Regression With Mathematica
This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA
Overview
Download & View Regression With Mathematica as PDF for free.
More details
- Words: 3,677
- Pages: 30
1
regression.nb
In[2]:=
<< Statistics`LinearRegression`
In[19]:=
<< Graphics`MultipleListPlot`
Page 387 ü 1. ü A In[27]:=
data = 880, 0<, 84, 2<, 86, 3<, 88, 4<, 812, 6<, 814, 7<, 816, 8<, 822, 11<, 826, 11<<;
In[28]:=
dplot = ListPlot@dataD;
10 8 6 4 2
5
10
15
20
25
In[29]:=
func = Fit@data, 81, x<, xD
Out[29]=
0.361111 + 0.451389 x
In[30]:=
regress = Regress@data, 81, x<, xD
Out[30]= 9ParameterTable → 1 x
Estimate 0.361111
SE 0.33646
TStat 1.07327
PValue 0.318751
0.451389
0.0233293
19.3486
2.45583 × 10−7
,
RSquared → 0.981645, AdjustedRSquared → 0.979023, EstimatedVariance → 0.313492, Model ANOVATable → Error Total In[31]:=
In[36]:=
DF 1 7 8
SumOfSq 117.361 2.19444 119.556
MeanSq 117.361 0.313492
FRatio 374.367
PValue 2.45583 × 10−7
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
=
2
regression.nb Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[37]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[38]:=
14 12 10 8 6 4 2 5
10
15
20
25
Graphics
Out[38]=
ü B In[39]:=
data = 880, 0<, 84, 2<, 86, 4<, 88, 3<, 812, 7<, 814, 6<, 816, 8<, 822, 11<, 826, 13<<;
In[40]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
In[41]:=
func = Fit@data, 81, x<, xD
Out[41]=
0.0833333 + 0.493056 x
20
25
3
regression.nb
In[42]:=
Out[42]=
regress = Regress@data, 81, x<, xD 9ParameterTable → 1 x
Estimate 0.0833333
SE 0.452677
TStat 0.18409
PValue 0.859162
0.493056
0.0313875
15.7087
1.02564 × 10−6
,
RSquared → 0.972415, AdjustedRSquared → 0.968474, EstimatedVariance → 0.56746,
ANOVATable →
In[43]:=
In[44]:= In[45]:=
In[46]:=
Model Error Total
DF 1 7 8
SumOfSq 140.028 3.97222 144.
MeanSq 140.028 0.56746
FRatio 246.762
PValue 1.02564 × 10−6
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD; Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
12.5 10 7.5 5 2.5 5
Out[46]=
10
15
20
25
Graphics
ü C In[47]:=
=
data = 880, 2<, 84, 8<, 86, 0<, 88, 6<, 812, 3<, 814, 4<, 816, 13<, 822, 7<, 826, 11<<;
4
regression.nb
In[48]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
20
25
In[49]:=
func = Fit@data, 81, x<, xD
Out[49]=
2.41667 + 0.298611 x
In[50]:=
regress = Regress@data, 81, x<, xD
Out[50]=
9ParameterTable → 1 x
Estimate 2.41667 0.298611
SE 2.18609 0.151578
TStat 1.10547 1.97002
PValue 0.305495 , 0.0894892
RSquared → 0.356674, AdjustedRSquared → 0.264771, EstimatedVariance → 13.2341, Model ANOVATable → Error Total In[51]:=
In[52]:= In[53]:=
DF 1 7 8
SumOfSq 51.3611 92.6389 144.
MeanSq 51.3611 13.2341
FRatio 3.88096
PValue 0.0894892
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD; Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
5
regression.nb
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[54]:=
20 15 10 5
5
10
15
20
25
-5
Graphics
Out[54]=
ü D In[56]:=
data = 880, 4<, 84, 3<, 86, 8<, 88, 6<, 812, 7<, 814, 13<, 816, 2<, 822, 11<, 836, 0<<;
In[57]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
20
25
30
In[58]:=
func = Fit@data, 81, x<, xD
Out[58]=
6.83255 − 0.0634995 x
In[59]:=
regress = Regress@data, 81, x<, xD
Out[59]=
9ParameterTable → 1 x
35
Estimate 6.83255 −0.0634995
SE 2.42255 0.145586
TStat 2.8204 −0.436166
PValue 0.0257584 , 0.675852
RSquared → 0.0264581, AdjustedRSquared → −0.112619, EstimatedVariance → 20.0271, Model ANOVATable → Error Total
DF 1 7 8
SumOfSq 3.80997 140.19 144.
