8. For each of the following situations, determine the sign (and, if possible, comment on the
likely size) of the expected variable bias introduced by omitting a variable:
a. In an equation for the demand for peanut butter, the impact on the coefficient o
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Subjects 1 and 2. Basic Ideas of Linear Regression: Two Variables case.
Francis Galton in 1886 observed that the heights of sons tend to regress toward the
average, or the mediocrity. Thus, with the given heights of sons, we can predict the
heights of t
Subject 5. 2014 Spring
Dummy i.e., qualitative Explanatory Variables such as gender, level of education,
different regions, level of education (not the years of schooling), race, etc.
Yi= 1+ 2Di + ui
Y=annual starting salary in $1000
D=Dummy for the level
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ECON5140 A summary of a multiple regression equation
Example. Demands for residential housings in the US.
Yi = 1+ 2X2i+ 3X3i+ 4X4i+ ui, ,
Yi = ith households purchase of residential housing, measured in $1000
X2= households annual income, in $1000
X3= h
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2014 Spring ECON3560
Subject 4, FUNCTIONAL FORMS OF REGRESSION MODEL
1. Linear Regression Model
Y= f(X2, X3),
Y= 1+ 2X2+ 3X3 +u
Each regression coefficient is independent from each other and this additive.
Advantage of linear model:
a) most general, no
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(1) Household saving.
Yi = 1+ 2X2i+ 3X3i+ 4X4i+ ui, ,
Yi = ith households annual saving, measured in $1000, i=50, cross-sectional data
X2= households annual income, in $1000
X3= households wealth, in $1000
X4= its annual travel expenditure in $1000
u= r
2014 Spring Subject 6, MODEL SELECTION, CRITERIA AND TESTS
1. Criteria for good model:
a) Parsimony, as simple as possible,
b) Identifiability and stability of regression parameters, the unique values of the
regression parameters for a given model and dat
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Subject 3. Multiple regression analysis: Estimations and Inferences.
Y i= 1 + 2 X2i + 3 X 3i + U i
1, intercept; mechanically, it is the value when both X2 = X 3 =0. However, statistically
it can be interpreted as average effect on Y of all the relevant
Subject 8, HETEROSCEDASTICITY FOR CROSS SECTIONAL DATA
Yi= 1+ 2X2i+ui
To use OLS, we need E(Ui)=0, E(Ui2)= 2, identical variance, homoscedasticity for each
observation in our sample ,i.e., each sample came from a population with identical
characteristics.
Subject 9 AUTOCORRELATION IN THEE TIME-SERIES DATA
For an accurate OLS estimation, the sample time-series data must be random, i.e. any two or
more data must not be systematically related between them.
1. Definition
Yt= 1+ 2Xt+ ut
E(uiuj)=0
If E(uiuj) 0
f
Subject 10, DISTRIBUTED LAG MODELS WITH TIME-SERIES DATA, Ch.17
Example: $20,000 increase in your income with MA degree, of which $4000 (0.2 of the
increase) is spent in the year of increase, $6000 (0.3) spent a year later and $10000 (0.5)
spent two years
Subject 7 MULTICOLLINEARITY
I. Definition:
Y= 1+ 2X2t+ 3X3t + 4X4t +u,
where 2X2+ 3X3+ 4X4=0, so X2=
3
4
X3
X4
2
2
example,
Consumption= F (income, education)
whereas income and education are highly correlated.
II. Reasons for Multicollinearity:
1) All ec
3. Look over the following equations and decide whether they are linear in the variables, linear
in the coefficients, both, or neither.
a. Not linear variables, but linear coefficients.
b. Linear in both slope coefficient and variables. Linear-log model
c
3. Consider the following annual model of the death rate (per million population) due to coronary
heart disease in the United States (Yt):
a. Create and test appropriate hypotheses at the 10% level - what, if anything, seems to
be wrong with the estimated
8. Consider the following hypothetical equation for a sample of divorced men who failed to make
at least one child support payment in the last four years:
P hat i = 2.0 + 0.5 Mi + 25 Yi + 0.8 Ai + 3 Bi - 0.15 Ci
(0.1)
(20) (1)
(3) (0.05)
a. Your friend ex
4. Consider the following estimated semilog equation
a. Degrees of freedom = (28-3) = 25
Critical value at 5% = 1.708
For ED, t = (0.1 - 0) / 0.025 = 4 4 > 1.708 therefore we reject the null hypothesis
For EXP, t = (0.11 - 0) / 0.05 = 2.2 2.2 > 1.708 ther
6. Using the techniques of Section 5.3, test the following two-sided hypotheses:
a. Hnot: B2 = 160
Ha: B2 =/= 160
At the 5% level of significance
Yhat = 300 + 10X1 + 200X2
SE
(1.0) (25.0)
t=
10.0
8.0
R^2 = .9 N = 30
t1 = (200-160)/25 = 40/25 = 1.6
t1 (1.6