**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*

Where:

y is the

b is the percentage of change in x for every 1 unit of change in y.

b is also known as the

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:

- People who marry early tend to get divorced in greater numbers than
people who wait to marry.
*Our measure of Early Marriage is Positively Related to our measure of Proneness to Divorce*. - People with low education levels also tend to get divorced in greater numbers than the educated. Education level is negatively related to Proneness to Divorce.
- People who's religious faith strongly prohibits divorce tend to divorce
less than those who's faith is more liberal where divorce is concerned.
*Religious Sanctions are negatively related to Proness to Divorce*. - People who have simply had more of a chance to mingle with the opposite
sex will tend to divorce more than people who are relatively cut off from
members of the opposite sex.
*Our measure of Opportunity to Mingle is positively related to Proneness to Divorce.*

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.