# Interpret coefficient for dummy variable in multiple linear regression

I have the a multiple linear regression looking like this:

$$y = \alpha + \beta_1 female + \beta_2 x_2 + \beta_3 x_3$$

"female" is a dummy variable (0=male, 1 = female)

My overall hypothesis is that "Being male increases the effect on Y".

The coefficient for female is -0.076 and the p-value is 0.516.

I am not entirely sure how to interpret this. I know there is no statistical significance as the p-value is high but what exactly does this mean... which of the following statements is correct?

1) "As the p-value is high the hypothesis stating that being a man increases the effect of y can be rejected"

OR

2) "As the p-value is high there is no statistical evidence that being a man increases the effect of Y but the hypotheses cannot be rejected, as there is no statistical significance.

This is more a question on p-value and hypothesis tests than on dummy variables.

The hypothesis here are:

H0: B1=0, that is, being male doesn't increase the effect. H1: B1<0, that is, being male increases the effect.

Please notice that those hypothesis could also be worded about being female, since in this context "being male increases the effect" is synonymous with "being female decreases the effect".

And just as an end note: please beware that your hypothesis fits a one-sided test, but most statistical packages perform two-sided tests by default. In a two-sided test H1 would be that B1 is different than 0, and could lead to different (and even misleading) results.

In an hypothesis test we find evidence to reject the null hypothesis (H0) or we don't find it. A large p-value means we don't have evidence to reject that being male doesn't increase the effect, and therefore we don't have evidence to affirm that being male increases the effect.

• Thanks a lot for your answer @pere. Ive used Stata to run the test. Do you know if i will have to calculate test statistic and p-value myself then to test the desired hypothesis or if stata automatically do a one-sided test for a dummy variable? – maS May 2 '19 at 14:41
• I'm not sure if Stata can perform an one-sided test on regression parameters, but the test statistic is the same for one-sided and two-sided tests. Therefore, you can take the test statistic (and number of degrees of freedom) from Stata and compute p-value using t-Student. – Pere May 2 '19 at 15:27