Deming regression: Difference between revisions

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Application: Can humans perform mental regression on a graph? Accuracy and bias in the perception of scatterplots
Fix error in SSR formula to match source Jensen (2007)
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: <math>y^* = \beta_0 + \beta_1 x^*,</math>
such that the weighted sum of squared residuals of the model is minimized:{{sfn|Fuller|1987|loc=Ch. 1.3.3}}
: <math>SSR = \sum_{i=1}^n\bigg(\frac{\varepsilon_i^2}{\sigma_\varepsilon^2} + \frac{\eta_i^2}{\sigma_\eta^2}\bigg) = \frac{1}{\sigma_\etaepsilon^2} \sum_{i=1}^n\Big((y_i-\beta_0-\beta_1x^*_i)^2 + \delta(x_i-x^*_i)^2\Big) \ \to\ \min_{\beta_0,\beta_1,x_1^*,\ldots,x_n^*} SSR</math>
 
See {{harvtxt|Jensen|2007}} for a full derivation.