Question

15-12: Consider the following regression model:

y=β_{0}+β_{1}x_{1}+β_{2}x_{2}+ε

where:

x_{1}=A quantitative variable

x_{2}=1 if x_{1}<20

0 if x_{1}>20

The following estimate regression equation was obtained from a sample of 30 observations:

y^=24.1+5.8x_{1}+7.9x_{2}

- Provide the estimate regression equation for instances in which
x
_{1}<20. - Determine the value of y^ when x
_{1}=10. - Provide the estimate regression equation for instances in which
x
_{1}>20. - Determine the value of y^ when x
_{1}=30.

please not handwritten so I can read it

Answer #1

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

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 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

In a multiple regression y = β0 +
β1x1 +
β2x2 +
β3x3, if based on the sample data,
the correlation coefficient between x1 and x3
is -0.8, is it going to cause multicollinearity? If so, how do we
deal with it?

Using 20 observations, the multiple regression model y
= β0 +
β1x1 +
β2x2 + ε was
estimated. A portion of the regression results is shown in the
accompanying table:
df
SS
MS
F
Significance
F
Regression
2
2.12E+12
1.06E+12
55.978
3.31E-08
Residual
17
3.11E+11
1.90E+10
Total
19
2.46E+12
Coefficients
Standard
Error
t
Stat
p-value
Lower 95%
Upper 95%
Intercept
−986,892
130,984
−7.534
0.000
−1,263,244
−710,540
x1
28,968
32,080
0.903
0.379
−38,715
96,651
x2
30,888
32,925
0.938
0.362
−38,578
100,354...

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.

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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