MeanSq 3.80997 20.0271
FRatio 0.19024
PValue 0.675852
=
6
regression.nb regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[60]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[61]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[62]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[63]:=
15 10 5
5
10
15
20
25
30
35
-5
Graphics
Out[63]=
ü E In[64]:=
data = 880, 8<, 84, 7<, 86, 6<, 88, 13<, 812, 0<, 814, 2<, 816, 11<, 822, 3<, 826, 4<<;
In[65]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
In[66]:=
func = Fit@data, 81, x<, xD
Out[66]=
8.20833 − 0.184028 x
20
25
7
regression.nb regress = Regress@data, 81, x<, xD
In[67]:=
9ParameterTable → 1 x
Out[67]=
SE 2.53422 0.175716
Estimate 8.20833 −0.184028
TStat 3.239 −1.0473
PValue 0.0142728 , 0.329771
RSquared → 0.135465, AdjustedRSquared → 0.0119599, EstimatedVariance → 17.7847, DF 1 7 8
Model ANOVATable → Error Total
SumOfSq 19.5069 124.493 144.
MeanSq 19.5069 17.7847
FRatio 1.09684
PValue 0.329771
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[68]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[69]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[70]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[71]:=
20 15 10 5
5
10
15
20
25
-5
Out[71]=
Graphics
ü F In[72]:=
data = 880, 12<, 84, 13<, 86, 8<, 88, 4<, 812, 7<, 814, 6<, 816, 3<, 822, 2<, 826, 0<<;
8
regression.nb
In[73]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
20
25
In[74]:=
func = Fit@data, 81, x<, xD
Out[74]=
11.6944 − 0.465278 x
In[75]:=
regress = Regress@data, 81, x<, xD
Out[75]=
9ParameterTable → 1 x
Estimate 11.6944 −0.465278
SE 1.24806 0.0865373
TStat 9.37011 −5.37662
PValue 0.0000327972 , 0.00103413
RSquared → 0.805057, AdjustedRSquared → 0.777208, EstimatedVariance → 4.31349, Model ANOVATable → Error Total In[76]:=
In[77]:= In[78]:=
DF 1 7 8
SumOfSq 124.694 30.1944 154.889
MeanSq 124.694 4.31349
FRatio 28.908
PValue 0.00103413
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD; Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
9
regression.nb
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[79]:=
15
10
5
5
10
15
20
25
-5
Graphics
Out[79]=
ü2 In[88]:=
data = 8832, 90<, 848, 105<, 864, 112.5<, 880, 105<, 896, 90<<;
In[90]:=
dplot = ListPlot@dataD;
110
105
100
95
40
50
60
70
In[91]:=
func = Fit@data, 81, x<, xD
Out[91]=
100.5 + 1.26353 × 10−16 x
80
90
10
regression.nb
In[92]:=
regress = Regress@data, 81, x<, xD DesignedRegress::badfit : Warning: unable to find a fit that is better than the mean response.
Out[92]=
9ParameterTable → 1 x
Estimate 100.5
SE 15.5885
TStat 6.44708
PValue 0.00756816 ,
2.64775 × 10−16
0.22964
1.153 × 10−15
1
RSquared → $Failed, AdjustedRSquared → $Failed, EstimatedVariance → 135., DF SumOfSq MeanSq 3 405. 135. = ANOVATable → Error Total 4 405.
هﻤﺒﺴﺘﮕﻲ
ﻧﺪارﻧﺪ ﺧﻄﻲ
ü3 In[93]:=
data = 8820, 22<, 822, 24<, 821, 23<, 818, 20<, 819, 21<, 827, 29<<;
In[94]:=
dplot = ListPlot@dataD;
28
26
24
22
20
22
24
In[95]:=
func = Fit@data, 81, x<, xD
Out[95]=
2. + 1. x
In[96]:=
regress = Regress@data, 81, x<, xD
Out[96]= 9ParameterTable → 1 x
26
Estimate
SE
TStat
2.
