Question

Suppose that your linear regression model includes a constant term, so that in the linear regression model

**Y = Xβ + ε**

The matrix of explanatory variables **X** can be
partitioned as follows: **X = [i X _{1}]**. The
OLS estimator of

a) Use partitioned regression to derive formulas for
**b _{1}** and

b) Derive **var (bb _{1} | X)**

c) What is **var (b _{0} | X)**

Answer #1

**first
answer**

Based on the definition of the linear regression model in its
matrix form, i.e., y=Xβ+ε, the assumption that
ε~N(0,σ2I), and
the general formula for the point estimators for the parameters of
the model
(b=XTX-1XTy);
show:
how to derivate the formula for the point estimators for the
parameters of the models by means of the Least Square Estimation
(LSE). [Hint: you must minimize
ete]
that the LSE estimator, i.e.,
b=XTX-1XTy,
is unbiased. [Hint:
E[b]=β]

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high if all the estimates of the regression coefficients are shown
to be insignificantly different from zero based on individual
t tests.
Suppose the CNLR applies to a simple linear regression y =
β1 +...

Consider the simple linear regression model for which the
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Derive the Ordinary Least Squares estimator (OLS) of beta
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A. Y - estimated average predicted value, X –
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(b0)
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predictor, Y-intercept (b0), slope
(b1)
C. X - estimated average predicted value, Y –
predictor, Y-intercept (b1), slope
(b0)
D. X - estimated average predicted value, Y –
predictor, Y-intercept (b0), slope
(b1)
The slope (b1)
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A. the estimated average change in Y per...

Use the following linear regression equation to answer the
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x1 = 1.1 + 3.0x2 –
8.4x3 + 2.3x4
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x3
x1
x2
x4
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apply.)
x1
x2
x3
x4
(b) Which number is the constant term? List the coefficients with
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constant =
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x3 coefficient=
x4 coefficient=
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questions.
x1 = 1.5 + 3.5x2 –
8.2x3 + 2.1x4
(a) Which variable is the response variable?
A. x3
B.
x1
C. x2
D. x4
(b) Which variables are the explanatory variables?
(Select all that apply.)
A. x4
B. x1
C. x3
D. x2
(c) Which number is the constant term? List the
coefficients with their corresponding explanatory variables.
constant ____________
x2 coefficient_________
x3 coefficient_________
x4 coefficient_________
(d) If x2 =...

Multiple choice!
Consider the model Yi = B0 + B1X1i + B2X2i + B3X3i + B4X4i + Ui.
To test the null hypothseis of B2 = B3 = 0, the restricted
regression is:
A. Yi = B0 + B1X1i + B2X2i + B3X3i + B4X4i + Ui
B. Yi = B0 + Ui
C. Yi = B0 + B1X1i + B4X4i + Ui
D. Yi = B0 + B2X2i + B3X3i + Ui
Consider the model Yi = B0 +...

CW 2
List 5 assumptions of the simple linear regression model.
You have estimated the following equation using OLS:
ŷ = 33.75 + 1.45 MALE
where y is annual income in thousands
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a) According to this model, what is the average income for
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b. If this model has an R2 = .75, what is the value of
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c. At the 1% level what is the CRITICAL value associated
with a global test...

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