5. A simple linear regression model with zero intercept term is specified as: y, = B,x; +ɛ, where ɛ is the error term This is a simple linear regression model through the origin and the OLS estimator of its slope is given as follows: ΣΧΥ B, = Note: You can derive this estimator of the slope using the same techniques we used in-class to derive the OLS estimators for the slope and intercept of the simple linear regression model with non-zero intercept. a. Assuming that this simple linear regression model fulfills all the classical assumptions we discussed in class, please show that the OLS estimator of its slope given above is an unbiased estimator. [Hint: Use the same technique we used in class to demonstrate the

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5. A simple linear regression model with zero intercept term is specified as:
y; = B,x, +E,
where ɛ is the error term
This is a simple linear regression model through the origin and the OLS estimator of its slope
is given as follows:
Σχ
ΣΧ
Note: You can derive this estimator of the slope using the same techniques we used in-class
to derive the OLS estimators for the slope and intercept of the simple linear regression model
with non-zero intercept.
a. Assuming that this simple linear regression model fulfills all the classical assumptions we
discussed in class, please show that the OLS estimator of its slope given above is an
unbiased estimator. [Hint: Use the same technique we used in class to demonstrate the
unbiasedness of the OLS estimator of the slope for a model with non-zero intercept.]
Transcribed Image Text:5. A simple linear regression model with zero intercept term is specified as: y; = B,x, +E, where ɛ is the error term This is a simple linear regression model through the origin and the OLS estimator of its slope is given as follows: Σχ ΣΧ Note: You can derive this estimator of the slope using the same techniques we used in-class to derive the OLS estimators for the slope and intercept of the simple linear regression model with non-zero intercept. a. Assuming that this simple linear regression model fulfills all the classical assumptions we discussed in class, please show that the OLS estimator of its slope given above is an unbiased estimator. [Hint: Use the same technique we used in class to demonstrate the unbiasedness of the OLS estimator of the slope for a model with non-zero intercept.]
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