2.86665 × 10−14
6.97677 × 1013
0.
7.45324 × 10
0.
1.
−15
1.3417 × 10
PValue 14
,
RSquared → 1., AdjustedRSquared → 1., EstimatedVariance → 9.15079 × 10−29 , ANOVATable →
In[97]:=
In[98]:=
Model
DF 1
SumOfSq 50.8333
MeanSq 50.8333
Error Total
4 5
3.66031 × 10−28 50.8333
9.15079 × 10−29
FRatio 5.55508 × 1029
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
PValue 0.
=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
11
regression.nb Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[99]:=
In[100]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
26
24
22
20
22
24
26
Out[100]=
Graphics
ü4 data = 88−4, 0.5<, 8−4, −.6<, 8−3, −.5<, 83, .5<, 84, .5<, 84, −.6<<;
In[101]:=
In[102]:=
dplot = ListPlot@dataD; 0.4 0.2
-4
-2
2 -0.2 -0.4 -0.6
func = Fit@data, 81, x<, xD
In[103]:=
Out[103]=
−0.0333333 + 0.0365854 x
4
12
regression.nb
regress = Regress@data, 81, x<, xD
In[104]:=
Out[104]=
9ParameterTable → 1 x
Estimate −0.0333333 0.0365854
SE 0.258487 0.0699211
TStat −0.128955 0.523238
PValue 0.903617, 0.628456
RSquared → 0.06406, AdjustedRSquared → −0.169925, EstimatedVariance → 0.400894, DF 1 4 5
Model ANOVATable → Error Total
SumOfSq 0.109756 1.60358 1.71333
MeanSq 0.109756 0.400894
FRatio 0.273778
PValue 0.628456
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[105]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[106]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[107]:=
In[108]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
1
-4
-2
2 -1
-2 Out[108]=
Graphics
4
13
regression.nb
ü B In[109]:=
data = data ê. 8x_, y_< → 9 99−
Out[109]=
x 10
, 10 y=
2 2 3 3 2 2 , 5.=, 9− , −6.=, 9− , −5.=, 9 , 5.=, 9 , 5.=, 9 , −6.== 5 5 10 10 5 5
In[110]:=
dplot = ListPlot@dataD;
4 2
-0.4
-0.2
0.2
0.4
-2 -4 -6
func = Fit@data, 81, x<, xD
In[111]:=
Out[111]=
−0.333333 + 3.65854 x regress = Regress@data, 81, x<, xD
In[112]:=
Out[112]=
9ParameterTable → 1 x
Estimate −0.333333 3.65854
SE 2.58487 6.99211
TStat −0.128955 0.523238
PValue 0.903617, 0.628456
RSquared → 0.06406, AdjustedRSquared → −0.169925, EstimatedVariance → 40.0894, Model ANOVATable → Error Total
DF 1 4 5
SumOfSq 10.9756 160.358 171.333
MeanSq 10.9756 40.0894
FRatio 0.273778
PValue 0.628456
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[113]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[114]:=
14
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[115]:=
In[116]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
10
-0.4
-0.2
0.2
0.4
-10
-20 Out[116]=
Graphics
ü C r1=0.06405997912119195` r2 =0.06405997912119195` ﺗﻐﻴﻴﺮهﻤﺎهﻨﮓ ﻃﻮر ﺑﻪ دادﻩهﺎ
آﺮدﻩاﻧﺪ
ü5 ü A data = 881.30, 0.11<, 82.40, .38<, 82.60, .41<, 82.80, .45<, 82.40, .39<, 83.00, .48<, 84.10, .61<<;
In[131]:=
15
regression.nb
In[132]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
1.5
2.5
3
3.5
4
func = Fit@data, 81, x<, xD
In[133]:=
Out[133]=
−0.063111 + 0.175902 x regress = Regress@data, 81, x<, xD
In[134]:=
Out[134]=
9ParameterTable → 1 x
Estimate −0.063111 0.175902
SE 0.0530339 0.0191619
TStat −1.19001 9.17977
PValue 0.28746 , 0.000257308
RSquared → 0.943989, AdjustedRSquared → 0.932787, EstimatedVariance → 0.0015411, Model ANOVATable → Error Total
