The OLS estimate of the β2 parameter in the given regression model indicates the effect of a 1% increase in parental income on the likelihood of watching the movie, while controlling for student status.
The OLS estimate of the β2 parameter in the regression model provided will inform us about the effect of a 1% increase in parental income on the likelihood of having watched the movie, controlling for whether the individual is a student.
The dependent variable, Watchedi, is binary, indicating whether someone has watched the movie or not, which is a typical setup for a probit or logit model.
However, OLS can still be used to estimate relationships of this nature. Since parental income is logged (ln(ParentalIncomei)), any coefficient estimated for this variable reflects the proportional (percentage) change rather than the absolute dollar change in parental income.
Thus, the correct interpretation of the β2 parameter would be that a one-unit increase in the natural logarithm of ParentalIncome, which equates to a 100% increase in income, would result in a β2 change in the probability of having watched the movie, all other factors held constant.
However, given that we are more often interested in smaller changes, we can use the coefficient to determine the effect of a 1% change by multiplying the β2 coefficient by 0.01.
The probable question may be: "Suppose a movie studio has surveyed 1,000 random 18-22 year olds to see if they've watched their latest movie, and they wish to estimate the following regression model using OLS: Watchedi = Bo + B1 Studenti + 82 In(ParentalIncome;) + ui Where Watchedi = 1 if person i has watched the movie (and = 0 otherwise), Studenti = 1 if person i was a student (and = 0 otherwise), and ln(ParentalIncome¡) is the natural log of person i's parents' income. The OLS estimate of the 82 parameter will tell us which of the following:
a. The effect of a $1 increase in parental income on the likelihood of having watched the movie, controlling for whether they are a student.
b. The effect of a 1% increase in parental income on the likelihood of having watched the movie, controlling for whether they are a student.
c. The effect of a $1,000 increase in parental income on the likelihood of having watched the movie, controlling for whether they are a student.
d. The effect of a 1% increase in parental income on the natural-log of the likelihood of having watched the movie, controlling for whether they are a student."