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 = 1,550 and SSE = 530.

(a) At *α* = 0.05, test whether
*x*_{1} is significant.State the
null and alternative hypotheses.

*H*_{0}: *β*_{1} ≠ 0

*H*_{a}: *β*_{1} = 0

*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

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?

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

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

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

Reject *H*_{0}. We conclude that
*x*_{1} is not 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 = 1,550 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}: *β*_{1} ≠ 0

*H*_{a}: *β*_{1} = 0

*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*_{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?

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

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

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

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

Answer #1

Source | SS | df | MS | F |

regression | 1020.00 | 1 | 1020.000 | 48.113 |

error | 530.00 | 25 | 21.200 | |

total | 1550.00 | 26 |

a)

*H*_{0}: *β*_{1} = 0

*H*_{a}: *β*_{1} ≠ 0

value of the test statistic =48.11

*p*-value.=0.000

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

b)

*H*_{0}: *β*_{2} =
*β*_{3} = 0

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

Partial F=((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) = | 49.45 |

*p*-value =0.000

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 = 1,600 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 = 1,815 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...

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,...

Refer to the following regression output:
Predictor
Coef
SE Coef
Constant
30.00
13.70
X1
-7.00
3.60
X2
3.00
9.30
X3
-19.00
10.80
Source
DF
SS
MS
F
Regression
3.00
8,200.00
Error
25.00
Total
28.00
10,000.00
a. What is the regression equation?
(Round the final answers to the nearest whole number.
Negative answer should be indicated by a minus sign.)
Y′
= + X1
+ X2
+ X3
b. If X1 = 4,
X2 = 6, and X3 = 8, what is
the value of...

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