Appendix - Λ Confidence interval(,): Pr[B₁-se (B.) t≤ B₁ ≤ ẞ₁ + se (B₁) · t] = 1 − a Pr|(n− Confidence interval (02):Pr (n Λ Bivariate regression parameters: B₂ ^ 02 k) →→ Xn-kia/2 Λ ^ B₁ = Y-B₂X Λ ·≤o² ≤ (n−k): σ2 Xn-k:1-a/2 = 1-a ΣXY-nXY == Σx²-nx² var r(ẞ1) ΣΧΕ = nΣ(Xi-X)² 02 var(B2) = 8² = = n-k Σ(Xi-x)² Σαξ Συμ n-2 (K-3)2- Variance of intercept parameter: Variance of slope parameter: Estimated variance of error terms: Jacque-Bera (JB) test of normality: JB = n [s² + (-3)²| Computed t-statistic: ^ ESS=(-)² B2-B2 se (ẞ2) RSS = (Y,-)²=A₁² i=1 TSS=(-Y)² Scaling: ₁ = w₁₁ i=1 Scaling: var w₁ var, var (61) = (6) 24 A W₁ Scaling: = P2 พ. W₁ var 2 W₂ (6) - (6) Scaling: var₂ = - Scaling: 0 2.3 Upon tasked with deriving estimates of B1, B2, 6 and the standard errors (SE) of B₁ and B2 for the replicated data. Mariana assistant calculates them to be: Dependent Variable: Blood (Y) Included observations: 62 Variable C c (ẞ1) Study (B2) Parameter Std. Error 139.8585 1.5490 -3.133 0.1786 S.E. of regression (ô) 2.7865 Using above information conduct the following: 2.3.1 the 99% confidence interval for ẞ1 2.2.2 the hypothesis test at a = 5% where Ho: ẞ₁ = 133 and H₁: ẞ₁ > 133 2.3.3 the hypothesis test at a = 5% where Ho: ẞ2 = -2.5 and H₁: ẞ2 +-2.5
Appendix - Λ Confidence interval(,): Pr[B₁-se (B.) t≤ B₁ ≤ ẞ₁ + se (B₁) · t] = 1 − a Pr|(n− Confidence interval (02):Pr (n Λ Bivariate regression parameters: B₂ ^ 02 k) →→ Xn-kia/2 Λ ^ B₁ = Y-B₂X Λ ·≤o² ≤ (n−k): σ2 Xn-k:1-a/2 = 1-a ΣXY-nXY == Σx²-nx² var r(ẞ1) ΣΧΕ = nΣ(Xi-X)² 02 var(B2) = 8² = = n-k Σ(Xi-x)² Σαξ Συμ n-2 (K-3)2- Variance of intercept parameter: Variance of slope parameter: Estimated variance of error terms: Jacque-Bera (JB) test of normality: JB = n [s² + (-3)²| Computed t-statistic: ^ ESS=(-)² B2-B2 se (ẞ2) RSS = (Y,-)²=A₁² i=1 TSS=(-Y)² Scaling: ₁ = w₁₁ i=1 Scaling: var w₁ var, var (61) = (6) 24 A W₁ Scaling: = P2 พ. W₁ var 2 W₂ (6) - (6) Scaling: var₂ = - Scaling: 0 2.3 Upon tasked with deriving estimates of B1, B2, 6 and the standard errors (SE) of B₁ and B2 for the replicated data. Mariana assistant calculates them to be: Dependent Variable: Blood (Y) Included observations: 62 Variable C c (ẞ1) Study (B2) Parameter Std. Error 139.8585 1.5490 -3.133 0.1786 S.E. of regression (ô) 2.7865 Using above information conduct the following: 2.3.1 the 99% confidence interval for ẞ1 2.2.2 the hypothesis test at a = 5% where Ho: ẞ₁ = 133 and H₁: ẞ₁ > 133 2.3.3 the hypothesis test at a = 5% where Ho: ẞ2 = -2.5 and H₁: ẞ2 +-2.5
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 4GP
Related questions
Question
Please all the 3 of these sub-questions. Make sure answer is rounded up to 4 decimals.
