Hello Yang -

Do you mean you are adding all of those things to make one independent variable? That does waste and even, I suppose, confuse a lot of information. You could look into using "multiple regression." You should research that term.

You could look into using a "graphical residual analysis" to check on model fit, but overfitting to a given sample can be a substantial problem. If you save some data not used in the model selection and estimation of regression coefficients, then you can see how well you predict for those other cases.

You could experiment with some models, but I suggest you make them ones you can support from a subject matter perspective, to avoid spurious results.

Best wishes - Jim

James R Knaub Dear Mr James, Thank you and I appreciate your prompt reply.

The multi-variable regression I meant was referring to the Multiple regression, maybe I used the wrong term.

so I have No. of Children, No.of adult and No. of elderly as predictor variables. Should I continue to add No. of female or No. of unmarried as well? They seems have multi-colinearity effect, but I am afraid loss of information if not adding them. May I ask for your suggestion or recommendation? Cheers

Ali H Abuzaid Dear Mr Ali, Thank you for your reply. Yes, I am trying to use AIC to stepwise my regression, in the end I still have to remove the female ratio and married ratio from the model as the AIC become higher with these two terms added.

A stepwise approach has been found, as I recall, to be disadvantageous. You can imagine different results if you try predictors in a different order. And if you try all of them, you may get spurious results just by chance. I suggest you compare graphical residual analysis results (maybe on the same scatterplot for two or more competing, reasonable models, with predicted y values on the x-axis and estimated residuals on the y-axis). Models should make sense from a subject matter perspective. If you can save some data to check performance on 'new' data, as I noted above, that may be helpful.

If you use a GLM (General Linear Model) procedure (which includes linear regression as a special case) it will automatically select one category of each factor as a reference category. In SPSS you have to ask for the regression coefficients to be displayed. The GLM procedure distinguishes between covariates (which are continuous independent variables) and factors (which are categorical independent variables).

Females and unmarried form a subset of both the adult and elderly. Adding these variables along with the total number of people (as defined by you) will introduce multicollinearity issues to your regression model. This could result in reduced stability of the corresponding parameter estimates and increased standard errors. Collinearity can also fudge the selection of important variables while using stepwise variable selection.

Including those other variables would amount to repeatition and will lead to multicollinearity which will badly affect your prediction