# OLS Regression Output interpretation (really urgent)

#### peter94

##### New Member
Hi guys,

I have the following output and I really need your help with this:  The questions are:

a) Regressor X3 is a dummy variable (X3 = 1 if individual belongs to group 1). What
interpretation can you give to the corresponding coefficient?
b) The dependent variable was generated by the command yi = ln(wi). How does the
interpretation in a) change?
c) Variable X5 is the interaction between X3 and X4 both being dummy variables.
What is the effect of X4 on the dependent variable
d) how do we interpret the t-ratio and the corresponding p-value of any of the estimated coefficients?
e) And can someone explain me the difference between the Standard error of the coefficient, the standard error of the dependent variable, standard error of regression and the sum of squared residuals in an easy manner?

a) Individuals in group 1 (X3=1) have 0.06 units more in the dependent Variable Yi than people not belonging to group 1.

b) the interpretation does not change.

c) if X4=0 the effect on yi is solely -0.0615 from X5 and if it is X4=1 it is -0.0615 + 0.04

d) the p-value basically tests whether the null-hypothesis holds or not (is the estimated value any different from 0). If it is alpha>p-value the estimated coeff. are significant and not equal to 0. But how to interpet the t-stat? How to use the t-stat to infer something about whether we reject the H0 or not.

e) i would be thankful if you explain the difference because I don't really understand it

Thank you very much in advance. I have an exam tomorrow so I would be grateful if anyone could answer my questions.

Last edited:

#### Karabiner

##### TS Contributor
a) Individuals in group 1 (X3=1) have 0.06 units more in the dependent Variable Yi than people not belonging to group 1.
b) the interpretation does not change.
I'd guess that they want you to be a little more exact regarding what you mean by "unit".
In the first interpretation, yi=wi. In the second, yi=ln(wi)

With kind regards

Karabiner

#### peter94

##### New Member
I'd guess that they want you to be a little more exact regarding what you mean by "unit".
In the first interpretation, yi=wi. In the second, yi=ln(wi)

With kind regards

Karabiner
These are just my answers, not the solution.

but is the second interpretation correct? what happens if X3 increases by one unit? do I need to look at the first derivative with regard to a change of X3?