Question

Use the following linear regression equation to answer the questions.

*x*_{3} = ?16.6 + 3.7*x*_{1} +
8.6*x*_{4} ? 1.9*x*_{7}

If *x*_{4} decreased by 2 units, what would we
expect for the corresponding change in
*x*_{3}?

(e) Suppose that *n* = 20 data points were used to construct
the given regression equation and that the standard error for the
coefficient of *x*_{4} is 0.924. Construct a 90%
confidence interval for the coefficient of *x*_{4}.
(Round your answers to two decimal places.)

lower limit | |

upper limit |

(f) Using the information of part (e) and level of significance 1%,
test the claim that the coefficient of *x*_{4} is
different from zero. (Round your answers to two decimal
places.)

t |
= | |

t critical |
= ± |

Conclusion

Reject the null hypothesis, there is sufficient evidence that
*?*_{4} differs from 0.

Fail to reject the null hypothesis, there is insufficient
evidence that *?*_{4} differs from
0.

Reject the null hypothesis, there is insufficient evidence that
*?*_{4} differs from 0.

Fail to reject the null hypothesis, there is sufficient evidence
that *?*_{4} differs from 0.

Explain how the conclusion has a bearing on the regression
equation.

If we conclude that *?*_{4} is not different from
0 then we would remove *x*_{1} from the model.

If we conclude that *?*_{4} is not different from
0 then we would remove *x*_{7} from the
model.

If we conclude that *?*_{4} is not different from
0 then we would remove *x*_{4} from the model.

If we conclude that *?*_{4} is not different from
0 then we would remove *x*_{3} from the model.

Answer #1

1) If x4 decreased by 2 units, what would we expect for the corresponding change in x3 =8.6*2=17.5

e)

for (n-4=16) degree of freedom and 90% confidence interval critical t=1.746

lower limit =estimate -t*std error =8.6-1.746*0.924=6.99 ( please try 6.98 if this comes wrong)

upper limit=estimate +t*std error =8.6+1.746*0.924=10.21 ( please try 10.22 if this comes wrong)

f)

t =8.6/0.924=9.31

tcriical =1.75

conclusion:Reject the null hypothesis, there is sufficient evidence that ?4 differs from 0.

If we conclude that ?4 is not different from 0 then we would remove x4 from the model.

Use the following linear regression equation to answer the
questions.
x1 = 1.1 + 3.0x2 –
8.4x3 + 2.3x4
(a) Which variable is the response variable?
x3
x1
x2
x4
Which variables are the explanatory variables? (Select all that
apply.)
x1
x2
x3
x4
(b) Which number is the constant term? List the coefficients with
their corresponding explanatory variables.
constant =
x2 coefficient=
x3 coefficient=
x4 coefficient=
(c) If x2 = 4, x3 = 10, and
x4 = 6, what...

Use the following linear regression equation to answer the
questions.
x1 = 1.5 + 3.5x2 –
8.2x3 + 2.1x4
(a) Which variable is the response variable?
A. x3
B.
x1
C. x2
D. x4
(b) Which variables are the explanatory variables?
(Select all that apply.)
A. x4
B. x1
C. x3
D. x2
(c) Which number is the constant term? List the
coefficients with their corresponding explanatory variables.
constant ____________
x2 coefficient_________
x3 coefficient_________
x4 coefficient_________
(d) If x2 =...

19) Use the following linear regression equation to answer the
questions.
x3 = −18.7 +
4.3x1 +
8.6x4 −
1.0x7
(b) Which number is the constant term? List the coefficients with
their corresponding explanatory variables.
constant
x1 coefficient
x4 coefficient
x7 coefficient
(c) If x1 = 5, x4 = -6, and
x7 = 4, what is the predicted value for
x3? (Round your answer to one decimal
place.)
x3 =
(d)
Suppose x1 and x7 were held
at fixed...

Use the following linear regression equation to answer the
questions.
x3 = −17.3 + 3.7x1 +
9.6x4 − 1.7x7
(e) Suppose that n = 20 data points were used to
construct the given regression equation and that the standard error
for the coefficient of x4 is 0.820. Construct a
90% confidence interval for the coefficient of
x4. (Round your answers to two decimal
places.)
lower limit
upper limit
(f) Using the information of part (e) and level of significance 5%,...

Use the following linear regression equation to answer the
questions.
x3 = −16.9 +
3.9x1 +
9.8x4 −
1.9x7
(e) Suppose that n = 19 data points were used to
construct the given regression equation and that the standard error
for the coefficient of x4 is 0.883. Construct a
90% confidence interval for the coefficient of
x4. (Round your answers to two decimal
places.)
lower
limit
?
upper limit
?
(f) Using the information of part (e) and level of...

Use the following linear regression equation to answer the
questions.
x1 = 1.7 + 3.6x2 –
7.7x3 + 2.4x4
Which number is the constant term? List the coefficients with
their corresponding explanatory variables.
constant
x2 coefficient
x3 coefficient
x4 coefficient
If x2 = 1, x3 = 8, and
x4 = 9, what is the predicted value for
x1? (Use 1 decimal place.)
Suppose x3 and x4 were
held at fixed but arbitrary values and x2
increased by 1 unit. What...

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.
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 Focus Problem at the beginning of this chapter asks you to
use a sign test with a 5% level of significance to test the claim
that the overall temperature distribution of Madison, Wisconsin, is
different (either way) from that of Juneau, Alaska. The monthly
average data (in °F) are as follows.
Month
Jan.
Feb.
March
April
May
June
Madison
17.4
21.9
31.4
46.7
57.9
67.5
Juneau
22.3
27.8
31.7
38.5
46.7
52.6
Month
July
Aug.
Sept.
Oct.
Nov.
Dec....

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