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 = 1,500 and SSE = 550. (a) At a = 0.05, test whether x₁ is significant. State the null and alternative hypotheses. OHP-0 H₁₂O # OHPO HB-0 OH BO Ha Bo=0 OH₁₁ =0 Ha B₁0 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 x₁ significant? O Reject Ho. We conclude that x₁ is significant. O Do not reject H. We conclude that x, is not significant. Type here to search 3 54°F w W E R F (b) Suppose that variables x and x3 are added to the model and the following regression equation is obtained. = ŷ 16.3 +2.3x, +12.1x,- 5.8x, For this estimated regression equation SST = 1,500 and SSE = 100. Use an F test and a 0.05 level of significance to determine whether x2 and x3 contribute significantly to the model. State the null and alternative hypotheses. O Ho B₂ =B3=0 H: One or more of the parameters is not equal to zero. OH B₁0 #0 HB, O O Ho: One or more of the parameters is not equal to zero. = = H₁₂-B-0 OHP-0 = HBO Find the value of the test statistic. Find the p-value. (Round your answer to three decimal places.) p-value = Is the addition of x2 and X3 significant? O Do not reject Ho. We conclude that the addition of variables x2 and X3 is significant. Reject Ho. We conclude that the addition of variables x, and X3 is not significant. O Reject Ho. We conclude that the addition of variables x2 and x3 is significant. Type here to search W E R S C L③ H N M 54°F
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 = 1,500 and SSE = 550. (a) At a = 0.05, test whether x₁ is significant. State the null and alternative hypotheses. OHP-0 H₁₂O # OHPO HB-0 OH BO Ha Bo=0 OH₁₁ =0 Ha B₁0 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 x₁ significant? O Reject Ho. We conclude that x₁ is significant. O Do not reject H. We conclude that x, is not significant. Type here to search 3 54°F w W E R F (b) Suppose that variables x and x3 are added to the model and the following regression equation is obtained. = ŷ 16.3 +2.3x, +12.1x,- 5.8x, For this estimated regression equation SST = 1,500 and SSE = 100. Use an F test and a 0.05 level of significance to determine whether x2 and x3 contribute significantly to the model. State the null and alternative hypotheses. O Ho B₂ =B3=0 H: One or more of the parameters is not equal to zero. OH B₁0 #0 HB, O O Ho: One or more of the parameters is not equal to zero. = = H₁₂-B-0 OHP-0 = HBO Find the value of the test statistic. Find the p-value. (Round your answer to three decimal places.) p-value = Is the addition of x2 and X3 significant? O Do not reject Ho. We conclude that the addition of variables x2 and X3 is significant. Reject Ho. We conclude that the addition of variables x, and X3 is not significant. O Reject Ho. We conclude that the addition of variables x2 and x3 is significant. Type here to search W E R S C L③ H N M 54°F
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section: Chapter Questions
Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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Transcribed Image Text: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 = 1,500 and SSE = 550.
(a) At a = 0.05, test whether x₁ is significant.
State the null and alternative hypotheses.
OHP-0
H₁₂O
#
OHPO
HB-0
OH BO
Ha Bo=0
OH₁₁ =0
Ha B₁0
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 x₁ significant?
O Reject Ho. We conclude that x₁ is significant.
O Do not reject H. We conclude that x, is not significant.
Type here to search
3
54°F
w
W
E
R
F
Transcribed Image Text:(b) Suppose that variables x and x3 are added to the model and the following regression equation is obtained.
=
ŷ 16.3 +2.3x, +12.1x,- 5.8x,
For this estimated regression equation SST = 1,500 and SSE = 100.
Use an F test and a 0.05 level of significance to determine whether x2 and x3 contribute significantly to the model.
State the null and alternative hypotheses.
O Ho B₂ =B3=0
H: One or more of the parameters is not equal to zero.
OH B₁0
#0
HB, O
O Ho: One or more of the parameters is not equal to zero.
=
=
H₁₂-B-0
OHP-0
=
HBO
Find the value of the test statistic.
Find the p-value. (Round your answer to three decimal places.)
p-value =
Is the addition of x2 and X3 significant?
O Do not reject Ho. We conclude that the addition of variables x2 and X3 is significant.
Reject Ho. We conclude that the addition of variables x, and X3 is not significant.
O Reject Ho. We conclude that the addition of variables x2 and x3 is significant.
Type here to search
W
E
R
S
C
L③
H
N
M
54°F
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