I have a Dependent Variable that is to be modeled against 3 Independent Variables. After drawing a scatter plot for each IV with DV, I found out that two of the three IVs show no linear relationship with DV at all. Plus, the correlation analysis shows that the coefficients of these two IVs with the DV are below 0.3 with p-values that are much larger than my significance level(0.05). The question is, should I include these two variables in my analysis and perform a multiple linear regression? Or a simple linear regression between the one IV that shows a linear relationship with the DV is enough?
P.S. The question specifically asks for Linear Regression so other alternatives are not considered.