosses the y-axis)
b is the percentage of change in x for every 1 unit of change in y.
b is also known as the slope of the regression line. and x is known for any given value of X
(Oh Lordy, I can just here your math anxieties starting to hum and rumble! - Have faith! Stay with me!)

Remember those terms - intercept, slope, and predicted value of Y.

In the Bivariate case of X and Y, the regression line is equivalent to a correlation coefficient. Correlations are also bivariate regressions, so you already know this in a way.

Here's the real payoff for using Regression Analysis.

One of the big problems of being limited to analyzing only two variables at a time is that you can never be sure about the effects of variables not in the equation.

There may be some easily measured variables that have common predictive power with the independent variable of interest.
Here is what I mean:
Suppose that through bivariate research, we found the following four relationships:

Second, you get an idea of the Combined Effects of all the Independent Variables'in the equation. A different bit of information. Here's an example of a Multiple Regression Print Out!

We'll talk more about this table in class - for now you should know that the b/Beta columns represent the relative statistical "influence" of each independent variable on the dependent variable.

Your Assignment for next time is this:

1. Think about your reseach topic - all the past research, ideas you've been having about the various relationships. Write hypotheses for each of the "relationship" pairs that are important to your topic.

2. Write out the Regression equation for each "group" of relationships.

3. Draw the relationships graphically.