       Re: Regressions in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg91969] Re: Regressions in Mathematica
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Mon, 15 Sep 2008 03:42:14 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <gag2m5\$3a8\$1@smc.vnet.net>

```Gregory Lypny wrote:

> I'm having trouble understanding the syntax of the Regress command.
> If data is an nx2 matrix where the first column is the explanatory
> variable and the second is the dependent variable,  then either
>
> 	Regress[data, {1, x}, x]
>
> or
>
> 	Regress[data, x, x]
>
> performs a standard regression of the second column on the first with
> a constant thrown in.  But how do I write the command for the case of
> more than one explanatory variable?  Say that my data matrix is now
> nx3, so that the first two columns are the explanatory variables and
> the last is the dependent variable.
>
> Regress[data, {x,x}, x] or Regress[data, {1, x,x}, x] gives the error
> message "Number of coordinates (2) is not equal to the number of
> variables (1)".  I'm not sure how I'm supposed to identify each
> explanatory variable.

I hope the following will help:

In:= Needs["LinearRegression`"]

In:= data = Flatten[Table[{x, y, x^2 + y^2}, {x, -1, 2}, {y, 3}], 1]

Out=
{{-1, 1, 2}, {-1, 2, 5}, {-1, 3, 10}, {0, 1, 1}, {0, 2, 4}, {0, 3, 9},
{1, 1, 2}, {1, 2, 5}, {1, 3, 10}, {2, 1, 5}, {2, 2, 8}, {2, 3, 13}}

In:= Regress[data, {1, x, y}, {x, y}]

Out=
{ParameterTable ->     Estimate   SE         TStat     PValue      ,
1   -2.33333   0.988826   -2.3597   0.0426223

x   1.         0.329609   3.0339    0.014157

-6
y   4.         0.451335   8.86259   9.68155 10

RSquared -> 0.906977, AdjustedRSquared -> 0.886305,

EstimatedVariance -> 1.62963,

ANOVATable ->         DF   SumOfSq   MeanSq    FRatio   PValue      }
Model   2    143.      71.5      43.875   0.0000228382

Error   9    14.6667   1.62963

Total   11   157.667

In:= Regress[data, {1, x, y, x^2, y^2}, {x, y}]

Out=
{ParameterTable ->

Estimate         SE              TStat          PValue  ,
-15              -15
1    -5.3843 10       6.47747 10      -0.831234      0.433276

-16             -15
x    -5.93487 10      1.13915 10      -0.520992      0.618443

-15              -15
y    4.74751 10       7.27927 10      0.652197       0.535096

2                              -16             15
x    1.               8.49071 10      1.17776 10     0.

2                              -15           14
y    1.               1.80115 10      5.552 10       0.

RSquared -> 1., AdjustedRSquared -> 1.,

-30
EstimatedVariance -> 8.65106 10   ,

ANOVATable ->

DF   SumOfSq         MeanSq          FRatio         PValue}
30
Model   4    157.667         39.4167         4.55628 10     0.

-29             -30
Error   7    6.05574 10      8.65106 10

Total   11   157.667

Best regards,
-- Jean-Marc

```

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