1. Consider the model Here, y = Xb+ e, X = b=b₁ 1 b₂ X is the design matrix, y the observed values of the y₁, (a) Find SST, SSR, SSE. (b) Find SSTm, SSRm, SSM. 10 1 1 0 1 1 02 1 1 1 1 1 1 1 2 1 2 1 1 2 1 122 13 1 1 3 1 132 1 4 1 1 4 1 1 42 15 1 15 1 52 e~ ~ N(0,0²1). (c) Find the least square estimate for b. (d) Find the estimate for ². bo 7 y = (e) Test Ho: b = 0 again H₁: b = 0. (f) Construct the 90% confidence interval for bo. 3 3 4 3 10 17 16 8 20 16 15 20 21 18
1. Consider the model Here, y = Xb+ e, X = b=b₁ 1 b₂ X is the design matrix, y the observed values of the y₁, (a) Find SST, SSR, SSE. (b) Find SSTm, SSRm, SSM. 10 1 1 0 1 1 02 1 1 1 1 1 1 1 2 1 2 1 1 2 1 122 13 1 1 3 1 132 1 4 1 1 4 1 1 42 15 1 15 1 52 e~ ~ N(0,0²1). (c) Find the least square estimate for b. (d) Find the estimate for ². bo 7 y = (e) Test Ho: b = 0 again H₁: b = 0. (f) Construct the 90% confidence interval for bo. 3 3 4 3 10 17 16 8 20 16 15 20 21 18
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Need help with parts e through f. I have already found the following:
- SST: 2,844
- SSM: 1,922
- SSR: 2,680.3047619047625
- SSE: 163.69523809523753
- SSTm: 158
- SSRm: 964.9714285714293
- The least square estimate for b: [2.19047619, 3.79047619, -1]
- estimate for σ2: 10.9130133333
- Test statistic F(R): 81.8687646893
Currently stuck on how to test H0 : b = 0 against H1 : b ≠ 0 and constructing the 90% confidence interval. The given design matrix X is 18x3, has full rank of 3, so we have 18 observations.
Transcribed Image Text:1. Consider the model
Here,
y = Xb + e,
X =
(a) Find SST, SSR, SSE.
(b) Find SSTm, SSRm, SSM.
b=b₁
b₂
X is the design matrix, y the observed values of the yi,
10 1
0 1
02
1 1
1 1 1
1
1 2
1 2 1
1
1
1
1 2 1
1
22
1 3 1
1
3 1
132
14 1
1 4 1
1 42
15 1
151
1 52
e~
~ N(0,0²1).
bo
7
7
y =
3
2
3
4
3
10
17
16
8
20
16
15
20
21
18
(c) Find the least square estimate for b.
(d) Find the estimate for ².
(e) Test Ho: b = 0 again H₁ : b = 0.
(f) Construct the 90% confidence interval for bo.
(g) Construct the 90% confidence interval for bo + b₁ + b₂.
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