Re: Equivalent functions generate different plots

• To: mathgroup at smc.vnet.net
• Subject: [mg26172] Re: [mg26112] Equivalent functions generate different plots
• From: BobHanlon at aol.com
• Date: Thu, 30 Nov 2000 01:04:13 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```data = {{0, 79.6}, {0.2, 79.2}, {0.4, 77.1}, {0.6, 73.7}, {0.8, 69.1}, {1.,
63.2}};

f[t_] := Evaluate[Fit[data, {1, t, t^2}, t]];

g[t_] := Fit[data, {1, t, t^2}, t];

f[t] == g[t]

True

Plot[{f[t], g[t]}, {t, 0, 2.2},
PlotStyle -> {{RGBColor[0, 0, 1], AbsoluteDashing[{5, 5}],
AbsoluteThickness[2]}, {RGBColor[1, 0, 0],
AbsoluteDashing[{5, 15}], AbsoluteThickness[2]}}];

Attributes[Plot]

{HoldAll, Protected}

Since Plot has attribute HoldAll, the iterator t is set before g[t] is
evaluated. This results in g[t] being improperly evaluated. You must Evaluate
the functions within Plot.

Plot[Evaluate[{f[t], g[t]}], {t, 0, 2.2},
PlotStyle -> {{RGBColor[0, 0, 1], AbsoluteDashing[{5, 5}],
AbsoluteThickness[2]}, {RGBColor[1, 0, 0],
AbsoluteDashing[{5, 15}], AbsoluteThickness[2]}}];

Bob Hanlon

In a message dated 11/28/00 3:15:10 AM, gerbual at col2.telecom.com.co writes:

>With:
>
>In[1]:=
>data = {{0, 79.6}, {0.2, 79.2}, {0.4, 77.1}, {0.6, 73.7}, {0.8, 69.1},
>
>{1., 63.2}};
>
>I can to get its cuadratic regression function:
>
>In[2]:=
>Fit[data, {1, t, t^2}, t]
>
>Out[2]=
>79.68214285714285` + 0.21249999999984936` t - 16.741071428571246` t^2
>
>Then, I can define the regression function in two different, but
>equivalent ways:
>
>First: copying and pasting the last output:
>
>In[3]:=
>f[t_] :=
>    79.68214285714285`+ 0.21249999999984936` t - 16.741071428571246 t^2
>
>Second: using directly the *Fit* function in the right hand:
>
>In[4]:=
>g[t_] := Fit[data, {1, t, t^2}, t]
>
>In this conditions:
>
>In[5]:=
>f[t] == g[t]
>
>Out[5]=
>True
>
>However:
>
>In[6]:=
>Plot[{f[t], g[t]}, {t, 0, 2.2}]
>
>Out[6]=
>
>(GRAPHICS ...!!!)
>
>genere two different plots (a straight line and a curve). The curve is
>
>well, but the straight line not. I DON'T UNDERSTAND. Can somebody
>explain to me this inconsistency?
>

```

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