DF 1 5 6
SumOfSq 0.129866 0.00770551 0.137571
MeanSq 0.129866 0.0015411
FRatio 84.2682
PValue 0.000257308
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[135]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[136]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[137]:=
=
16
regression.nb
In[138]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.6
0.4
0.2
1.5
2.5
3
3.5
4
Out[138]=
Graphics
ü B data = data ê. 8x_, y_< → 8x2 , y<
In[139]:=
881.69, 0.11<, 85.76, 0.38<, 86.76, 0.41<, 87.84, 0.45<, 85.76, 0.39<, 89., 0.48<, 816.81, 0.61<<
Out[139]=
In[140]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
4
6
8
10
func = Fit@data, 81, x<, xD
In[141]:=
Out[141]=
0.178021 + 0.0295385 x
12
14
16
17
regression.nb
regress = Regress@data, 81, x<, xD
In[142]:=
Out[142]=
9ParameterTable → 1 x
SE 0.0544383 0.00619835
Estimate 0.178021 0.0295385
TStat 3.27015 4.76553
PValue 0.0221949 , 0.00503469
RSquared → 0.819562, AdjustedRSquared → 0.783474, EstimatedVariance → 0.00496463, Model ANOVATable → Error Total
DF 1 5 6
SumOfSq 0.112748 0.0248232 0.137571
MeanSq 0.112748 0.00496463
FRatio 22.7103
PValue 0.00503469
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[143]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[144]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[145]:=
In[146]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.8
0.6
0.4
0.2
2.5 Out[146]=
Graphics
5
7.5
10
12.5
15
=
18
regression.nb
ü C data = data ê. 8x_, y_< → 8Log@xD, y<
In[148]:=
880.262364, 0.11<, 80.875469, 0.38<, 80.955511, 0.41<, 81.02962, 0.45<, 80.875469, 0.39<, 81.09861, 0.48<, 81.41099, 0.61<<
Out[148]=
In[149]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
0.4
0.6
0.8
1.2
1.4
func = Fit@data, 81, x<, xD
In[150]:=
Out[150]=
−0.00130688 + 0.436253 x regress = Regress@data, 81, x<, xD
In[151]:=
Out[151]=
9ParameterTable → 1 x
Estimate −0.00130688
SE 0.00645851
TStat −0.202349
PValue 0.847619
0.436253
0.006566
66.4412
1.46239 × 10−8
,
RSquared → 0.998869, AdjustedRSquared → 0.998642, EstimatedVariance → 0.0000311288, ANOVATable → Model Error Total
DF 1 5 6
SumOfSq 0.137416 0.000155644 0.137571
MeanSq 0.137416 0.0000311288
FRatio 4414.43
PValue 1.46239 × 10−8
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[152]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[153]:=
19
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[154]:=
In[155]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.6
0.8
1.2
1.4
Out[155]=
Graphics
ü D è!!!! data = data ê. 8x_, y_< → 9 x , y=
In[157]:=
881.14018, 0.11<, 81.54919, 0.38<, 81.61245, 0.41<, 81.67332, 0.45<, 81.54919, 0.39<, 81.73205, 0.48<, 82.02485, 0.61<<
Out[157]=
In[158]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
1.2
1.4
1.6
1.8
20
regression.nb
func = Fit@data, 81, x<, xD
In[159]:=
Out[159]=
−0.511247 + 0.568088 x regress = Regress@data, 81, x<, xD
In[160]:=
Out[160]=
9ParameterTable → 1 x
SE 0.0541346 0.0332099
Estimate −0.511247 0.568088
TStat −9.44399 17.106
PValue 0.00022476 , 0.0000124966
RSquared → 0.9832, AdjustedRSquared → 0.97984, EstimatedVariance → 0.000462247, ANOVATable → Model Error Total
