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Classic calibration Standard regression assumes x values have no error Orthogonal distance regression (ODR) assumes both x and y have the same error variance

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Calibrating buoys and satellites (and errors) at the same time Peter Challenor SOC

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New method Assume that the true values are fixed but unknown Estimate the x’s as well as the regression parameters Indeterminacy so fix one regression to slope 1 and intercept 0

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Mathematically Standard regression: all error on y Orthogonal Distance Regression : error equal on x and y New method. Estimate true value x

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Results NDBCJASONTOPEXUKCMENVISAT Intercept (m) 0.0-0.216 (0.014) -0.088 (0.007) 0.616 (0.029) 0.125 (0.007) Slope 1.0001.035 (0.005) 1.008 (0.002) 0.802 (0.011) 0.980 (0.002) Residual std dev (m) 0.1460.1840.0880.3920.088

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CHAPTER 3 ECONOMETRICS x x x x x Chapter 2: Estimating the parameters of a linear regression model. Y i = b 1 + b 2 X i + e i Using OLS Chapter 3: Testing.

CHAPTER 3 ECONOMETRICS x x x x x Chapter 2: Estimating the parameters of a linear regression model. Y i = b 1 + b 2 X i + e i Using OLS Chapter 3: Testing.

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