Question

Consider the following simple linear regression model $Y = \alpha + \beta D + u$ where $D$ is a binary variable denoting treatment and takes the value 1 if the individual is treated and ) otherwise, $Y$ is a continuous variable and is the realized outcome of interest. You have a total of $n$ number of observations, with $n_1$ observed to be treated and $n_0$ without treatment. Suppose $\hat{\beta}_{OLS}$ is your OLS estimator of the parameter $\beta$. Show that $\hat{\beta}_{OLS}$ is the observed difference in the sample means of $Y$ between the treated and the untreated group. How does the above result relate to the interpretation of $\beta$?

          Consider the following simple linear regression model
$Y = \alpha + \beta D + u$
where $D$ is a binary variable denoting treatment and takes the value 1 if the individual is treated and
) otherwise, $Y$ is a continuous variable and is the realized outcome of interest. You have a total of $n$
number of observations, with $n_1$ observed to be treated and $n_0$ without treatment. Suppose $\hat{\beta}_{OLS}$ is
your OLS estimator of the parameter $\beta$. Show that $\hat{\beta}_{OLS}$ is the observed difference in the sample means
of $Y$ between the treated and the untreated group.
How does the above result relate to the interpretation of $\beta$?

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Consider the following simple linear regression model
Y = α + β D + u
where D is a binary variable denoting treatment and takes the value 1 if the individual is treated and
) otherwise, Y is a continuous variable and is the realized outcome of interest. You have a total of n
number of observations, with n1 observed to be treated and n0 without treatment. Suppose β̂OLS is
your OLS estimator of the parameter β. Show that β̂OLS is the observed difference in the sample means
of Y between the treated and the untreated group.
How does the above result relate to the interpretation of β?

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Consider the following simple linear regression model Y =alpha +eta D+u where D is a binary variable denoting treatment and takes the value 1 if the individual is treated and ) otherwise, Y is a continuous variable and is the realized outcome of interest. You have a total of n number of observations, with n1 observed to be treated and n0 without treatment. Suppose eta ˆols is your OLS estimator of the parameter eta . Show that eta ˆols is the observed difference in the sample means of Y between the treated and the untreated group. How does the above result relate to the interpretation of eta ? Consider the following simple linear regression model Y=a+3D+u where D is a binary variable denoting treatment and takes the value 1 if the individual is treated and ) otherwise, Y is a continuous variable and is the realized outcome of interest. You have a total of n number of observations, with ni observed to be treated and no without treatment. Suppose ols is your OLS estimator of the parameter B. Show that ols is the observed difference in the sample means of Y between the treated and the untreated group. How does the above result relate to the interpretation of ?

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