Question

1. Consider the bivariate model: Yi = β0+β1Xi+ui . Explain what it means for the OLS estimator, βˆ 1, to be consistent. (You may want to draw a picture.)

2. (Circle all that applies) Which of the following regression functions is/are linear in the parameters a) Yi = β1 + β2 1 Xi b) Yi = β1 + β 3 2Xi c) Yi = β1 + β2Xi

Answer #1

1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this
regression using OLS and get the following results: b0=-3.13437;
SE(b0)=0.959254; b1=1.46693; SE(b1)=21.0213; R-squared=0.130357;
and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and
b1, respectively. The total number of observations is
2950.According to these results the relationship between C and Y
is:
A. no relationship
B. impossible to tell
C. positive
D. negative
2. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this...

What happens to the OLS estimators of β2 in the model
yi=β1+β2xi+ui when ui and uj are not independent?
a. b2is biased and its t-statistic needs an adjustment.
b. b2is biased. but its t-statistic is correct.
c. b2is unbiased. but its t-statistic needs an adjustment.
d. b2 is unbiased and its t-statistic is correct.
Please Explained

Consider the model ln(Yi)=β0+β1Xi+β2Ei+β3XiEi+ui, where Y is an
individual's annual earnings in dollars, X is years of work
experience, and E is years of education. Consider an individual
with a high-school degree (E=12yrs) who has been working for 20
years. The expected increase in log earnings next year (when
X=21yrs) compared to this year is, dropping units,
β1
β1+12β3
β1+β3
β0+21β1+12β2+252β3

7)
Consider the following regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + β5X5i + ui
This model has been estimated by OLS. The Gretl output is
below.
Model 1: OLS, using observations 1-52
coefficient
std. error
t-ratio
p-value
const
-0.5186
0.8624
-0.6013
0.5506
X1
0.1497
0.4125
0.3630
0.7182
X2
-0.2710
0.1714
-1.5808
0.1208
X3
0.1809
0.6028
0.3001
0.7654
X4
0.4574
0.2729
1.6757
0.1006
X5
2.4438
0.1781
13.7200
0.0000
Mean dependent var
1.3617
S.D. dependent...

1. Consider the following linear regression model which
estimates only a constant:
Yi = β1 + ui
What will the value of ˆβ1 be? Remember we are minimizing the sum
of the squared residuals.
2. Consider the following regression model with K parameters:
Yi = β1 + β2X2i + β3X3i + ... + βKXKi + ui
Now consider the F-test of the null hypothesis that all slope
parameters (β2,β3,...,βK) are equal to zero. Using the equation
from class:
F =（(RSSk...

Consider the following (generic) population regression
model:
Yi = β0 + β1X1,i + β2X2,i + β3X3,i + ui, i = 1,...,n . Transform
the regression to allow you to easily test the null hypothesis that
β1 + β3 = 1. State the new null hypothesis associated to this
transformed regression.

Consider the following (generic) population regression model: Yi
= β0 + β1X1,i + β2X2,i + β3X3,i + ui, i = 1, ..., n (∗) Transform
the regression to allow you to easily test the null hypothesis that
β1 + β3 = 1. State the new null hypothesis associated to this
transformed regression. Would you expect to reject or accept the
null hypothesis? Why?

Consider the simple regression model yi = β0 + β1xi + ei,i =
1,...,n. The Gauss-Markov conditions hold and also ei ∼ N(0,σ).
Suppose we center both the response variable and the predictor.
Estimate the intercept and the slope of this model.

1. The Central Limit Theorem
A. States that the OLS estimator is BLUE
B. states that the mean of the sampling distribution of the
mean is equal to the population mean
C. none of these
D. states that the mean of the sampling distribution of the
mean is equal to the population standard deviation divided by the
square root of the sample size
2. Consider the regression equation Ci= β0+β1 Yi+ ui where C is
consumption and Y is disposable...

The regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + ui
has been estimated using Gretl. The output is below.
Model 1: OLS, using observations 1-50
coefficient
std. error
t-ratio
p-value
const
-0.6789
0.9808
-0.6921
0.4924
X1
0.8482
0.1972
4.3005
0.0001
X2
1.8291
0.4608
3.9696
0.0003
X3
-0.1283
0.7869
-0.1630
0.8712
X4
0.4590
0.5500
0.8345
0.4084
Mean dependent var
4.2211
S.D. dependent var
2.3778
Sum squared resid
152.79
S.E. of regression
1.8426
R-squared
0
Adjusted...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 15 minutes ago

asked 20 minutes ago

asked 22 minutes ago

asked 38 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago