Question 6: Simulate a data set with 150 observations y; = 40+ 6x+2r²+3r³+₁, where €; follows independent normal distribution N(0, 1). a) Perform polynomial regression on your simulated data set and using x, 1(x²), 1(x³) as the predictors. Compare the estimated coefficients with the true model and report the R-square. b) Formulate the design matrix of this regression and write down the first two rows of the design matrix based on your data set. c) Perform polynomial regression on your simulated data set and using z, I(x²), 1 (x³), 1 (xª) as the predictors. Compare the estimated coefficients with the true model.
Question 6: Simulate a data set with 150 observations y; = 40+ 6x+2r²+3r³+₁, where €; follows independent normal distribution N(0, 1). a) Perform polynomial regression on your simulated data set and using x, 1(x²), 1(x³) as the predictors. Compare the estimated coefficients with the true model and report the R-square. b) Formulate the design matrix of this regression and write down the first two rows of the design matrix based on your data set. c) Perform polynomial regression on your simulated data set and using z, I(x²), 1 (x³), 1 (xª) as the predictors. Compare the estimated coefficients with the true model.
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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Question

Transcribed Image Text:Question 6: Simulate a data set with 150 observations y; = 40+ 6x + 2x² + 3x³ +€, where
€; follows independent normal distribution N(0, 1).
a) Perform polynomial regression on your simulated data set and using x, I(x²), 1(x³) as the
predictors. Compare the estimated coefficients with the true model and report the R-square.
b) Formulate the design matrix of this regression and write down the first two rows of the
design matrix based on your data set.
c) Perform polynomial regression on your simulated data set and using z, I(x²), 1 (x³), 1 (x¹)
as the predictors. Compare the estimated coefficients with the true model.
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