DF 1 5 6
SumOfSq 0.13526 0.00231124 0.137571
MeanSq 0.13526 0.000462247
FRatio 292.614
PValue 0.0000124966
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[161]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[162]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[163]:=
In[164]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
Graphics
1.4
1.6
1.8
21
regression.nb
ü E In[166]:=
data = data ê. 8x_, y_< → 9
1 x
, y=
880.769231, 0.11<, 80.416667, 0.38<, 80.384615, 0.41<, 80.357143, 0.45<, 80.416667, 0.39<, 80.333333, 0.48<, 80.243902, 0.61<<
Out[166]=
In[167]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
0.4
0.5
0.6
0.7
func = Fit@data, 81, x<, xD
In[168]:=
Out[168]=
0.778439 − 0.896463 x regress = Regress@data, 81, x<, xD
In[169]:=
Out[169]=
9ParameterTable → 1 x
Estimate 0.778439 −0.896463
SE 0.0325635 0.0732069
TStat 23.9053 −12.2456
PValue 2.38631 × 10−6 , 0.0000642482
RSquared → 0.967733, AdjustedRSquared → 0.961279, EstimatedVariance → 0.000887815, ANOVATable → Model Error Total
DF 1 5 6
SumOfSq 0.133132 0.00443908 0.137571
MeanSq 0.133132 0.000887815
FRatio 149.955
PValue 0.0000642482
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[170]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[171]:=
22
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[172]:=
In[173]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.25
0.35
0.4
0.45
0.5
Out[173]=
Graphics
Page 406 ü7 data = 881, 8.1<, 81.1, 7.5<, 81.2, 8.5<, 81.3, 9.5<, 81.4, 9.5<, 81.5, 8.9<, 81.6, 8.6<, 81.7, 10.2<, 81.8, 9.3<, 81.9, 9.1<, 82, 10.5<<;
In[175]:=
23
regression.nb
ü A In[167]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
0.4
0.5
0.6
0.7
ü B func = Fit@data, 81, x<, xD
In[168]:=
Out[168]=
0.778439 − 0.896463 x
ü C a = 0.778438553758127` b = −0.8964633841626545`
ü D 0.778438553758127` − 0.8964633841626545` x ê. x → 1.75
In[176]:=
Out[176]=
−0.790372
24
regression.nb
ü E&F regress = Regress@data, 81, x<, xD
In[177]:=
Out[177]=
9ParameterTable → 1 x
Estimate 6.15909 1.93636
SE 0.924545 0.603106
TStat 6.66176 3.21065
PValue 0.0000924862 , 0.0106478
RSquared → 0.533879, AdjustedRSquared → 0.482087, EstimatedVariance → 0.400111, Model ANOVATable → Error Total
DF 1 9 10
SumOfSq 4.12445 3.601 7.72545
MeanSq 4.12445 0.400111
FRatio 10.3083
PValue 0.0106478
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[178]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[179]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[180]:=
In[181]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
11 10 9 8
1.2 Out[181]=
Graphics
1.4
1.6
1.8
2
25
regression.nb
ü8 data = 880, 8 + 5 + 8<, 815, 12 + 10 + 14<, 830, 25 + 21 + 24<, 845, 31 + 33 + 28<, 860, 44 + 39 + 42<, 875, 48 + 51 + 44<<;
In[182]:=
In[183]:=
dplot = ListPlot@dataD; 140 120 100 80 60 40
10
20
30
40
50
60
70
50
60
70
ü A func = Fit@data, 81, x<, xD
In[184]:=
Out[184]=
16.9524 + 1.71238 x pl = Plot@func, 8x, 0, 75
In[186]:=
140 120 100 80 60 40 20 10 Out[186]=
Graphics
20
30
40
26
regression.nb
ü B In[187]:=
Show@dplot, plD 140 120 100 80 60 40 20 10
20
30
40
50
60
70
Out[187]=
Graphics
ü C func ê. x → 50
