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[1]:= Needs["LinearRegression`"]
In[2]:= data = Flatten[Table[{x, y, x^2 + y^2}, {x, -1, 2}, {y, 3}], 1]
Out[2]=
{{-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[3]:= Regress[data, {1, x, y}, {x, y}]
Out[3]=
{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[4]:= Regress[data, {1, x, y, x^2, y^2}, {x, y}]
Out[4]=
{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