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Any summary of linear regression ought to at least point out that the "cost function", which depending on the circumstances is often viewed as modeling the vari

Any summary of linear regression ought to at least point out that the "cost function", which depending on the circumstances is often viewed as modeling the variance in the data, is typically limited to one data coordinate. That is, the separations to the fit line to be minimized go entirely along the y-axis; which has the effect of assuming that there's perfect knowledge of the x value. And while that can be the case for some sampling protocols, it is also often not the case. So please consider including something like: If there is uncertainty in both the x and y coordinates then one needs to pursue alternate approaches which admit variation in both, one of the most popular being "Deming regression"[1] [1] https://en.wikipedia.org/wiki/Deming_regression https://en.wikipedia.org/wiki/Deming_regression

ced 11y ago
Can you give examples? It seems to me that in my cases, I never use X='temperature' as a predictor, but rather X='temperature reported by thermometer', and this is of course always known with 100% accuracy. In a predictive context, that's all we need. Are you referring to a social science context?
- theophrastus 11y ago
  Here's an easy one to conceptualize: A good friend of mine is a state hydrologist. He crawls over streams with a ladder-like platform and at increments lowers a depth gauge to eventually estimate the stream's volume flow rate. For a number of reasons (including wild weather conditions) the cross stream increment is known only to an inch or so, that's the uncertainty in X, the depth gauge reading has another uncertainty in Y. These are applied to a function where the slope, via Deming regression, gives him an estimate of the flow rate. By the bye, most lab thermometers i've dealt with have an accuracy of about 0.1°C
oilywater 11y ago
Looks closer to support vector machine and its regression capabilities. Although, linear regression, logistic regression, svm regression, are all almost the same thing, the loss function is different, all can be trained with gradient descent.

ced 11y ago

Can you give examples? It seems to me that in my cases, I never use X='temperature' as a predictor, but rather X='temperature reported by thermometer', and this is of course always known with 100% accuracy. In a predictive context, that's all we need. Are you referring to a social science context?

theophrastus 11y ago
Here's an easy one to conceptualize: A good friend of mine is a state hydrologist. He crawls over streams with a ladder-like platform and at increments lowers a depth gauge to eventually estimate the stream's volume flow rate. For a number of reasons (including wild weather conditions) the cross stream increment is known only to an inch or so, that's the uncertainty in X, the depth gauge reading has another uncertainty in Y. These are applied to a function where the slope, via Deming regression, gives him an estimate of the flow rate. By the bye, most lab thermometers i've dealt with have an accuracy of about 0.1°C

oilywater 11y ago

Looks closer to support vector machine and its regression capabilities. Although, linear regression, logistic regression, svm regression, are all almost the same thing, the loss function is different, all can be trained with gradient descent.