1. Short Answer (3 points each): a. Agree or Disagree (and justify your answer): If the distribution of u in a population regression model is not normal, then the OLS estimators are not BLUE. b. Agree...

Homework 4. Due by 11:00 PM, Tuesday, July 31st
(Worth 42 points total)

1. Short Answer (3 points each):

a. Agree or Disagree (and justify your answer): If the distribution of u in a population regression model is
not normal, then the OLS estimators are not BLUE.

Answer:

Agree: The OLS estimators are not best linear unbiased estimators if the distribution of u in a population
egression model is not normal because it violate the assumption of normality.

. Agree or Disagree (and justify your answer): If you add an independent variable to a multiple
egression model and the R-squared value rises, this indicates that adding the variable to the model was
a good idea.
Answer:

Disagree: The R-squared value rises even if we have entered the variable which is not helpful in
predicting the dependent variable. So if we are adding an to a multiple regression model and the
Adjusted R-squared value rises, this indicates that adding the variable to the model was a good idea.
c. Consider the following population regression model explaining the yield per acre of a plot of land
planted with corn (yield) as a function of the inches of rain falling on the plot in the first month of the
growing season (rain) and the kilograms of a certain
and of fertilizer added to the plot (fertilizer).

yield = β0 + β1rain + β2fertilizer + β3fertilizer*rain + u

If the value of β3 is positive, what does this tell us about the effectiveness of this
and of fertilizer?

Answer:
It means that the interaction of Rain and Fertilizer help in more yields. In other words we can say that
this
and of fertilizer works best with the rain and it is effective.

d. A regression was estimated in which the dependent variable was the median home price in a
neighborhood. The independent variables were crime, the crime rate in the neighborhood, nox, the
amount of nitrous oxide in the neighborhood’s air (a measure of pollution), and rooms, the average
number of rooms in the neighborhood’s houses. The Stata output from this regression is below.

------------------------------------------------------------------------------
price | Coef. Std. E
. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
crime | -199.701 35.0532 -5.70 0.000 -268.5701 -130.8319
nox | -1306.057 266.1392 -4.91 0.000 -1828.941 -783.1733
rooms | 7933.184 407.8665 19.45 0.000 7131.849 8734.52
_cons | -19371.47 3250.938 -5.96 0.000 -25758.59 -12984.35
------------------------------------------------------------------------------

Agree or Disagree (and justify your answer): these results indicate that air pollution is a more important
determinant of housing prices than is crime.

Answer:

Disagree: Both the variables are significant at 5% level of significance and both variables have the
negative coefficient. We can see if there is a one unit increase in nox variable then the median home
price will decrease by 1306.057 time and if there is one unit increase in the crime then the median home
price will decrease by 199.701 times. So it does not indicate that air pollution is a more important
determinant of housing prices than is crime.

e. In a multiple regression model using 310 students to explain college grade point average, the following
explanatory variables are initially included in the regression: high school GPA, ACT score, number of
credits completed, mother’s years of education, and father’s years of education. The R-squared is .436.
When the two parents’ education variables are dropped, the R-squared becomes .381. Are the parents’
education variables significant at the 5% level? (Hint: remember that the lectures and the book both
explain how to conduct an F-test of joint significance using R-squared values from two regressions).

Answer:








F = ((0.436-0.381)/3)/((0.381/(310-5)) = 14.67629
Critical value = 2.696

Yes, he parents’ education...