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(c) Identify observations with large standardized residual value.

(c) Identify observations with large standardized residual value.

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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2. Using the linear model of y = Bo + Bi +, a researcher calculated the hat-matrix H and the residual e using 6 observations. H = X(X'X)−¹X' = [0.2516 0.1101 0.3931 0.0534 0.1101 0.0818 0.1101 0.2044 0.0157 0.2421 0.2044 0.2233 0.3931 0.1572 0.7704 -0.1352 0.0157 -0.0597 0.0535 0.2421 -0.1352 0.3176 0.2421 0.2233 0.1101 0.2044 0.0157 0.2421 0.2044 0.22327 0.2232 -0.0597 0.2799 0.0818 0.2233 0.2516 _tattu. 1 Hat IS, us obentions wil Mathe. sage (c) Identify observations with large standardized residual value. -alue i lalgt w.... TY villuaUL 1 1. Jinta 2 e = -0.02] 0.12 -0.56 0.88 -0.01 -0.07
Transcribed Image Text:2. Using the linear model of y = Bo + Bi +, a researcher calculated the hat-matrix H and the residual e using 6 observations. H = X(X'X)−¹X' = [0.2516 0.1101 0.3931 0.0534 0.1101 0.0818 0.1101 0.2044 0.0157 0.2421 0.2044 0.2233 0.3931 0.1572 0.7704 -0.1352 0.0157 -0.0597 0.0535 0.2421 -0.1352 0.3176 0.2421 0.2233 0.1101 0.2044 0.0157 0.2421 0.2044 0.22327 0.2232 -0.0597 0.2799 0.0818 0.2233 0.2516 _tattu. 1 Hat IS, us obentions wil Mathe. sage (c) Identify observations with large standardized residual value. -alue i lalgt w.... TY villuaUL 1 1. Jinta 2 e = -0.02] 0.12 -0.56 0.88 -0.01 -0.07
Standardized Residual • Detects outliers with respect to y • Labeled as "rstandard" in R How to detect unusual y from the trend? Use the residual y¡ — ŷ¡ = e¡ (residual of ith observation) • For the best use, We need to standardize e; by dividing ei • By the matrix calculation, we can show that ● Var (ei) = o² = 0² (1 - hii) Replacing ² by s² = MSE and taking the square root, we obtain %e₁ = √ = √√s² (1 — hii) = ) = s√√(1- -hii) • Then, ith standardized residual = r; is large if ei ri = ·- | 20 | = 15√/₁² - ₁ /> > 2. (Large
Transcribed Image Text:Standardized Residual • Detects outliers with respect to y • Labeled as "rstandard" in R How to detect unusual y from the trend? Use the residual y¡ — ŷ¡ = e¡ (residual of ith observation) • For the best use, We need to standardize e; by dividing ei • By the matrix calculation, we can show that ● Var (ei) = o² = 0² (1 - hii) Replacing ² by s² = MSE and taking the square root, we obtain %e₁ = √ = √√s² (1 — hii) = ) = s√√(1- -hii) • Then, ith standardized residual = r; is large if ei ri = ·- | 20 | = 15√/₁² - ₁ /> > 2. (Large
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