Question

g Consider a multiple regression model: y = ????0 + ????1x1 + ????2x2 + ????. Which of the following is NOT the correct expression of the interpretation of the slope parameter ????1? (a) The partial effect of x1 on y (b) The effect of x1 on y holding x2 constant (c) The Ceteris Paribus effect of x1 on y (d) All of the above are correct interpretation.

Answer 1

Completed Equation of Question:

$y = \beta_{o}\;+\;\beta_{1}x_1\;+\;\beta_{2}x_2\;+\mu$

Answer:

Option (d): All of the above are correct interpretation.

Explanation:

In the given equation:

$y = \beta_{o}\;+\;\beta_{1}x_1\;+\;\beta_{2}x_2\;+\mu$

It would be inaccurate to state that: For every unit change in x1, y changes by $\beta_1$ units.

The correct statement would be: For every unit change in x1, y changes by $\beta_1$ units, keeping $x_2$ constant. This is the same as taking partial derivative or applying Ceteris Paribus effect (which means keeping all other variables equal which in this case is $x_2$. Hence, the slope parameter is correctly interpreted by all options.