CBE20258 Lecture 12: NASA lecture 12
22 Mar 2016
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Use it to make a model linear so that it can be modeled with linear regression (cid:3040) (cid:1854)(cid:3036) (cid:3533)(cid:1876)(cid:3037)(cid:2038)(cid:3037)((cid:1872)(cid:3036)) (cid:3037)(cid:2880)(cid:2869) (cid:1854)(cid:3036)(cid:4652)(cid:4652)(cid:4652)(cid:1318) (cid:1827)(cid:1318)(cid:1876)(cid:1318) This can be used for weighting your functions. And there must be a matrix of covariance because the matrix is computed with values that are not independent! Assumption of linear regression is that the model is perfect -- no covariance. There is usually something missing from the model. Under the above assumptions, you can get a model prediction of: (cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)=(cid:1827)((cid:3040)) (cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)(cid:1876)(cid:1318) Modeling functions evaluated at new times (cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318) (cid:3051)(cid:2870)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)(cid:1827)((cid:3040)) (cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:4652)(cid:1318)(cid:3021) (cid:2870) =(cid:1827)((cid:3040)) (cid:3029)((cid:3288)) (cid:2026)(cid:3029)((cid:3288))(cid:2870) =(cid:1856)(cid:1861)(cid:1853)(cid:1859)(cid:1867)(cid:1866)(cid:1853)(cid:1864) (cid:1857)(cid:1864)(cid:1857)(cid:1865)(cid:1857)(cid:1866)(cid:1872)(cid:1871) (cid:1867)(cid:1858) (cid:4672) (cid:3029)((cid:3288)) (cid:4673) (cid:2870) We are going to do things that excel doesn"t do (i. e. , we aren"t making these assumptions. We are going to do things that excel doesn"t do (i. e. , we aren"t making these assumptions anymore). Weight each point by the inverse of its variance! Either use weighted linear regression, or just don"t use linear regression at all.
