In https://stats.oarc.ucla.edu/stata/dae/multivariate-regression-analysis/#:~:text=As%20the%20name%20implies%2C%20multivariate,is%20a%20multivariate%20multiple%20regression they suggest that as a check you could do under "Analysis methods you might consider."

But I suggest you might also consider weighted least squares, as ideally there should be increased residual variance with larger predicted-Y values.

In a multivariate regression model, where you have multiple predictor variables and a single outcome variable, you do not necessarily need to conduct separate independent simple regressions for each predictor variable before constructing the multivariate regression model. The multivariate regression model inherently takes into account the relationships between all the predictor variables and the outcome variable simultaneously.

In fact, conducting separate independent simple regressions for each predictor variable can lead to issues like omitted variable bias and incorrect interpretation of the individual effects. This is because simple regressions do not account for the potential correlations or interactions between predictor variables.

In a multivariate regression analysis, all predictor variables are included in the model at the same time, and the coefficients associated with each predictor are estimated while controlling for the presence of the other predictors. This approach allows you to examine the unique contributions of each predictor variable while considering the joint influence of all predictors on the outcome variable. Additionally, it can help to account for potential multicollinearity among the predictor variables.

So, instead of conducting separate independent simple regressions, you can directly use a multivariate regression model to analyze the relationships between multiple predictors and a single outcome variable. This approach provides a more comprehensive and accurate understanding of the relationships among variables.

Ma'Mon Abu Hammad -

Note that multivariate regression is not multiple regression, although you can have multivariate multiple regression.

You are referring to multiple regression, not multivariate regression. Here, the topic is more than one Y, with the same predictor(s).

But for multiple regression, I agree with your comment that "...potential correlations or interactions between predictor variables" is a concern with multiple regression, and have often said so myself, except you might use another word other than "interactions" or one might think you mean terms like x_1x_2.

Cheers - Jim

Dennis M. Bulla and Ma'Mon Abu Hammad -

Actually, looking at the question again, it says "multivariate regression," but the question might really be about "multiple regression," a different topic which has been asked about a number of times, I think.

So, Dennis Bulla, what is your question?

- Jim

I would certainly do that, just to check if your independent variables have a linear influence to the DV or not!