use the appendix for further assistance
![Appendix
-
Λ
Confidence interval(,): Pr[B₁-se (B.) t≤ B₁ ≤ ẞ₁ + se (B₁) · t] = 1 − a
Pr|(n−
Confidence interval (02):Pr (n
Λ
Bivariate regression parameters: B₂
^
02
k) →→
Xn-kia/2
Λ
^
B₁ = Y-B₂X
Λ
·≤o² ≤ (n−k):
σ2
Xn-k:1-a/2
= 1-a
ΣXY-nXY
==
Σx²-nx²
var
r(ẞ1)
ΣΧΕ
=
nΣ(Xi-X)²
02
var(B2)
=
8² =
=
n-k
Σ(Xi-x)²
Σαξ Συμ
n-2
(K-3)2-
Variance of intercept parameter:
Variance of slope parameter:
Estimated variance of error terms:
Jacque-Bera (JB) test of normality: JB = n [s² + (-3)²|
Computed t-statistic:
^
ESS=(-)²
B2-B2
se (ẞ2)
RSS = (Y,-)²=A₁²
i=1
TSS=(-Y)²
Scaling: ₁ = w₁₁
i=1
Scaling: var w₁ var,
var (61) = (6)
24
A
W₁
Scaling:
=
P2
พ.
W₁
var 2
W₂
(6) - (6)
Scaling: var₂ =
-
Scaling: 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffcfb970f-840a-46b4-b203-e5e6e84a6a90%2F6cbe4b21-fc7b-4ce8-a08a-48515ade4f7b%2Fjqlbdtg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Appendix
-
Λ
Confidence interval(,): Pr[B₁-se (B.) t≤ B₁ ≤ ẞ₁ + se (B₁) · t] = 1 − a
Pr|(n−
Confidence interval (02):Pr (n
Λ
Bivariate regression parameters: B₂
^
02
k) →→
Xn-kia/2
Λ
^
B₁ = Y-B₂X
Λ
·≤o² ≤ (n−k):
σ2
Xn-k:1-a/2
= 1-a
ΣXY-nXY
==
Σx²-nx²
var
r(ẞ1)
ΣΧΕ
=
nΣ(Xi-X)²
02
var(B2)
=
8² =
=
n-k
Σ(Xi-x)²
Σαξ Συμ
n-2
(K-3)2-
Variance of intercept parameter:
Variance of slope parameter:
Estimated variance of error terms:
Jacque-Bera (JB) test of normality: JB = n [s² + (-3)²|
Computed t-statistic:
^
ESS=(-)²
B2-B2
se (ẞ2)
RSS = (Y,-)²=A₁²
i=1
TSS=(-Y)²
Scaling: ₁ = w₁₁
i=1
Scaling: var w₁ var,
var (61) = (6)
24
A
W₁
Scaling:
=
P2
พ.
W₁
var 2
W₂
(6) - (6)
Scaling: var₂ =
-
Scaling: 0
Transcribed Image Text:2.3
Upon tasked with deriving estimates of B1, B2, 6 and the standard errors (SE) of B₁ and
B2 for the replicated data. Mariana assistant calculates them to be:
Dependent Variable: Blood (Y)
Included observations: 62
Variable
C
c (ẞ1)
Study (B2)
Parameter
Std. Error
139.8585
1.5490
-3.133
0.1786
S.E. of regression (ô)
2.7865
Using above information conduct the following:
2.3.1 the 99% confidence interval for ẞ1
2.2.2 the hypothesis test at a = 5% where Ho: ẞ₁ = 133 and H₁: ẞ₁ > 133
2.3.3 the hypothesis test at a = 5% where Ho: ẞ2 = -2.5 and H₁: ẞ2 +-2.5
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