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".