Dating the Almagest Star Catalogue Using Proper Motions: A Reconsideration

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Given N pairs of data points (x_i, y_i), and defining and , the least squares fit of y = bx yields b = S_xy/S_xx. If the standard deviation σ of the y's is known, then the estimated uncertainty of the slope b is . If the standard deviation of the y's is unknown, then it must be estimated from the fit and the error in b is instead .

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