Consider the following data for a dependent variable y and two independent variables, x₁ and x₂. X1 X2 30 47 25 51 51 74 36 59 12 94 10 108. 17 40 5 94 y 16 178 112 19 175 7 170 12 117 13 142 76 16 211 me estimated regression equation for these data is y = -18.36827 +2.01019x₁ +4.73781x2. ere, SST = 15,182.9, SSR = 14,052.2, Sb₁ = 0.24712, and Sp₂ = 0.94844. (SST represents the Total Sum of Squares presents the Regression Sum of Squares) a) Test for a significant relationship among X₁, X₂, and y. Use α = 0.05. State the null and alternative hypotheses. O Ho: B1 = B2 = 0 o Ho Bì > B2 H₂: B₁ ≤ B₂ H₂: : One or more of the parameters is not equal to zero. o Ho Bi
Consider the following data for a dependent variable y and two independent variables, x₁ and x₂. X1 X2 30 47 25 51 51 74 36 59 12 94 10 108. 17 40 5 94 y 16 178 112 19 175 7 170 12 117 13 142 76 16 211 me estimated regression equation for these data is y = -18.36827 +2.01019x₁ +4.73781x2. ere, SST = 15,182.9, SSR = 14,052.2, Sb₁ = 0.24712, and Sp₂ = 0.94844. (SST represents the Total Sum of Squares presents the Regression Sum of Squares) a) Test for a significant relationship among X₁, X₂, and y. Use α = 0.05. State the null and alternative hypotheses. O Ho: B1 = B2 = 0 o Ho Bì > B2 H₂: B₁ ≤ B₂ H₂: : One or more of the parameters is not equal to zero. o Ho Bi
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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Need help solving a b and c
Transcribed Image Text:Consider the following data for a dependent variable y and two independent variables, x₁ and x₂.
X1 X₂
30 12 94
47
25
51
40
74
36
59
76
y
10 108
51 19 175
17 112
16 178
5 94
7 170
12 117
13. 142
16 211
The estimated regression equation for these data is
y = -18.36827 + 2.01019x, +4.73781x2.
= 0.24712, and Sb₂
Here, SST = 15,182.9, SSR = 14,052.2, S₁
represents the Regression Sum of Squares)
(a) Test for a significant relationship among X₁, X₂, and y. Use α = 0.05.
State the null and alternative hypotheses.
o Hoi B1 = B2 = 0
H: One or more of the parameters is not equal to zero.
o Ho Bì> B2
Ha: B₁ ≤ B₂
O Ho: B₁ #0 and ₂ # 0
H₂:
: One or more of the parameters is equal to zero.
o Ho Bi<B2
H₂: B₁ ≥ ß₂
= 0.94844. (SST represents the Total Sum of Squares, SSR
O Ho: B₁0 and ₂ = 0
H₂: B₁ = 0 and ₂ #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.
O Reject Ho. There is insufficient evidence to conclude that there is a significant relationship among the variables.
O Do not reject Ho. There is insufficient evidence to conclude that there is a significant relationship among the
variables.
O Reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the variables.
O Do not reject Ho. There is sufficient evidence to conclude that there is a significant relationship among the
variables.
Transcribed Image Text:(b) Is ₁ significant? Use α = 0.05.
State the null and alternative hypotheses.
O Ho: B₁ = 0
Ha: B₁ = 0
O Ho: B₁ #0
H₁: B₁ = 0
O Ho: B₁ <0
H: B₁ 20
O Ho: B₁ > 0
H: B₁ ≤0
O Ho: B₁ = 0
H₂: B₁ > 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.
O Do not reject Ho. There is insufficient evidence to conclude that
₁ is significant.
O Do not reject Ho. There is sufficient evidence to conclude that is significant.
O Reject Ho. There is insufficient evidence to conclude that is significant.
O Reject Ho. There is sufficient evidence to conclude that ₁ is significant.
(c) Is , significant? Use a = 0.05.
State the null and alternative hypotheses.
O Ho: B₂ = 0
Ha: B₂ > 0
O Ho: B₂ #0
H₂: B₂ = 0
O Ho: B₂ <0
Ha: B₂ 20
O Ho: B₂ > 0
H₂: B₂ ≤0
O H₁: B₂ = 0
H₂: B₂ #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.
O Reject Ho. There is insufficient evidence to conclude that ₂ is significant.
O Do not reject Ho. There is sufficient evidence to conclude that ₂ is significant.
O Do not reject Ho. There is insufficient evidence to conclude that ₂ is significant.
O Reject Ho. There is sufficient evidence to conclude that ₂ is significant.
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