So what you end up with in multiple regression is an equation where a value is
given to every predictor variable in terms of how much it influences the measurements
that we're taking in the dependent variable, or the criterion variable.
How much of memory variance is predicted by aging,
the biological processes of aging?
How much of the dependent variable memory is predicted by health?
So that's the equation that the multiple regression analysis gives us.
So Y, in this equation, Y is the criterion variable.
And the Y criterion variable is predicted by a whole bunch of
different predictor variables, that is, the Xs.
And then b is actually the weight in the equation for each predictor variable.
There's always some noise in the way the asymptote of the relationship's going to
be, and that's represented by b0.
But b1, b2, and b3 are the values that the multiple regression gives us for
each of the predictor variables in the equation.
So let's look at an example.
This is the example by Kliewer and colleagues on what are the effects of
violence, stress and social support on internalizing behavioral problems.
So you have measures of each one.
These case participants of children, 8 to 12-years-old.
They lived in high violence areas of the US.
And so our hypotheses are that violence and
stress will increase internalizing behaviors, and
social support will actually decrease internalizing behaviors.
And we'll look to see whether that's true by using multiple linear regression.
So our predictor variables are degree of witnessing violence.
They're living in a violent area.
Measures of life stress, measuring stress on the part of the children.
And then measuring social support, the one that's supposed to decrease internalizing.
And we measure all of those.
And then we have an outcome, or criterion variable,
which is internalizing behavior, things like depression, anxiety, withdrawal.
These are symptoms of internalizing the behavior,
bringing it into us rather than dealing with it.
And we use that by measuring the Child Behavior Checklist,
which is a measure of anxiety and depression in children.