BENG449 Problem 6 5

# BENG449 Problem 6 5 - BENG449 Problem Set 6 Question 5 Alex...

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Alex Lemon March 11, 2008 1 Remarks Consider the model η = β 1 ( 1 - e - β 2 t ) . It can be shown that the correlation between the OLS parameter estimates, b 1 and b 2 , is inversely proportional to the mean-squared deviation of the indepen- dent variable, t : ρ ( b 1 , b 2 ) MSD - 1 ( t ) = p N s i =1 ( t i - ¯ t ) 2 P - 1 Thus, the theoretical and empirical results both indicate that the parameter estimates for b 1 and b 2 are more highly correlated in the narrow-range experi- ment than in the wide-range experiment. This makes sense intuitively because a wide-range experiment allows the regression technique to make more of a distinction between the eFects of the two parameters. In both cases, the the- oretical and empirical results diFered signi±cantly. This appears to be due to the comparatively large magnitude of the disturbance terms. As a result, there were several instances in which numerical stability became an issue, producing specious outliers. This phenomenon was especially prevalent in the wide-range experiment. Additionally, it should be noted that the experiment had to be run twice because the lsqcurve±t failed due to numerical instability on the ±rst trial run. 1

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BENG449 Problem 6 5 - BENG449 Problem Set 6 Question 5 Alex...

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