Question

Suppose the error variance of a model is describe by the equation σt2 = α0 + α1 Z1 + α2Z2 + εt Describe how to use Feasible Generalized Least Squares to get efficient estimates of the coefficients of the model.

Answer #1

Suppose you have a cross-country dataset with values for GDP
(yi) and investment in research & development (xi). Describe
the method of ordinary least squares (OLS) to estimate the
following univariate linear regression model, i.e.
yi = β0 + β1 xi + εi
In particular, describe in your words which are the dependent
and the explanatory variables; how the OLS estimation method works;
how to interpret the estimates for the coefficients β0 and β1; what
is the coefficient of determination...

Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.816
.666
.629
1.23721
a. Predictors:
(Constant),x
ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig
Regression
Residual
Total
27.500
13.776
41.276
1
9
10
27.500
1.531
17.966
.002b
a. Dependent Variable: Y
b. Predictors: (Constant), X
Coefficients
Model
Understand Coefficients
B
Std Error
Standardized
Coefficients
Beta
t
Sig
1 (Constant)
x
3.001
1.125
.500
.118
.816
2.667...

Consider the simple linear regression model y=10+30x+e where the
random error term is normally and independently distributed with
mean zero and standard deviation 1. Do NOT use
software. Generate a sample of eight observations, one each at the
levels x= 10, 12, 14, 16, 18, 20, 22, and 24.
Do NOT use software!
(a) Fit the linear regression model by least squares and find
the estimates of the slope and intercept.
(b) Find the estimate of ?^2 .
(c) Find...

econometrics.
explain how to test for contegration for the two and describe
the error correction model.

Describe the Pooled variance assumption. How does it change the
standard error? What impact does it have on a test statistic? What
impact does it have on a p-value?
How do you justify making the assumption?

Consider the linear regression model ? = ? +?? + ? Suppose the
variance of e increases as X increases. What implications, if any,
does this have for the OLS estimators and how would you proceed to
estimate β in this case.

__________ refers to the degree of correlation among independent
variables in a regression model.
a. Multicollinearity
b. Confidence level
c. Rank
d. Tolerance
__________ is used to test the hypothesis that the values of the
regression parameters ß1,
ß2,
...ßq are all zero.
a. Extrapolation
b. A t test
c. An F test
d. The least squares method
What would be the coefficient of determination if the total sum
of squares (SST) is 23.29 and the sum of squares due...

Question 1:
In the normal error simple linear regression model, suppose all
assumptions hold except constancy of error variance with respect to
X. Suppose E(Y) = V(Y). What transformation of y works to stabilize
the variance?
Question 2:
Let Y1,Y2,...Yn be a random sample for a normal distribution with
mean 10 and variance 4. Let Y(k) denote the Kth order statistics of
this random sample. Approximate the probability:
P(Y(k) <= 8.5) , if K =15 and n = 50.
Please...

#8
An article used an estimated regression equation to describe the
relationship between y = error percentage for subjects
reading a four-digit liquid crystal display and the independent
variables
x1 = level of backlight,
x2 = character subtense,
x3 = viewing angle, and
x4 = level of ambient light. From a
table given in the article, SSRegr = 23.1, SSResid = 24, and
n = 30.
Calculate the test statistic. (Round your answer to two decimal
places.)
F =
Calculate...

What are the requirements of the least-squares regression
model?
What is a correlation matrix?
How can you use technology to find a multiple regression
equation?
Why is it important to perform graphical as well as analytical
analyses when analyzing relations between two quantitative
variables?

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