In[188]:=
Out[188]=
102.571
ü D regress = Regress@data, 81, x<, xD
In[194]:=
Out[194]=
9ParameterTable → 1 x
Estimate 16.9524 1.71238
SE 3.63867 0.0801208
TStat 4.65895 21.3725
PValue 0.00959707 , 0.0000283413
RSquared → 0.991319, AdjustedRSquared → 0.989149, EstimatedVariance → 25.2762, Model ANOVATable → Error Total
DF 1 4 5
SumOfSq 11545.7 101.105 11646.8
MeanSq 11545.7 25.2762
FRatio 456.783
PValue 0.0000283413
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[195]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[196]:=
27
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[197]:=
In[198]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
10
20
30
40
50
60
70
Out[198]=
Graphics
ü E regress = Regress@data, 81, x<, x, RegressionReport → 8AdjustedRSquared
In[200]:=
8AdjustedRSquared → 0.989149<
Out[200]=
ü 11 data = 881, 0.1<, 82, 0.2<, 83, 0.25<, 84, 0.4<, 85, 0.4<, 86, 0.5<, 87, 1<, 88, 1<<;
In[203]:=
ﺑﻴﻦ راﺑﻄﻪ
ln(x) , -ln(y) اﺳﺖ ﺧﻄﻲ data = data ê. 8x_, y_< → 8Log@xD, −Log@yD< êê N
In[204]:=
880., 2.30259<, 80.693147, 1.60944<, 81.09861, 1.38629<, 81.38629, 0.916291<, 81.60944, 0.916291<, 81.79176, 0.693147<, 81.94591, 0.<, 82.07944, 0.<<
Out[204]=
28
regression.nb
In[205]:=
dplot = ListPlot@dataD;
2
1.5
1
0.5
0.5
1
1.5
2
func = Fit@data, 81, x<, xD
In[206]:=
Out[206]=
2.41171 − 1.08157 x regress = Regress@data, 81, x<, xD
In[207]:=
Out[207]=
9ParameterTable → 1 x
Estimate 2.41171 −1.08157
SE 0.168761 0.114036
TStat 14.2907 −9.48446
PValue 7.34449 × 10−6 , 0.0000782631
RSquared → 0.937471, AdjustedRSquared → 0.927049, EstimatedVariance → 0.0450385, Model ANOVATable → Error Total
DF 1 6 7
SumOfSq 4.05144 0.270231 4.32167
MeanSq 4.05144 0.0450385
FRatio 89.955
PValue 0.0000782631
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[208]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[209]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[210]:=
=
29
regression.nb
In[211]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
1
1.5
2
-0.5 Out[211]=
Graphics
ü 12 data = 881280, 5<, 81300, 10<, 81320, 31<, 81340, 31<, 81360, 50<, 81380, 70<<;
In[212]:=
In[213]:=
dplot = ListPlot@dataD; 70 60 50 40 30 20 10 1300
1320
1340
func = Fit@data, 81, x<, xD
In[214]:=
Out[214]=
−812.667 + 0.635714 x
1360
1380
30
regression.nb
regress = Regress@data, 81, x<, xD
In[215]:=
Out[215]=
9ParameterTable → 1 x
Estimate −812.667 0.635714
SE 97.3472 0.0731693
TStat −8.34812 8.68827
PValue 0.00112552 , 0.00096606
RSquared → 0.949677, AdjustedRSquared → 0.937096, EstimatedVariance → 37.4762, Model ANOVATable → Error Total
DF 1 4 5
SumOfSq 2828.93 149.905 2978.83
MeanSq 2828.93 37.4762
FRatio 75.486
PValue 0.00096606
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[216]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[217]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[218]:=
In[219]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
1300 -20 Out[219]=
Graphics func ê. x → 1400
In[220]:=
Out[220]=
77.3333
1320
1340
1360
1380
regression.nb
In[2]:=
<< Statistics`LinearRegression`
In[19]:=
<< Graphics`MultipleListPlot`
Page 387 ü 1. ü A In[27]:=
