How do you regress out nuisance variables from response variable and save the residuals for further regression analysis?

I’m trying to do a multiple regression, and I have variables of interest and nuisance variables. All the variables (independent and dependent) are continuous; they are all column vectors. I would like to fully regress out the nuisance variables before doing the multiple regression with the variables of interest. So I would like to remove the variance in the response variable that can be explained by the nuisance variables, and save the residuals of the response variable as a new variable. Then do the multiple regression with the variables of interest and the response residuals variable. How can I do the first regression (with the nuisance variables) and save the residuals as a new variable?

[Sudip Kumar Kundu]

can you show the array data