Question

You may need to use the appropriate technology to answer this question.

In a regression analysis involving 27 observations, the following estimated regression equation was developed.

*ŷ* = 25.2 + 5.5*x*_{1}

For this estimated regression equation SST = 1,525 and SSE = 560.

(a)

At *α* = 0.05, test whether

*x*_{1}

is significant.Suppose that variables

*x*_{2} and
*x*_{3}

are added to the model and the following regression equation is obtained.

*ŷ* = 16.3 + 2.3*x*_{1} +
12.1*x*_{2} −
5.8*x*_{3}

For this estimated regression equation SST = 1,525 and SSE = 100.

(b)

Use an *F* test and a 0.05 level of significance to
determine whether

*x*_{2} and
*x*_{3}

contribute significantly to the model.

Answer #1

You may need to use the appropriate technology to answer this
question.
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 =
590.
(a)
At α = 0.05, test whether
x1
is significant.
State the null and alternative hypotheses.
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 = 0
Ha: β1 ≠ 0
H0: β0 = 0
Ha:...

You may need to use the appropriate technology to answer this
question.
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 =
1,790.
(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...

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...

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...

You may need to use the appropriate technology to answer this
question.
The following estimated regression equation based on 10
observations was presented. ŷ = 25.1670 +
0.5102x1 +
0.4960x2
Here, SST = 6,734.125, SSR =
6,227.375, sb1
=
0.0813, and sb2
= 0.0567.
(a)Compute MSR and MSE. (Round your answers to three decimal
places.)
MSR=
MSE=
b) Compute F and perform the appropriate F
test. Use α = 0.05.
Find the value of the test statistic. (Round your answer to two
decimal...

You may need to use the appropriate technology to answer this
question.
The following estimated regression equation based on 10
observations was presented.
ŷ = 23.1570 + 0.5303x1 +
0.4920x2
Here, SST = 6,736.125, SSR = 6,228.375,
sb1 =
0.0815, and
sb2 =
0.0567.
(a) Compute MSR and MSE. (Round your answers to three decimal
places.)
MSR=
MSE=
(b) Compute F and perform the appropriate F
test. Use α = 0.05.
Find the value of the test statistic. (Round your...

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