Question

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 + 3.8*x*_{1} −
2.3*x*_{2} +
7.6*x*_{3} +
2.7*x*_{4}

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.

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

*H*_{a}: *β*_{0} =
*β*_{1} = *β*_{2} =
*β*_{3} = *β*_{4} = 0

*H*_{0}: *β*_{0} =
*β*_{1} = *β*_{2} =
*β*_{3} = *β*_{4} = 0

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

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

*H*_{a}: *β*_{1} =
*β*_{2} = *β*_{3} =
*β*_{4} = 0

*H*_{0}: *β*_{1} =
*β*_{2} = *β*_{3} =
*β*_{4} = 0

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

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

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

*p*-value =

State your conclusion.

Reject *H*_{0}. We conclude that the overall
relationship is significant.

Reject *H*_{0}. We conclude that the overall
relationship is not significant.

Do not reject *H*_{0}. We conclude that the
overall relationship is not significant.

Do not reject *H*_{0}. We conclude that the
overall relationship is significant.

Suppose variables *x*_{1} and
*x*_{4} are dropped from the model and the
following estimated regression equation is obtained.

*ŷ* = 11.1 − 3.6*x*_{2} +
8.1*x*_{3}

For this model, SST = 1,835 and SSR = 1,735.

(b)

Compute SSE(*x*_{1},
*x*_{2}, *x*_{3},
*x*_{4})

SSE(*x*_{1},
*x*_{2}, *x*_{3},
*x*_{4}) =

(c)

Compute SSE(*x*_{2},
*x*_{3}).

SSE(*x*_{2},
*x*_{3}) =

(d)

Use an *F* test and a 0.05 level of significance to
determine whether *x*_{1} and
*x*_{4} contribute significantly to the
model.

State the null and alternative hypotheses.

*H*_{0}: *β*_{1} =
*β*_{4} = 0

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

*H*_{0}: *β*_{2} =
*β*_{3} = 0

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

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

*H*_{a}: *β*_{1} =
*β*_{4} = 0

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

*H*_{a}: *β*_{2} =
*β*_{3} = 0

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

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

*p*-value =

State your conclusion.

Reject *H*_{0}. We conclude that
*x*_{1} and *x*_{4} contribute
significantly to the model.

Do not reject *H*_{0}. We conclude that
*x*_{1} and *x*_{4} contribute
significantly to the model.

Do not reject *H*_{0}. We conclude that
*x*_{1} and *x*_{4} do not contribute
significantly to the model.

Reject *H*_{0}. We conclude that
*x*_{1} and *x*_{4} do not contribute
significantly to the model.

Answer #1

*H*_{0}: *β*_{0} =
*β*_{1} = *β*_{2} =
*β*_{3} = *β*_{4} = 0

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

SSE =SST-SSR= | 45.0 | |

MSR=SSR/k= | 447.5 | |

MSE=SSE/(n-k-1)= | 1.8 | |

F =MSR/MSE = | 248.61 | |

p value =0.000 |

Reject *H*_{0}. We conclude that the overall
relationship is significant.

b)

SSE(x1,x2,x,3,x4) = | 45 |

c)

SSE(x2x3) = | 100 |

d)

*H*_{0}: *β*_{1} =
*β*_{4} = 0

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

F = | ((100-45)/2)/(45/25)= | 15.28 | |

p value =0.000 |

Reject *H*_{0}. We conclude that
*x*_{1} and *x*_{4} contribute
significantly to the model.

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:...

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...

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 = 1,525 and SSE =
560.
(a)
At α = 0.05, test whether
x1
is significant.Suppose that variables
x2 and
x3
are added to the model and the following regression equation is
obtained.
ŷ = 16.3 + 2.3x1 +
12.1x2 −
5.8x3
For...

You may need to use the appropriate technology to answer this
question.
Consider the following data on x = weight (pounds) and
y = price ($) for 10 road-racing bikes.
Brand
Weight
Price ($)
A
17.8
2,100
B
16.1
6,250
C
14.9
8,370
D
15.9
6,200
E
17.2
4,000
F
13.1
8,500
G
16.2
6,000
H
17.1
2,580
I
17.6
3,300
J
14.1
8,000
These data provided the estimated regression equation
ŷ = 28,458 − 1,433x.
For these data, SSE...

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...

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
71
C
95
61
D
70
58
E
70
42
F
35
28
(a)
The estimated regression...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 15 minutes ago

asked 19 minutes ago

asked 19 minutes ago

asked 25 minutes ago

asked 25 minutes ago

asked 28 minutes ago

asked 52 minutes ago

asked 56 minutes ago

asked 57 minutes ago

asked 59 minutes ago

asked 59 minutes ago