# Why we need to investigate the relationship between independent variables in multiple regression

I am new to the linear regression. It seems very easy and interesting. I have one question (apologies if it is simple). Suppose that I need to predict blood pressure using age, weight and height. So, the multiple linear regression equation is given by:

$$Y = \beta + \beta_{1} X_{1} + \beta_{2} X_{2} + \beta_{3} X_{3}$$

I read a nice paper that explains the simple and multiple linear regression models (here). At the multiple linear regression section, the authors explain the relationship between the independent variables. I wonder what is the reason for that investigation? Why do we need to investigate the relationship between the independent variables? I think as I understand, we can check the relationship between the dependent and independent variables one by one in order to select the variables with a strong effect on the dependent variable! Then, we can build a multiple linear regression model based on the selected variables (Is that correct?)