Suppose a housing advocacy group is interested in looking at what affects housin
ID: 3295370 • Letter: S
Question
Suppose a housing advocacy group is interested in looking at what affects housing costs,so they collect data for 351 counties in their state and compare the fair market rent for a four-bedroom unit with the following county-level data: population per square mile, per capita income, percent of population speaking language other than English at home (ESL), and percent of population with at least a bachelor’s education. The results of the regression are shown in the following table:
a. Indicate which, if any, of these variables, is a significant predictor of housing prices.
b. Solve for the rent for a county with a population density of 550/square mile, $30,000 income per capita, 8% ESL, and 40% with a college degree (Note: for the “percent,” do not make these into decimals; for example, “10%” = 10, not 0.10).
C. Interpret the regression coefficients for population density and a college degree.
b
se
t
sig
constant
301.765
66.260
4.554
0.001
Population density
0.033
0.009
3.498
0.001
Income per capita
0.054
0.004
13.274
0.001
Esl %
0.989
1.975
0.501
0.617
College degree %
-15.723
2.600
-6.047
0.001
b
se
t
sig
constant
301.765
66.260
4.554
0.001
Population density
0.033
0.009
3.498
0.001
Income per capita
0.054
0.004
13.274
0.001
Esl %
0.989
1.975
0.501
0.617
College degree %
-15.723
2.600
-6.047
0.001
Explanation / Answer
a) Let's assume alpha = 0.05
In the output below, we can see that the predictor variables of Population density, Income per capita and College degree % are significant because of their p-values are 0.001. However, the p-value for Esl % (0.617) is greater than the common alpha level of 0.05, which indicates that it is not statistically significant.
b) Equation:
Housing price = 0.033 * PD + 0.054 * IPC + 0.989 * ESL - 15.723 * CD + 301.765
Put given values:
Housing price = 0.033 * 550 + 0.054 * 30000 + 0.989 * 8 - 15.723 * 40 + 301.765
Housing price = 1318.907
c) Population density coefficient = 0.033 is positive which means as we increase this by 1 unit the house price will increase by 0.033 units.
College degree coefficient = -15.723 is negative which means as we increase this by 1 unit the housing price will decrease by 15.723 units.
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