you have at least two independent/explanatory variables, therefore, you should use multiple regression

Thank you. Why not Multilevel regression? and could you please tell how the multi-variable regression can be done to compare both materials? I am actually looking for how "within" copper and Aluminum, the porosity and PPi effect velocity loss.

FYI: I already ran simple linear regression and it didn't work.

Assuming that porosity, PPI, and velocity loss are continuous variables, then this is a straightforward multiple regression. You regress velocity loss on porosity, PPI, metal (coded as a dummy variable or something), and whatever interactions are relevant.

To enhance Stephen Politzer-Ahles answer, you can run either of the following models (I am using SAS Proc REG or GLM syntax).   Set up a 0, 1 indicator for Copper or Aluminum (I will call this Metal).

1.  Model VelLoss=Metal porosity metal*porosity PPI metal*PPI;  Here the t-test for metal*porosity and metal*PPI will test the equality of the regression coefficient for the two metals.

2. Create a 0, 1 indicator for both copper and aluminum and run the no intercept model   MODEL  VelLoss=Alum Copper Alum*porosity Copper*porosity Alum*PPI copper*PPI /NOINT;     The coefficients in this model should be the same as you get running separate models for alum and copper.   The fit of the model should be the same as the first model.   They are essentially the same models with different parametrizations for the coefficients.

Depending on your package (or whether you use the REG or GLM procedures in SAS) you may have to create variables that are the product of the indicated variables if interaction terms are not allowed.

Thank you people. I will try your suggestions.