ETF2100/5900 Introductory Econometrics
Assignment 1 — A Case Study on the House Price of Stockton California
Important notes:
1. This is an individual assignment. This assignment is worth 20% of this unit’s total mark.
Marks will be deducted for late submission on the following basis: 10% for each day late,
up to a maximum of 3 days. Assignments more than 3 days late will not be marked.
2. Submission deadline for coursework is 12 pm noon Friday of Week 7 (i.e., 23/04/2021).
Please submit a soft copy through Moodle. Name the soft copy as follows: student
ID Name.doc (or .pdf). Pdf file is preferred, but word file is also fine. Also, on the
title page, please make sure you provide the student ID and name correctly.
3. Notation used in the assignment needs to be typed correctly and properly. Incorrect (or
inconsistent) notations are treated as wrong answers.
Please pay attention to the words in bold.
There are 6660 observations of data on houses sold from 1999-2002 in Stockton California
in the file “hedonic1.xls”. Use the data of 2001 only to estimate the next linear model and
answer the associated questions below.
LSP = β01 + β02 SFLA + β03 BEDS + β04 BATHS + β05 STORIES
+β06 VACANT + β07 AGE + u, (1)
where u is an error term. Note that the sub-index i of each variable has been suppressed in the
above equation.
LSP = ln(Selling Price), which is a function of:
• SFLA – Size of Living Area (in square feet)
• BEDS – Number of Bedrooms
• BATHS – Number of Bathrooms
• STORIES – Number of Stories
• VACANT – Vacancy Status (1 if vacant, 0 if not at the time of the sale)
• AGE – Age of the House in Years
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Questions: (20 marks in total)
1. Calculate the descriptive statistics for LSP and all explanatory variables (i.e., 7 VARI-
ABLES IN TOTAL), and report them in a table. (2 points)
2. Estimate the above hedonic model for the houses sold from in Stockton California.
(a). Write down the estimated model (including estimates of the coefficients and the
associated standard deviations, and R2 at least). (3 points)
(b). Discuss the estimation results using Goodness of fit. (1 points)
3. Keep two decimals for the calculation involved.
(a). At the 5% significance level, test the OVERALL significance of the model. What is
the restricted model in this case? Write down the details of your test. (3 points)
(b). At the 5% significance level, test if “the age of the house in years” has NEGATIVE
impacts on “ln(Selling Price)”. (3 points)
4. Write the model (1) using a vector form in a sample version as follows:
yi = β01xi1 + β02xi2 + · · ·+ β07xi7 + ui = x′iβ0 + ui, (2)
where i = 1, . . . , N , β0 = (β01, . . . , β07)
′, xi = (xi1, . . . , xi7)′ = (1, SFLA, . . . ,AGE)′, and
the definition of yi should be obvious. Further define X = (x1, . . . , xN)
′ in case one may
need this notation to answer the following questions.
(a). To obtain the OLS estimate of β0 of (2), we need to minimize an objective function.
Please write down the correct function form of the objective function. (1 point)
(b). Describe the basic assumptions of the classic linear regression models using the nota-
tions of (2). (2 points)
(c). Provided that these assumptions hold, what conclusions can you make about the OLS
estimators? (1 points)
5. For ETF2100 students only! Let’s simplify the model (2). Suppose that there is only
one regressor, and we do not even include an intercept for the new model. So it becomes
yi = β0xi + ui, (3)
where every variable is a scalar. Suppose that (xi, ui) is independent and identically
distributed across i, and {ui | i = 1 . . . , N} is independent of {xi | i = 1 . . . , N}. ui is
an error term satisfies that E[ui] = 0 and E[u
2
i ] = 1. In addition, let E[xi] = 1 and
2
E[x2i ] = 2. While calculating the standard errors, one always needs to consider the value
of E
[
( 1
N
∑N
i=1 xiui)
2
]
. Please calculate its value and provide the detailed steps. (4 points)
5. For ETF5910 students only! Provide detailed steps to prove that by minimizing the ob-
jective function in question (4), your OLS estimate has the form β̂ =
(∑N
i=1 xix
′
i
)−1∑N
i=1 xiyi.
We assume that
∑N
i=1 xix
′
i is invertible. (4 points)
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