Question

Consider a regression equation that attempts to explain the general health condition of a cross section of persons. If the regression produced a negative coefficient on a measure of regular exercise (which you hypothesize to be positive), what would this suggest about the omitted variable that you might be looking for? Include symbols and signs in your answer if you can.

Answer 1

The Regression Equation is:

,

where

Y = General Health condition

X₁ = Regular exercise.

Suppose the coefficient is got as negative value, it indicates that that there is inverse relation between general health condition and regular exercise. This is not correct because there is direct relation between general health condition and regular exercise. The reason for the incorrect result is that we have omitted a variable: X₂ = alcohol drinking. We know if a person is addict to alcohol drinking, his general health condition will deteriorate even with regular exercise.

Thus, the correct Regression Equation with correct symbol and sign isas follows:

where

X₂ is the omitted variable = alcohol drinking

The sign of is negatibve because as the alcohol drinking increases, general health condition deteriorates.