Re: Linear Regression and Hat Matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg44631] Re: Linear Regression and Hat Matrix*From*: koopman at sfu.ca (Ray Koopman)*Date*: Tue, 18 Nov 2003 06:42:04 -0500 (EST)*References*: <bpa1m8$19f$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

kowald at molgen.mpg.de (Axel Kowald) wrote in message news:<bpa1m8$19f$1 at smc.vnet.net>... > > I'm doing some linear regression and am a bit confused by Mathematicas > output. I do: > <<Statistics`LinearRegression` > data = {{1, 0.1}, {2, 0.2}, {3, 0.3}, {4, 0.4}, {5, 0.5}, > {6,0.6}, {7, 0.7}, {8, 0.8}, {9, 0.3}}; > Regress[data, {1, x}, x, RegressionReport -> {HatDiagonal}] > > and get the HatDiagonal: > {HatDiagonal -> {0.377778, > 0.261111, 0.177778, 0.127778, 0.111111, 0.127778, 0.177778, > 0.261111, 0.377778}} > > That's fine. But if I try to construct the Hat Matrix by hand I get > something completely different. The hat matrix is defined as: X(X^T > X)^-1 X^T, so I do: > > hat = data.Inverse[Transpose[data].data].Transpose[data] > > However, the diagonal elements of the resulting matrix are completely > different. > > {0.00490196, 0.0196078, 0.0441176, 0.0784314, 0.122549, 0.176471, > 0.240196, 0.313725, 1.} > > What am I doing wrong? > X = Table[{1,x},{x,9}], not "data".