In the linear regression model with n sample points (m1,91),...(Xn, Jn), the best fit line is given by y = a + bx where n *Στι-(2») (Στ) Σrigi i=1 i=1 b= i=1 and a = y-br. 2 n n nΣ - (Σ r i=1 The estimated y-value is given by ji = a + bri. Prove the ff. n (2) Σy = Σ i=1 i=l n (b) Σ(y. – 9:); = 0. - i=1 (c) SST = SSR + SSE [see lecture 12 for definition.] (Hint: Expand both LHS and RHS then add/subtract missing terms.)
In the linear regression model with n sample points (m1,91),...(Xn, Jn), the best fit line is given by y = a + bx where n *Στι-(2») (Στ) Σrigi i=1 i=1 b= i=1 and a = y-br. 2 n n nΣ - (Σ r i=1 The estimated y-value is given by ji = a + bri. Prove the ff. n (2) Σy = Σ i=1 i=l n (b) Σ(y. – 9:); = 0. - i=1 (c) SST = SSR + SSE [see lecture 12 for definition.] (Hint: Expand both LHS and RHS then add/subtract missing terms.)
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
![In the linear regression model with n sample points (m1,91),...(Xn, Jn), the best fit line
is given by y = a + bx where
n
*Στι-(2») (Στ)
Σrigi
i=1
i=1
b=
i=1
and a = y-br.
2
n
n
nΣ - (Σ
r
i=1
The estimated y-value is given by ji = a + bri. Prove the ff.
n
(2) Σy = Σ
i=1
i=l
n
(b) Σ(y. – 9:); = 0.
-
i=1
(c) SST = SSR + SSE [see lecture 12 for definition.]
(Hint: Expand both LHS and RHS then add/subtract missing terms.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bccc854-4ebe-4194-97f1-969cd12e908e%2F3bcb5c0a-fcf1-4f29-b05c-b957ed076ddb%2F00uqal_processed.png&w=3840&q=75)
Transcribed Image Text:In the linear regression model with n sample points (m1,91),...(Xn, Jn), the best fit line
is given by y = a + bx where
n
*Στι-(2») (Στ)
Σrigi
i=1
i=1
b=
i=1
and a = y-br.
2
n
n
nΣ - (Σ
r
i=1
The estimated y-value is given by ji = a + bri. Prove the ff.
n
(2) Σy = Σ
i=1
i=l
n
(b) Σ(y. – 9:); = 0.
-
i=1
(c) SST = SSR + SSE [see lecture 12 for definition.]
(Hint: Expand both LHS and RHS then add/subtract missing terms.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman