1. You have obtained a sub-sample of 1744 individuals from the Current Population
Survey (CPS) and are interested in the relationship between weekly earnings and
age. The regression yielded the following result:
???????????????? = 239.16 + 5.20Age, R2 = 0.05, SER = 287.21
where Earnings and Age are measured in dollars and years respectively.
a. Interpret the intercept.
b. Interpret the coefficient on Age.
c. The average age in this sample is 37.5 years. What are average weekly
earnings in the sample?
d. At a significance level of 5%, we would say that the slope coefficient is
not statistically significantly different from zero. Calculate the relevant
confidence interval to show this.
e. Consider a 45-year-old in the sample with weekly earnings of $1,000.
Calculate the residual for this person. Explain what your answer means in
f. Interpret R2.
g. Give an example of a factor that may be causing omitted variable bias.
Based on the direction of the bias, after adding the omitted variable, will
the coefficient on Age in this multiple regression be > 5.20 or < 5.20?
2. As we all know, correlation does not imply causation. On other words, if X and
Y are correlated, it doesn’t necessarily mean that X causes Y; there are two other
possible explanations. What are they? Take two of these three explanations for
the correlation between X and Y and, using an example, show that these two
explanations do not have to be mutually exclusive. In other words, give an
example of an X and Y that are related in, simultaneously, two different ways.
3. You have estimated an earnings function, where you regressed the log of earnings
on two binary variables, one for gender and the other for marital status.
a) Write down the regression equation such that the intercept corresponds to
a single male, without allowing for interaction between marital status and
b) According to your regression equation from part (a), what are the…