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 = 1,800.

**(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}: *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

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

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

**(d)State your conclusion.**

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

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

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

-Reject *H*_{0}. We conclude that the overall
relationship is not 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 = 1,745.

**(e)Compute SSE(x_{1},
x_{2}, x_{3},
x_{4}).**

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

**(f)Compute SSE(x_{2},
x_{3}).**

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

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

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

**(j)State your conclusion.**

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

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

Answer #1

a)

*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.

k=independent variables = | 4 | ||

n=sample size = | 30 | ||

SST= | 1835 | SSR = | 1800 |

SSE =SST-SSR= | 35.0 | ||

MSR=SSR/k= | 450.0 | ||

MSE=SSE/(n-k-1)= | 1.4 | ||

b)F
=MSR/MSE = |
321.43 |
||

c)p value =0.000 |

d)

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

e)

SSE(x1,x2,x,3,x4) = | 35 |

f)

SSE(x2x3) = | 90 |

g)

Ho: ß1 =ß4 =0

Ha: at least one of the variable is not zero

h)

F = | ((90-35)/2)/(35/25)= | 19.64 | |

i)p value =0.000 |

j)

-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...

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...

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 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...

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 = 18.9 + 3.2x1 − 2.2x2 +
7.8x3 + 2.9x4
(a)
Interpret
b1
in this estimated regression equation.
b1 = 7.8 is an estimate of the change in
y corresponding to a 1 unit change in
x3 when x1,
x2, and x4 are held
constant.b1 = 3.2 is an estimate of the change
in y corresponding to a 1 unit change in
x1 when x2,...

The following regression output was obtained from a study of
architectural firms. The dependent variable is the total amount of
fees in millions of dollars.
Predictor
Coeff
SE
Coeff
t
p-value
Constant
8.366
3.002
2.787
0.010
X1
0.225
0.301
0.748
0.000
X2
–1.216
0.538
–2..260
0.028
X3
-0.070
0.377
–0.186
0.114
X4
0.552
0.322
1.714
0.001
X5
-0.049
0.028
–1.750
0.112
Analysis of Variance
Source
DF
SS
MS
F
p-value
Regression
5
2197.68
439.5
9.68
0.000
Residual Error
59
2679.56...

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