Least squares why

There are, in fact, an infinite number of possible candidates for best fitting line. The approach we used above clearly won't work in practice. On the next page, we'll instead derive some formulas for the slope and the intercept for least squares regression line. Breadcrumb Home 7 7.

Font size. Font family A A. Content Preview Arcu felis bibendum ut tristique et egestas quis: Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris Duis aute irure dolor in reprehenderit in voluptate Excepteur sint occaecat cupidatat non proident.

Lorem ipsum dolor sit amet, consectetur adipisicing elit. Odit molestiae mollitia laudantium assumenda nam eaque, excepturi, soluta, perspiciatis cupiditate sapiente, adipisci quaerat odio voluptates consectetur nulla eveniet iure vitae quibusdam? Is Maxwell really more famous than Gauss? Also, Pasteur is probably almost as well known as a chemist as he is as a microbiologist. Darwin I certainly give you. Any computation advantage of least square is just by-product.

Without normal assumption, lse is much less justified. However, with approximated normal error structure, for example t distribution with modest df, using least squares is still recommended. I've fixed it. The normal approximation to the binomial distribution is not what tells us the expected value and the variance of the binomial distribution.

I haven't yet figured out what your question actually means. Show 9 more comments. Chris Taylor Chris Taylor 27k 4 4 gold badges 74 74 silver badges bronze badges. After reading Michael Hardy's answer I didn't feel enlightened, and I wanted to ask him for elaboration.

Your answer was exactly the elaboration I hoped to get. There may be perhaps non-intuitive or "unnatural" mathematical reasons for deviating from this norm towards others. I feel that would better respect the author's wishes regardless of how valid one considers those wishes to be. Michael Hardy 1. Nikhil Panikkar Nikhil Panikkar 6 6 silver badges 12 12 bronze badges.

Also, these are values of a probability density rather than actual probabilities. Other than that, this is a decent answer. Courtesy: Graphpad. Bindu Bindu 51 1 1 silver badge 1 1 bronze badge. Steve Steve 41 2 2 bronze badges. For example, the best fit line is the same for the following two sets of data: 0 1 0 5 1 5 2 6 and 0 3 0 3 1 5 2 6 If you use minimum-distance fitting, this is no longer the case.

William Jockusch William Jockusch 2 2 silver badges 10 10 bronze badges. Note how the non-square errors exaggerate different error combinations. Justas Justas 3 3 bronze badges. And here we're discussing the estimation error not projection distance.

Sign up or log in Sign up using Google. Sign up using Facebook. New York: McGraw-Hill, Chatterjee, S. New York: Wiley, pp. Edwards, A. San Francisco, CA: W. Freeman, pp. Farebrother, R.

New York: Springer-Verlag, Gauss, C. Gonick, L. The Cartoon Guide to Statistics. New York: Harper Perennial, Kenney, J. Princeton, NJ: Van Nostrand, pp. Lancaster, P. Curve and Surface Fitting: An Introduction. London: Academic Press, Laplace, P. Paris: Courcier, Lawson, C. Solving Least Squares Problems. Ledvij, M. Institute of Mathematical Statistics, Financial Analysis. Financial Ratios.

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Key Takeaways The least-squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.