Consider the model y = Bi +x2B2 + x3ß3 +e and suppose that application of least squares to 20 observations on these variables yields the following results (cov (b) denotes the estimated covariance matrix): [0.96587' 0.69914 0.21812 0.019195 -0.050301 b2 cov(b) = 0.019195 0.048526 -0.031223 %3D %3D bz 1.7769 -0.050301 –0.031223 0.037120 ở = 2.5193 R² = 0.9466 %3D (a) Find the total variation, unexplained variation, and explained variation for this model. (b) Find 95% interval estimates for B2 and B3. (c) Use a t-test to test the hypothesis Ho: B2 >1 against the alternative H1 :B2< 1. (d) Use your answers in part (a) to test the joint hypothesis Ho:B2 = 0, B3 = 0. (e) Test the hypothesis Ho:2B2 = B3. %3D %3D %3D
Consider the model y = Bi +x2B2 + x3ß3 +e and suppose that application of least squares to 20 observations on these variables yields the following results (cov (b) denotes the estimated covariance matrix): [0.96587' 0.69914 0.21812 0.019195 -0.050301 b2 cov(b) = 0.019195 0.048526 -0.031223 %3D %3D bz 1.7769 -0.050301 –0.031223 0.037120 ở = 2.5193 R² = 0.9466 %3D (a) Find the total variation, unexplained variation, and explained variation for this model. (b) Find 95% interval estimates for B2 and B3. (c) Use a t-test to test the hypothesis Ho: B2 >1 against the alternative H1 :B2< 1. (d) Use your answers in part (a) to test the joint hypothesis Ho:B2 = 0, B3 = 0. (e) Test the hypothesis Ho:2B2 = B3. %3D %3D %3D
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Do parts (a) (d) and (e) of the following:
Consider the model
y = B1 +x2B2 + x3ß3 + e
and suppose that application of least squares to 20 observations on these variables
yields the following results (cov (b) denotes the estimated covariance matrix):
[0.96587]
bị
b2
b3
0.21812
0.019195 -0.050301
0.69914
cov(b)
0.019195
0.048526 –0.031223
1.7769
-0.050301 -–0.031223
0.037120
ở = 2.5193
R = 0.9466
%3D
(a) Find the total variation, unexplained variation, and explained variation for this model.
(b) Find 95% interval estimates for B2 and B3.
(c) Use a t-test to test the hypothesis Ho:B2 >1 against the alternative Hj :B2< 1.
(d) Use your answers in part (a) to test the joint hypothesis Họ:B2 = 0, B3 = 0.
(e) Test the hypothesis Ho:2B2 = B3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F09b3e228-14e2-411c-aaa4-27b70bae9f04%2F1f559291-dd34-4092-8c27-8d43ed442585%2Fq7rm7s9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Do parts (a) (d) and (e) of the following:
Consider the model
y = B1 +x2B2 + x3ß3 + e
and suppose that application of least squares to 20 observations on these variables
yields the following results (cov (b) denotes the estimated covariance matrix):
[0.96587]
bị
b2
b3
0.21812
0.019195 -0.050301
0.69914
cov(b)
0.019195
0.048526 –0.031223
1.7769
-0.050301 -–0.031223
0.037120
ở = 2.5193
R = 0.9466
%3D
(a) Find the total variation, unexplained variation, and explained variation for this model.
(b) Find 95% interval estimates for B2 and B3.
(c) Use a t-test to test the hypothesis Ho:B2 >1 against the alternative Hj :B2< 1.
(d) Use your answers in part (a) to test the joint hypothesis Họ:B2 = 0, B3 = 0.
(e) Test the hypothesis Ho:2B2 = B3.
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