Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

ŷ = 18.9 + 3.2x_{1} − 2.2x_{2} +
7.8x_{3} + 2.9x_{4}

(a)

Interpret

b_{1}

in this estimated regression equation.

*b*_{1} = 7.8 is an estimate of the change in
*y* corresponding to a 1 unit change in
*x*_{3} when *x*_{1},
*x*_{2}, and *x*_{4} are held
constant.*b*_{1} = 3.2 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{1} when *x*_{2},
*x*_{3}, and *x*_{4} are held
constant. *b*_{1} = 3.2 is an
estimate of the change in *y* corresponding to a 1 unit
change in *x*_{2} when *x*_{1},
*x*_{3}, and *x*_{4} are held
constant.*b*_{1} = −2.2 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{1} when *x*_{2},
*x*_{3}, and *x*_{4} are held
constant.*b*_{1} = 2.9 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{4} when *x*_{1},
*x*_{2}, and *x*_{3} are held
constant.

Interpret

b_{2}

in this estimated regression equation.

*b*_{2} = −2.2 is an estimate of the change in
*y* corresponding to a 1 unit change in
*x*_{1} when *x*_{2},
*x*_{3}, and *x*_{4} are held
constant.*b*_{2} = 7.8 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{3} when *x*_{1},
*x*_{2}, and *x*_{4} are held
constant. *b*_{2} = −2.2 is
an estimate of the change in *y* corresponding to a 1 unit
change in *x*_{2} when *x*_{1},
*x*_{3}, and *x*_{4} are held
constant.*b*_{2} = 3.2 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{1} when *x*_{2},
*x*_{3}, and *x*_{4} are held
constant.*b*_{2} = 2.9 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{4} when *x*_{1},
*x*_{2}, and *x*_{3} are held
constant.

Interpret

b_{3}

in this estimated regression equation.

*b*_{3} = 3.2 is an estimate of the change in
*y* corresponding to a 1 unit change in
*x*_{3} when *x*_{1},
*x*_{2}, and *x*_{4} are held
constant.*b*_{3} = 7.8 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{2} when *x*_{1},
*x*_{3}, and *x*_{4} are held
constant. *b*_{3} = −2.2 is
an estimate of the change in *y* corresponding to a 1 unit
change in *x*_{1} when *x*_{2},
*x*_{3}, and *x*_{4} are held
constant.*b*_{3} = −2.9 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{4} when *x*_{1},
*x*_{2}, and *x*_{3} are held
constant.*b*_{3} = 7.8 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{3} when *x*_{1},
*x*_{2}, and *x*_{4} are held
constant.

Interpret

b_{4}

in this estimated regression equation.

*b*_{4} = −2.2 is an estimate of the change in
*y* corresponding to a 1 unit change in
*x*_{2} when *x*_{1},
*x*_{3}, and *x*_{4} are held
constant.*b*_{4} = 2.9 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{3} when *x*_{1},
*x*_{2}, and *x*_{4} are held
constant. *b*_{4} = 2.9 is an
estimate of the change in *y* corresponding to a 1 unit
change in *x*_{4} when *x*_{1},
*x*_{2}, and *x*_{3} are held
constant.*b*_{4} = 7.8 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{2} when *x*_{1},
*x*_{3}, and *x*_{3} are held
constant.*b*_{4} = 3.2 is an estimate of the change
in *y* corresponding to a 1 unit change in
*x*_{4} when *x*_{1},
*x*_{2}, and *x*_{3} are held
constant.

(b)

Predict *y* when

x_{1} = 10, x_{2} = 5, x_{3} = 1, and
x_{4} = 2.

Answer #1

In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 −
2.3x2 +
7.6x3 +
2.7x4
For this estimated regression equation, SST =
1,805 and SSR = 1,770
a. Find the value of the test
statistic. (Round your answer to two decimal places.)
_________
b. Suppose variables x1 and
x4 are dropped from the model and the following
estimated regression equation is obtained.
ŷ = 11.1 − 3.6x2 + 8.1x3
Compute...

In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 −
2.3x2 +
7.6x3 +
2.7x4
For this estimated regression equation, SST = 1,835 and SSR =
1,800.
(a)At α = 0.05, test the significance of the
relationship among the variables.State the null and alternative
hypotheses.
-H0: One or more of the parameters is not
equal to zero.
Ha: β0 =
β1 = β2 =
β3 = β4 = 0
-H0:...

In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4
For this estimated regression equation, SST = 1,815 and SSR =
1,780. (a) At α = 0.05, test the significance of the relationship
among the variables.
State the null and alternative hypotheses.
H0: β0 = β1 = β2 = β3 = β4 = 0
Ha: One or more of the parameters is not equal to...

The estimated regression equation for a model involving two
independent variables and observations follows. y = 29.1379 + .7302
x1 + .5196 x2
A. Interpret and in this estimated regression equation.
b1 =
b2 =
B. Estimate when y x1=180 and x2=310 (to 3 decimals).

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
Y= 30.7752 + 0.6659x1+ 0.3724x2
a. Interpret b1 and b2 in this estimated
regression equation.
b1= -------
Select your answer:
-y changes by 0.6659 when x1 increases by 1 unit and x2
stays the same
-y changes by 0.6659 when x2 increases by 1 unit and x1
stays the same
- y changes by 0.3724 when x1 increases by 1 unit and x2
stays the...

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
^
y = 25.0793 + 0.6944x1 + 0.8028x2
a. Interpret and in this estimated regression equation.
b1 = ____
Select your answer: y changes by 0.6944 when x1 increases by 1 unit
and x2 stays the same
y changes by 0.6944 when x2
increases by 1 unit and x1 stays the same
y changes by 0.8028 when x1
increases by 1...

The estimated regression equation for a model involving two
independent variables and 10 observations follows.
y=27.1671 + 0.7533x1 + 0.7419x2
b1=
b2=
estimate y when x1=180 and x2= 310

In a regression analysis involving 27 observations, the
following estimated regression equation was developed. ŷ =
25.2 + 5.5x1 For this estimated
regression equation SST = 1,550 and SSE = 530.
(a) At α = 0.05, test whether
x1 is significant.State the
null and alternative hypotheses.
H0: β1 ≠ 0
Ha: β1 = 0
H0: β0 ≠ 0
Ha: β0 =
0
H0: β0 = 0
Ha: β0 ≠ 0
H0: β1 = 0
Ha: β1 ≠ 0
Find the value...

In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,600 and SSE =
550.
(a) At α = 0.05, test whether
x1is significant.State the null and
alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠ 0
H0: β0 ≠ 0
Ha: β0 =
0
H0: β1 ≠ 0
Ha: β1 = 0
H0: β1 = 0
Ha: β1 ≠ 0
Find the value...

In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,600 and SSE =
550.
(a) At α = 0.05, test whether
x1 is significant.
State the null and alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠
0H0: β0 ≠ 0
Ha: β0 =
0 H0:
β1 ≠ 0
Ha: β1 =
0H0: β1 = 0
Ha: β1 ≠ 0
Find the value of...

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