5. Here we want to test whether the assessed housing price (assess below) is a r
ID: 3042003 • Letter: 5
Question
5. Here we want to test whether the assessed housing price (assess below) is a rational prediction for the actual housing price (price below) using variables
price = house price
assess = the assessed housing value (before the house was sold)
Consider a simple regression model price = 1 + 2assess + , the assessment is rational if 1 = 0 and 2 = 1. The estimated equation and other related information are given by
price = 14.47 + 0.976 assess
(16.27) (0.049)
n = 88, RSS = 165,644, R2 = 0.82
where the numbers in the parentheses are standard errors. Assume that Classical Assumptions for
SLRM (Simple Linear Regression Model) hold. Do the following questions.
(a) Obtain a 99% confidence interval of 2.
(b) Assume 1 = 0 is true. Test the hypothesis that the assessment is rational.
(c) On average, what is the estimated difference in housing prices with a house having an assessment of $100,000 versus a house with an assessment of $140,000 ?
Explanation / Answer
Answer:
5. Here we want to test whether the assessed housing price (assess below) is a rational prediction for the actual housing price (price below) using variables
price = house price
assess = the assessed housing value (before the house was sold)
Consider a simple regression model price = 1 + 2assess + , the assessment is rational if 1 = 0 and 2 = 1. The estimated equation and other related information are given by
price = 14.47 + 0.976 assess
(16.27) (0.049)
n = 88, RSS = 165,644, R2 = 0.82
where the numbers in the parentheses are standard errors. Assume that Classical Assumptions for
SLRM (Simple Linear Regression Model) hold. Do the following questions.
(a) Obtain a 99% confidence interval of 2.
Df for t= n-2=88-2=86
99% t critical at 86 df =2.634
CI=±t*se
99% lower confidence interval of 2 = 0.976-2.634*0.049 =0.846934
99% upper confidence interval of 2 = 0.976+2.634*0.049 =1.105066
(b) Assume 1 = 0 is true. Test the hypothesis that the assessment is rational.
The assessment is rational if 1 = 0 and 2 = 1.
The 99% confidence interval for 2 is ( 0.8469, 1.1051) contains the value 1.
2 is not different from 1.
The assessment is rational.
(c) On average, what is the estimated difference in housing prices with a house having an assessment of $100,000 versus a house with an assessment of $140,000 ?
0.976*140000 - 0.976*100000 = 39040
Estimated difference in housing prices = $ 39040.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.