Econometrics Suppose that you estimate a model of house prices to determine the
ID: 3129267 • Letter: E
Question
Econometrics
Suppose that you estimate a model of house prices to determine the impact of having beach frontage on the value of a house. You do some research, and you decide to use the size of the lot instead of the size of the house for a number of theoretical and data availability reasons. Using 30 observations, your estimated regression results are (with PRICE, measured in thousands of dollars, as the dependent variable):
Variable Estimated Standard
Coefficient Error
Constant 40
LOT 35 5
AGE -2.5 1
BED 10 10
FIRE -4 4
BEACH 100 10
where LOT is the size of the lot measured in thousands of square feet, AGE is the age of the house in years, BED is the number of bedrooms in the house, FIRE equals 1 if the house has a fireplace and 0 otherwise, and BEACH equals 1 if the house has a beach frontage and 0 otherwise.
a. You expect the variables BED and BEACH to have positive coefficients. For each variable individually, formulate and test the appropriate one-sided hypothesis to evaluate the expected sign at the 5-percent level of significance.
b. You expect AGE to have a negative coefficient. Formulate and test the appropriate hypothesis at the 5-percent level of significance.
c. At first you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces are messy and are a pain to keep clean, so you are not sure about the expected sign. Run a two-sided test (around zero) to test the statistical significance of this coefficient at the 5-percent level of significance.
Explanation / Answer
PRICEi = 40 + 35.0 LOTi – 2.0 AGEi + 10.0 BEDi – 4.0FIREi + 100 BEACHi
n = 30, R2 = .63
where,
PRICEi = the price of the ith house (in thousands of dollars)
LOTi = the size of the lot of the ith house (in thousands of square feet)
AGEi = the age of the ith house in years
BEDi = the number of bedrooms in the ith house
FIREi = a dummy variable for a fireplace (1 = yes for the ith house)
BEACHi = a dummy for having beach frontage (1 = yes for the ith house)
a) You expect the variables BED, and BEACH to have positive coefficients. Create and test the appropriate hypotheses to evaluate these expectations at the 5 percent level.
For BED;
Ho: BED = 0
Ha: BED > 0
t – score: (10.0) / (10.0) = 1.0
t-critical: 1.711 because d.f. is 24 and 5% level of significance.
Since 1.0 < 1.711, we cannot reject the null hypothesis that the true coefficient of BED is not positive.
For BEACH;
Ho: BEACH = 0
Ha: BEACH > 0
t – score: (100) / (0.9) = 11.1
t-critical: 1.711 because d.f. is 24 and 5% level of significance.
Since 10.0 > 1.711, we can reject the null hypothesis that the true coefficient of BEACH is not positive.
b) You expect AGE to have a negative coefficient. Create and test the appropriate hypothesis to evaluate these expectations at the 10 percent level.
For AGE;
Ho: AGE = 0
Ha: AGE < 0
t – score: ( - 2.0) / (1.1) = - 1.81
t-critical: 1.318 because d.f. is 24 and 10% level of significance.
Since | - 1.81 | > |1.318|, we can reject the null hypothesis that the true coefficient of AGE is not negative.
c) At first you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces are messy and are a pain to keep clean, so you are not sure. Run a two-sided t-test around zero to test these expectations at the 5 percent level.
For FIRE;
Ho: FIRE = 0
Ha: FIRE 0
t – score: ( - 4.0 ) / (3.0) = - 1.3
t-critical:: 2.064 because d.f. is 24 and 5% level of significance.
Since | - 1.3 | < 2.064, we cannot reject the null hypothesis that the true coefficient of FIRE is not different from zero.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.