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 = 1,600 and SSE = 550.

(a) At *α* = 0.05, test whether
*x*_{1} is significant.

State the null and alternative hypotheses.

*H*_{0}: *β*_{0} = 0

*H*_{a}: *β*_{0} ≠
0*H*_{0}: *β*_{0} ≠ 0

*H*_{a}: *β*_{0} =
0 *H*_{0}:
*β*_{1} ≠ 0

*H*_{a}: *β*_{1} =
0*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

*F* =

Find the *p*-value. (Round your answer to three decimal
places.)

*p*-value =

Is *x*_{1} significant?

A)Reject *H*_{0}. We conclude that
*x*_{1} is significant.

B)Do not reject *H*_{0}. We conclude that
*x*_{1} is not
significant.

C)Reject *H*_{0}. We conclude that
*x*_{1} is not significant.

D)Do not reject *H*_{0}. We conclude that
*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 = 1,600 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.

State the null and alternative hypotheses.

*H*_{0}: One or more of the parameters is not
equal to zero.

*H*_{a}: *β*_{2} =
*β*_{3} = 0*H*_{0}:
*β*_{1} ≠ 0

*H*_{a}: *β*_{1} =
0 *H*_{0}:
*β*_{1} = 0

*H*_{a}: *β*_{1} ≠
0*H*_{0}: *β*_{2} =
*β*_{3} = 0

*H*_{a}: One or more of the parameters is not equal
to zero.

Find the value of the test statistic.

=

Find the *p*-value. (Round your answer to three decimal
places.)

*p*-value =

Is the addition of *x*_{2} and
*x*_{3} significant?

A)Reject *H*_{0}. We conclude that the addition
of variables *x*_{2} and *x*_{3} is
not significant.

B)Do not reject *H*_{0}. We conclude that the
addition of variables *x*_{2} and
*x*_{3} is significant.

C)Do not reject *H*_{0}. We conclude that the
addition of variables *x*_{2} and
*x*_{3} is not significant.

D)Reject *H*_{0}. We conclude that the addition
of variables *x*_{2} and *x*_{3} is
significant.

Answer #1

a)

*H*0: *β*1 = 0

*H*a: *β*1 ≠ 0

SS | DF | MS | F | p value | |

regression | 1050 | 1 | 1050 | 47.73 | 0.0000 |

error | 550 | 25 | 22 | ||

total | 1600 | 26 |

F = 47.73

p value=0.000

**A)Reject H0. We conclude that x1 is
significant.**

===================

b)

*H*0: *β*2 = *β*3 = 0

*H*a: One or more of the parameters is not equal to
zero.

SS | DF | MS | F | p value | |

regression | 1500 | 3 | 500 | 115.00 | 0.00000 |

error | 100 | 23 | 4.347826 | ||

total | 1600 | 26 |

test stat=115

p vaue = 0.000

D)Reject *H*0. We conclude that the addition of variables
*x*2 and *x*3 is significant.

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 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...

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:...

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...

The following estimated regression equation based on 10
observations was presented.
ŷ = 21.1370 + 0.5509x1 +
0.4980x2
Here, SST = 6,724.125, SSR = 6,222.375,
sb1 =
0.0814, and
sb2 =
0.0565.
1. Compute MSR and MSE. (Round your answers to three decimal
places.)
MSR=
MSE=
2. Compute F and perform the appropriate F
test. Use α = 0.05.
2a. State the null and alternative hypotheses.
(a) H0: β1 =
β2 = 0
Ha: One or more of the parameters...

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...

Consider the following data on price ($) and the overall score
for six stereo headphones tested by a certain magazine. The overall
score is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest).
Brand
Price ($)
Score
A
180
74
B
150
71
C
95
63
D
70
54
E
70
38
F
35
24
(a)
The estimated regression equation for this data is
ŷ = 21.659 + 0.323x,
where x...

You may need to use the appropriate technology to answer this
question.
Consider the following data on price ($) and the overall score
for six stereo headphones tested by a certain magazine. The overall
score is based on sound quality and effectiveness of ambient noise
reduction. Scores range from 0 (lowest) to 100 (highest).
Brand
Price ($)
Score
A
180
76
B
150
69
C
95
63
D
70
56
E
70
38
F
35
28
(a)
The estimated regression...

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