00:02
Once again, welcome to a new problem.
00:04
When you think about simple linear regression, when you think about simple linear regression, a typical equation or expression would look something like y equals to beta non plus beta 1x, where this is the slope and this is the intercept.
00:26
So we have both the slope and the intercept.
00:30
And when we're looking at multiple regressions, so when you're looking at multiple regression, a typical equation would be y equals to beta not plus beta 1 x1 plus beta 2 x2 up until beta n x -n.
00:51
We could always add the error for both of them.
00:55
And this is a multiple regression.
00:59
It can happen that a typical independent variable in regression analysis is not, is not, instead of saying is not, so a typical variable is a dichotomous variable such as a dichotomous variable such as a dichotomous variable.
01:30
Variables such as gender.
01:35
So gender is one example of the dichotomous variable.
01:40
And the treatment of this is that we run it like a binary variable where the, say, the female would be one and the male would be zero or the female could be zero and the male one.
01:58
One.
01:59
So that's dichotomous dummy variable that we're looking at in the problem.
02:08
So assume assume y -i, y sub -i is binary and the binary variable has two indications, has indication of whether worker or an employee worker i is employed employed after after job training uh or not so in that case i we're going to say if i have y i and uh y i is one this simply means that uh has a job so the worker has a job if y i is zero it means that uh uh the they don't have a job.
03:11
So these are the binary options for this variable.
03:16
And then we also have xi.
03:20
This has to do with participation, participation in job training programs.
03:32
So we are doing participation in job training programs such that if i have beta, if i see beta one heart, then this simply means is that this reflects differences in employment, differences in employment based on job participation.
04:13
So we're looking at differences in employment based on job participation.
04:21
So in this case, in this case, i was saying that the binary assignment, the binary assignment of variables is for purposes.
04:55
This is for purposes of transforming categorical dichotomous variables into numerical variables.
05:25
So that's the transition that you're doing in the problem.
05:31
You're doing a transformation or conversion for purposes.
05:36
Of regression analysis.
05:40
And so the simple linear regression, the simple linear regression, looks like the following.
05:58
X, i equals to beta not plus beta 1, y, i plus u.
06:08
The application of zero conditional means to this equation.
06:33
So we are applying zero conditional means to this equation.
06:41
Give expected value of x given y equals expected value of x given y equals to beta not plus beta 1 y plus expected value of you given y and so the result for this one becomes beta not plus beta 1 y and then the next step is introducing the dummy variables with values with values with values of 1 and 0...