Linear Regression and Hat Matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg44589] Linear Regression and Hat Matrix*From*: kowald at molgen.mpg.de (Axel Kowald)*Date*: Mon, 17 Nov 2003 03:38:20 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi everybody, 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? Many thanks, Axel Kowald