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Say that I have a model $\hat Y_i=\hat \beta_0+\hat \beta_1X_{i1}+\hat \beta_2X_{i2}+u_i$, where $X_{i1}$ is a binary variable that takes the value 1 if female and 0 if male, and $\hat Y$ is the estimated weight of the baby. The question asks to test whether the estimated model is statistically different for male and female babies. I am confused which test the question is asking for and which variable is to be tested.

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I suppose that you have to prove that coefficient beta_1 is statistically significant or not. If it is not, then you perform the regression ignoring if it is male or female. The interest of introducing this binary variable is that, if significant, you have a model with three parameters instead of four if regressions were built independently for males and females. If beta_1 is not significant, you are done with only two parameters.

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