data = 880, 0<, 84, 2<, 86, 3<, 88, 4<, 812, 6<, 814, 7<, 816, 8<, 822, 11<, 826, 11<<;
In[28]:=
dplot = ListPlot@dataD;
10 8 6 4 2
5
10
15
20
25
In[29]:=
func = Fit@data, 81, x<, xD
Out[29]=
0.361111 + 0.451389 x
In[30]:=
regress = Regress@data, 81, x<, xD
Out[30]= 9ParameterTable → 1 x
Estimate 0.361111
SE 0.33646
TStat 1.07327
PValue 0.318751
0.451389
0.0233293
19.3486
2.45583 × 10−7
,
RSquared → 0.981645, AdjustedRSquared → 0.979023, EstimatedVariance → 0.313492, Model ANOVATable → Error Total In[31]:=
In[36]:=
DF 1 7 8
SumOfSq 117.361 2.19444 119.556
MeanSq 117.361 0.313492
FRatio 374.367
PValue 2.45583 × 10−7
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
=
2
regression.nb Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[37]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[38]:=
14 12 10 8 6 4 2 5
10
15
20
25
Graphics
Out[38]=
ü B In[39]:=
data = 880, 0<, 84, 2<, 86, 4<, 88, 3<, 812, 7<, 814, 6<, 816, 8<, 822, 11<, 826, 13<<;
In[40]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
In[41]:=
func = Fit@data, 81, x<, xD
Out[41]=
0.0833333 + 0.493056 x
20
25
3
regression.nb
In[42]:=
Out[42]=
regress = Regress@data, 81, x<, xD 9ParameterTable → 1 x
Estimate 0.0833333
SE 0.452677
TStat 0.18409
PValue 0.859162
0.493056
0.0313875
15.7087
1.02564 × 10−6
,
RSquared → 0.972415, AdjustedRSquared → 0.968474, EstimatedVariance → 0.56746,
ANOVATable →
In[43]:=
In[44]:= In[45]:=
In[46]:=
Model Error Total
DF 1 7 8
SumOfSq 140.028 3.97222 144.
MeanSq 140.028 0.56746
FRatio 246.762
PValue 1.02564 × 10−6
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD; Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
12.5 10 7.5 5 2.5 5
Out[46]=
10
15
20
25
Graphics
ü C In[47]:=
=
data = 880, 2<, 84, 8<, 86, 0<, 88, 6<, 812, 3<, 814, 4<, 816, 13<, 822, 7<, 826, 11<<;
4
regression.nb
In[48]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
20
25
In[49]:=
func = Fit@data, 81, x<, xD
Out[49]=
2.41667 + 0.298611 x
In[50]:=
regress = Regress@data, 81, x<, xD
Out[50]=
9ParameterTable → 1 x
Estimate 2.41667 0.298611
SE 2.18609 0.151578
TStat 1.10547 1.97002
PValue 0.305495 , 0.0894892
RSquared → 0.356674, AdjustedRSquared → 0.264771, EstimatedVariance → 13.2341, Model ANOVATable → Error Total In[51]:=
In[52]:= In[53]:=
DF 1 7 8
SumOfSq 51.3611 92.6389 144.
MeanSq 51.3611 13.2341
FRatio 3.88096
PValue 0.0894892
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD; Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
5
regression.nb
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[54]:=
20 15 10 5
5
10
15
20
25
-5
Graphics
Out[54]=
ü D In[56]:=
data = 880, 4<, 84, 3<, 86, 8<, 88, 6<, 812, 7<, 814, 13<, 816, 2<, 822, 11<, 836, 0<<;
In[57]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
20
25
30
In[58]:=
func = Fit@data, 81, x<, xD
Out[58]=
6.83255 − 0.0634995 x
In[59]:=
regress = Regress@data, 81, x<, xD
Out[59]=
9ParameterTable → 1 x
35
Estimate 6.83255 −0.0634995
SE 2.42255 0.145586
TStat 2.8204 −0.436166
PValue 0.0257584 , 0.675852
RSquared → 0.0264581, AdjustedRSquared → −0.112619, EstimatedVariance → 20.0271, Model ANOVATable → Error Total
DF 1 7 8
SumOfSq 3.80997 140.19 144.
