Question

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 regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=0.0697828; 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. The t-ratio for the regression slope coefficient is

- A. 0.959254
- B. 0.0697828
- C. -3.2675
- D. 21.0213

Answer #1

1. We have given b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=21.0213; R-squared=0.130357; and SER=8.769363.

The total number of observations is 2950. the value of correlatoon coefficient is = 0.361

D positive

2. 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)=0.0697828; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively.

the value of t for b1 is 1.46693/21.0213 = 0.0697828

- B. 0.0697828

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

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...

Suppose the true model is
Yi = B0 + B1 Xi +
B2Zi + ui
but you estimate the model:
Yi = a0 + a1Xi+
ui
If Z is positively correlated with Y and negatively correlated
with X, a1 will be a positively biased estimate of
B1.
Explain.

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 +...

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...

How would you estimate the regression model, {testscri = β0 + β1
stri + β2 incomei + ui}
in Stata if testscr, str, and income
are the variable names in the dataset, corresponding to the
variables in the regression modeld? no additional information is
needed to answer this.
1) type the command "reg testscr str, r" to get the estimate of
β1 and then type the command "reg testscr income, r" to get the
estimate of β2 .
2) type...

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.

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. Would you expect to reject or accept the
null hypothesis? Why?

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

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