Question

A linear regression of a variable Y against the explanatory variables X1 and X2 produced the following estimation model:

*Y = 1615.495 + 9.957 X1 + 0.081 X2 +
e*

*(527.96) (6.32) (0.024)*

The number in parentheses are the standard errors of each coefficients

i. State the null and alternative hypothesis for the coefficients

Select the appropriate test, compute the test statistic based on the information above, and test the null hypothesis for each coefficient by using a level of significance equal to 5%

ii. Which parameters are statistically significant? Rewrite the model again by using only the coefficients, which are statistically significant

Answer #1

Consider a regression of y on two explanatory variables, x1 and
x2, which are potentially correlated (though not perfectly). Say
that x1 can take on any value between 1 and 100. A researcher draws
a random sample of observations, with information on y, x1 and x2.
She runs a regression on this sample, which we refer to as
regression A.
She then takes the subset of the data where x1 is restricted to
only take values between 1 and 50,...

1.Consider a regression of y on two explanatory variables, x1
and x2, which are potentially correlated (though not perfectly).
Say that x1 can take on any value between 1 and 100. A researcher
draws a random sample of observations, with information on y, x1
and x2. She runs a regression on this sample, which we refer to as
regression A. She then takes the subset of the data where x1 is
restricted to only take values between 1 and 50,...

6. Consider the following sample regression
results:
Y hat = 15.4 + 2.20 X1 +
48.14
X2
R2 = .355
(6.14)
(.42)
(5.21)
n = 27
The numbers in the parentheses are the estimated standard errors
of the sample regression coefficients.
6. (continued)
a. Construct a 95% confidence interval for
b1.
b. Is there evidence of a linear relationship
between X2 and Y at the 5% level of
significance?
c. If you were to use a global test...

Consider a regression of y on x1,
x2 and x3. You are told
that x1 and x3 are
positively correlated but x2 is uncorrelated
with the other two variables.
[3] What, if anything, can you say about the relative
magnitudes of the estimated coefficients on each of the three
explanatory variables?
[6] What, if anything, can you say about the precision with
which we can estimate these coefficients?

Use the following linear regression equation to answer the
questions.
x1 = 1.1 + 3.0x2 –
8.4x3 + 2.3x4
(a) Which variable is the response variable?
x3
x1
x2
x4
Which variables are the explanatory variables? (Select all that
apply.)
x1
x2
x3
x4
(b) Which number is the constant term? List the coefficients with
their corresponding explanatory variables.
constant =
x2 coefficient=
x3 coefficient=
x4 coefficient=
(c) If x2 = 4, x3 = 10, and
x4 = 6, what...

Assume one of the explanatory variable (named X1) in your
logistic regression is a categorical variable with the following
levels: low, average and high, and another explanatory variable
(named X2) is also categorical with the following levels: Sydney,
Melbourne, Hobart and Brisbane. Explain how you will use them in
developing your logistic regression model. How many coefficients
you will have in your final model?

Assume one of the explanatory variable (named X1) in
your logistic regression is a categorical variable with the
following levels: low, average and high, and another explanatory
variable (named X2) is also categorical with the
following levels: Sydney, Melbourne, Hobart and Brisbane. Explain
how you will use them in developing your logistic regression model.
How many coefficients you will have in your final model?

Use the following linear regression equation to answer the
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 =...

(By Hand) For the dependent variable Y and the independent
variables X1 and X2, the linear regression model is given by:
Y=0.08059*X1-0.16109*X2+5.26570. Complete the following table:
Actual Y
X1
X2
Predicted Y
Prediction Error
6
6.8
4.7
3.1
5.3
5.5
5.8
4.5
6.2
4.5
8.8
7
4.5
6.8
6.1
3.7
8.5
5.1
5.4
8.9
4.8
5.1
6.9
5.4
5.8
9.3
5.9
5.7
8.4
5.4

Question 1
Suppose you estimate the following regression function where Y,
X1, and X2 are continuous variables measured in integers:
Yhat=0.5+0.25*X1 −0.01*X2−0.43*X
3
Suppose that X2=X1*X1
The standard error of beta0hat is 0.10.
The standard error of beta1hat is 0.05.
The standard error of beta2hat is 0.005.
The standard error of beta3hat is 0.05.
What is the marginal effect of X1 when it increases from 3 to 4?
Round to two decimal places.
10 points
Question 2
Refer to question...

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