Question

In a multiple regression y = *β*_{0} +
*β*_{1}x_{1} +
*β*_{2}x_{2} +
*β*_{3}x_{3}, if based on the sample data,
the correlation coefficient between x_{1} and x_{3}
is -0.8, is it going to cause multicollinearity? If so, how do we
deal with it?

Answer #1

In a multiple linear regression y = β0 +
β1x1 +
β2x2 +
β3x3, based on two-tailed t tests,
if β1 is not significant, but
β2 and β3 are significant,
what shall we do the next?

Consider the multiple linear regression model
y = β0 +β1x1 +β2x2 +β3x3 +β4x4 +ε
Using the procedure for testing a general linear hypothesis, show
how to test
a. H 0 : β 1 = β 2 = β 3 = β 4 = β
b. H 0 : β 1 = β 2 , β 3 = β 4
c. H0: β1-2β2=4β3
β1+2β2=0

The accompanying table shows the regression results when
estimating y = β0 +
β1x1 +
β2x2 +
β3x3 + ε.
df
SS
MS
F
Significance F
Regression
3
453
151
5.03
0.0030
Residual
85
2,521
30
Total
88
2,974
Coefficients
Standard Error
t-stat
p-value
Intercept
14.96
3.08
4.80
0.0000
x1
0.87
0.29
3.00
0.0035
x2
0.46
0.22
2.09
0.0400
x3
0.04
0.34
0.12
0.9066
At the 5% significance level, which of the following explanatory
variable(s) is(are) individually significant?
Multiple Choice:...

The accompanying table shows the regression results when
estimating y = β0 +
β1x1 +
β2x2 +
β3x3 +
ε.
df
SS
MS
F
Significance F
Regression
3
453
151
5.03
0.0030
Residual
85
2,521
30
Total
88
2,974
Coefficients
Standard Error
t-stat
p-value
Intercept
14.96
3.08
4.86
0.0000
x1
0.87
0.29
3.00
0.0035
x2
0.46
0.22
2.09
0.0400
x3
0.04
0.34
0.12
0.9066
At the 5% significance level, which of the following explanatory
variable(s) is(are) individually significant?
Multiple Choice...

Consider the multiple regression model E(Y|X1
X2) = β0 + β1X1 +
β2X2 +
β3X1X2
Can we interpret β1 as the change in the conditional
mean response for a unit change in X1 holding all the
other predictors in the model fixed?
Group of answer choices
a. Yes, because that is the traditional way of interpreting a
regression coefficient.
b. Yes, because the response variable is quantitative and thus
the partial slopes are interpreted exactly in that manner.
c. No,...

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.

In the model Y = β0 + β1X1 + β2X2 + ε, which of these parameters
represents a coefficient of an independent variable?
Group of answer choices
the β1
the X1
the Y
the ε

15-12: Consider the following regression model:
y=β0+β1x1+β2x2+ε
where:
x1=A quantitative variable
x2=1 if x1<20
0 if x1>20
The following estimate regression equation was obtained from a
sample of 30 observations:
y^=24.1+5.8x1+7.9x2
Provide the estimate regression equation for instances in which
x1<20.
Determine the value of y^ when x1=10.
Provide the estimate regression equation for instances in which
x1>20.
Determine the value of y^ when x1=30.
please not handwritten so I can read it

1.
Suppose the variable x2 has been omitted from
the following regression equation, y = β0 +
β1x1 +β2x2 + u.
b1 is the estimator obtained when x2 is
omitted from the equation. The bias in b1 is positive
if
A.
β2<0 and x1 and x2 are
positive correlated
B.
β2=0 and x1 and x2 are negative
correlated
C.
β2>0 and x1 and x2 are
negative correlated
D.
β2>0 and x1 and x2 are
positive correlated
2.
Suppose the true...

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?

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