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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
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. 

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.
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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