多元非线性回归分析 函数模型的表达式说明.htm

很不错的非线性回归分析程序

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Exp<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>自然指数</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Exp(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span><span style="mso-spacerun: yes">&nbsp;</span>Exp(2)=e*e=e^2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Ln<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:
9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>自然对数</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Ln(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>; x&gt;0<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Ln(e)=1<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Log<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>10</span><span style='font-size:
9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>的对数</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Log(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:ZH-CN'>或者</span><span
lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;
mso-font-kerning:0pt'>: Log10(x)<span style="mso-spacerun: yes">&nbsp; </span>;
x&gt;0<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Log(100)=2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Log2<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp; </span>2</span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>的对数</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp; </span>Log2(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>; x&gt;0<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Log2(8)=3<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Abs<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="mso-spacerun:
yes">&nbsp;</span></span><span style='font-size:9.0pt;mso-bidi-font-size:8.0pt;
font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:ZH-CN'>绝对值</span><span
lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;
mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Abs(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Abs(-2)=2 ; Abs(2)=2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Int<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>取整</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Int(x)<span
style="mso-spacerun: yes">&nbsp;&nbsp; </span></span><span style='font-size:
9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>或者</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'>: Floor(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Int(2.3)=2 ; Int(-2.3)=-3<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Sgn<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>符号函数</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Sgn(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Sgn(-2)=-1 ;<span style="mso-spacerun: yes">&nbsp; </span>Sgn(0)=0 ;
Sgn(2)=1<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><![if !supportEmptyParas]>&nbsp;<![endif]><o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Sinh<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>双曲正弦</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Sinh(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Sinh(2)=3.62686040784702=(e^2-e^(-2))/2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Cosh<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>双曲余弦</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Cosh(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Cosh(2)=3.76219569108363=(e^2+e^(-2))/2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Tanh<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp; </span></span><span style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt;mso-ansi-language:
ZH-CN'>双曲正切</span><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>Tanh(x)<span style="mso-spacerun: yes">&nbsp;
</span></span><span style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:
宋体;mso-font-kerning:0pt;mso-ansi-language:ZH-CN'>或者</span><span lang=EN-US
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt'>: tgh(x)<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Tanh(2)=0.964027580075817=Sinh(2)/Cosh(2)<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>ArcSinh<span style="mso-spacerun: yes">&nbsp;
</span></span><span style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:
宋体;mso-font-kerning:0pt;mso-ansi-language:ZH-CN'>反双曲正弦</span><span lang=EN-US
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt'><span style="mso-spacerun: yes">&nbsp; </span>ArcSinh(x) </span><span
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt;mso-ansi-language:ZH-CN'>或者</span><span lang=EN-US style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt'>: ASinh(x)<span
style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>ArcSinh(3.62686040784702)=2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>ArcCosh<span style="mso-spacerun: yes">&nbsp;
</span></span><span style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:
宋体;mso-font-kerning:0pt;mso-ansi-language:ZH-CN'>反双曲余弦</span><span lang=EN-US
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt'><span style="mso-spacerun: yes">&nbsp; </span>ArcCosh(x) </span><span
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt;mso-ansi-language:ZH-CN'>或者</span><span lang=EN-US style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt'>: ACosh(x) ;
x&gt;=1<span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>ArcCosh(3.76219569108363)=2<o:p></o:p></span></p>

<p class=MsoNormal align=left style='text-align:left;mso-layout-grid-align:
none;text-autospace:none'><span lang=EN-US style='font-size:9.0pt;mso-bidi-font-size:
8.0pt;font-family:宋体;mso-font-kerning:0pt'><span style="mso-spacerun:
yes">&nbsp;&nbsp;&nbsp; </span>ArcTanh<span style="mso-spacerun: yes">&nbsp;
</span></span><span style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:
宋体;mso-font-kerning:0pt;mso-ansi-language:ZH-CN'>反双曲正切</span><span lang=EN-US
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt'><span style="mso-spacerun: yes">&nbsp; </span>Arctanh(x) </span><span
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt;mso-ansi-language:ZH-CN'>或者</span><span lang=EN-US style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt'>: ATanh(x)</span><span
style='font-size:9.0pt;mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:
0pt;mso-ansi-language:ZH-CN'>、</span><span lang=EN-US style='font-size:9.0pt;
mso-bidi-font-size:8.0pt;font-family:宋体;mso-font-kerning:0pt'>Arctgh(x)<span
style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>Arctanh(0.761594155955765)=1<o:p></o:p></span></p>