Multiple Regression & Multiple Linear Regression: 2 Qu's

#1
I know these are 2 very basic question, but if someone could please confirm them for me I'd be very grateful indeed:

1. Am I correct in thinking that the difference between multiple regression and multiple linear regression is fundamentally about the level of data of the DV? So that:

a. multiple linear regression would be used with 1 dichotomous DV and multiple continuous/dichotomous IV's, and
b. multiple regression would be used with 1 continuous DV and multiple continuous/dichotomous IV's

2. Can multiple regression be used when there is more than 1 DV? (I'm thinking not!) If not, is there another technique that is more appropriate, or is it more a case of running a number of individual regressions (i.e. testing the DV's individually).

I hope to avoid SEM techniques as I think they may be rather too sophisticated for my level of statistical knowledge!

Thank you so much for any help, I really am very glad to have stumbled upon this forum!! :)
 
#2
Hi Gemma7,

Mulitple regression usually refers to muliple linear regression--there isn't really a difference. Technically, there is nonlinear regression, but most people mean linear regression if they don't specify otherwise.

The multiple refers to the fact that there is more than one independent variable. The linear refers to the type of relationship between Y, the dependent variable, and the independent variables. Any linear regression requires a continuous DV and normal residuals.

A dichotomous DV requires logistic regression. If there is more than one IV, it would be multiple logistic regression.

There is something called multivariate linear regression which allows more than one DV, but I've never actually encountered it. Multivariate always refers to multiple DVs (as in MANOVA).

If your multiple DVs are independent, then it is reasonable to run a series of individual regressions. If they are not, especially if they are conceptually related, you can run a Principal Components analysis to reduce the dimensionality of the DV (that's a fancy way of saying turning multiple variables into one). Save the component scores, then use those as the new DV.

It's conceptually the same as doing a SEM, but done as separate steps.

Karen
 
#3
Thank you so much Karen, that is a really clear and helpful answer and has clarified a lot of things for me - I'm very grateful!
 
#4
Sorry, I thought that "multivariate" referred to the independent variables, not the dependent variables.

As far as I know, a multivariate regression equation is of the form
y = a0 + a1*x1 + a2*x2 +... +an*xn

And in my understanding, regression is defined as having only one dependent variable. Otherwise it doesn't really make sense, as you are trying to fit an explanatory curve for that variable. If you had more than one, what is the significance of the curve?

MANOVA is for multiple dependent vars, yes, but it is not regression.
 
#5
It is true MANOVA can handle multiple DVs, but if you are looking for relationships, not differences, you can get multiple-multiple R (multiple DVs and multiple IVs) via canonical correlation.