Question

Consider the following multiple regression model: y = β₀ + β₁x₁ + ... + β_kx_k + u. Which of the following statements is correct?

	a.	The multiple linear regression model with a binary dependent variable is called the linear probability model (LPM).
	b.	In the LPM, because the response probability is linear in the parameters βj, βj measures the change in the probability of success when xj changes, holding other factors fixed.
	c.	In the LPM, beta with hat on top subscript 0, is the predicted probability of success when each xj is set to zero, which may or may not be interesting.
	d.	All of the above.

Answer 1

Here the dependent variable (Y) for each observation takes values which are either 0 or 1. The probability of observing a 0 or 1 in any one case is treated as depending on one or more explanatory variables, x₁,x₂,...,x_p, say.

Hence

The multiple linear regression model with a binary dependent variable is called the linear probability model (LPM).

In the LPM, because the response probability is linear in the parameters , measures the change in the probability of success when changes, holding other factors fixed.

In the LPM, beta with hat on top subscript 0, is the predicted probability of success when each is set to zero, which may or may not be interesting.

Option d. All of the above.