Re: Weights option to Regress command not behaving as expected

• To: mathgroup at smc.vnet.net
• Subject: [mg70934] Re: [mg70804] Weights option to Regress command not behaving as expected
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Thu, 2 Nov 2006 06:47:13 -0500 (EST)
• References: <c2baae590610041434g12698b38uef586f9c10381b1d@mail.gmail.com> <200610280921.FAA16058@smc.vnet.net>

```The equivalence of the two weighted results is due to the symmetry in
the data.  If we break that symmetry by, for instance, replacing the
first response with a 1, the two weightings provide different results.

In[1]:= << Statistics`LinearRegression`

In[2]:= binaryjumpdata =
Transpose[{Table[x, {x, 1, 100}],
Flatten[Union[{Table[0, {50}], Table[1, {50}]}]]}];

In[3]:= forwardweights = Table[1/n, {n, 1, 100}];

In[4]:= backweights = Table[1/(100 - n + 1), {n, 1, 100}];

In[5]:= newdata = binaryjumpdata;

In[6]:= newdata[[1, 2]] = 1;

In[7]:= BestFit /.
Regress[newdata, {1, x}, x, RegressionReport -> {BestFit},
Weights -> forwardweights]

Out[7]= 0.211485 + 0.00591118 x

In[8]:= BestFit /.
Regress[newdata, {1, x}, x, RegressionReport -> {BestFit},
Weights -> backweights]

Out[8]= -0.0710847 + 0.0115066 x

Darren Glosemeyer
Wolfram Research

Stern wrote:
> I am looking to run regressions to fit a curve to a time series, and I
> want older data to weigh less in the fitting than newer data does.
> However, I can't seem to make this work as expected.
>
> For the sake of example, imagine 100 periods with a binary time series
> -- it's 0 until time 50, then 1 until time 100.
>
> binaryjumpdata =
> Transpose[{Table[x,{x,1,100}],Flatten[Union[{Table[0,{50}],Table[1,{50}]}]]}];
>
>  simplefit =
>   BestFit/.Regress[binaryjumpdata,{1,x},x,RegressionReport\[Rule]{BestFit}];
>
> Out = -0.257576+0.0150015 x
>
> Fine. Now, compare the following two weighting functions:
>
> forwardweights = Table[1/n, {n, 1, 100}]);
>
> backweights = Table[1/(100-n+1), {n, 1, 100}]);
>
> forwardweights drops from 1 to .01, while backweights runs the other
> way, from .01 to 1. Applying these two weighting lists to the
> binaryjumpdata curve and running the Regress function *should* produce
> different best fit line. Forwardweights should produce a lower line,
> and backweights should produce a higher one. However,
>
> weightedfit =
>   BestFit/.Regress[binaryjumpdata,{1,x},x,RegressionReport\[Rule]{BestFit},
>       Weights->forwardweights]
>
> and
>
> reverseweightedfit =
>   BestFit/.Regress[binaryjumpdata,{1,x},x,RegressionReport\[Rule]{BestFit},
>       Weights\[Rule]backweights]
>
> The answer is different from that of the unweighted series, as
> expected, but both the forward and reverse application of the weights
> produce the exact same output -- -0.0941409+0.0117652  x
>
> Clearly, the Weights command is not doing what I expect. What am I missing?
>
> Thanks in advance for any help.
>
> Michael Stern
>

```

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