MeanSq 3.80997 20.0271
FRatio 0.19024
PValue 0.675852
=
6
regression.nb regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[60]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[61]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[62]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[63]:=
15 10 5
5
10
15
20
25
30
35
-5
Graphics
Out[63]=
ü E In[64]:=
data = 880, 8<, 84, 7<, 86, 6<, 88, 13<, 812, 0<, 814, 2<, 816, 11<, 822, 3<, 826, 4<<;
In[65]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
In[66]:=
func = Fit@data, 81, x<, xD
Out[66]=
8.20833 − 0.184028 x
20
25
7
regression.nb regress = Regress@data, 81, x<, xD
In[67]:=
9ParameterTable → 1 x
Out[67]=
SE 2.53422 0.175716
Estimate 8.20833 −0.184028
TStat 3.239 −1.0473
PValue 0.0142728 , 0.329771
RSquared → 0.135465, AdjustedRSquared → 0.0119599, EstimatedVariance → 17.7847, DF 1 7 8
Model ANOVATable → Error Total
SumOfSq 19.5069 124.493 144.
MeanSq 19.5069 17.7847
FRatio 1.09684
PValue 0.329771
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[68]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[69]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[70]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[71]:=
20 15 10 5
5
10
15
20
25
-5
Out[71]=
Graphics
ü F In[72]:=
data = 880, 12<, 84, 13<, 86, 8<, 88, 4<, 812, 7<, 814, 6<, 816, 3<, 822, 2<, 826, 0<<;
8
regression.nb
In[73]:=
dplot = ListPlot@dataD;
12 10 8 6 4 2
5
10
15
20
25
In[74]:=
func = Fit@data, 81, x<, xD
Out[74]=
11.6944 − 0.465278 x
In[75]:=
regress = Regress@data, 81, x<, xD
Out[75]=
9ParameterTable → 1 x
Estimate 11.6944 −0.465278
SE 1.24806 0.0865373
TStat 9.37011 −5.37662
PValue 0.0000327972 , 0.00103413
RSquared → 0.805057, AdjustedRSquared → 0.777208, EstimatedVariance → 4.31349, Model ANOVATable → Error Total In[76]:=
In[77]:= In[78]:=
DF 1 7 8
SumOfSq 124.694 30.1944 154.889
MeanSq 124.694 4.31349
FRatio 28.908
PValue 0.00103413
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD; Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
9
regression.nb
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
In[79]:=
15
10
5
5
10
15
20
25
-5
Graphics
Out[79]=
ü2 In[88]:=
data = 8832, 90<, 848, 105<, 864, 112.5<, 880, 105<, 896, 90<<;
In[90]:=
dplot = ListPlot@dataD;
110
105
100
95
40
50
60
70
In[91]:=
func = Fit@data, 81, x<, xD
Out[91]=
100.5 + 1.26353 × 10−16 x
80
90
10
regression.nb
In[92]:=
regress = Regress@data, 81, x<, xD DesignedRegress::badfit : Warning: unable to find a fit that is better than the mean response.
Out[92]=
9ParameterTable → 1 x
Estimate 100.5
SE 15.5885
TStat 6.44708
PValue 0.00756816 ,
2.64775 × 10−16
0.22964
1.153 × 10−15
1
RSquared → $Failed, AdjustedRSquared → $Failed, EstimatedVariance → 135., DF SumOfSq MeanSq 3 405. 135. = ANOVATable → Error Total 4 405.
هﻤﺒﺴﺘﮕﻲ
ﻧﺪارﻧﺪ ﺧﻄﻲ
ü3 In[93]:=
data = 8820, 22<, 822, 24<, 821, 23<, 818, 20<, 819, 21<, 827, 29<<;
In[94]:=
dplot = ListPlot@dataD;
28
26
24
22
20
22
24
In[95]:=
func = Fit@data, 81, x<, xD
Out[95]=
2. + 1. x
In[96]:=
regress = Regress@data, 81, x<, xD
Out[96]= 9ParameterTable → 1 x
26
Estimate
SE
TStat
2.
2.86665 × 10−14
6.97677 × 1013
0.
7.45324 × 10
0.
1.
−15
1.3417 × 10
PValue 14
,
RSquared → 1., AdjustedRSquared → 1., EstimatedVariance → 9.15079 × 10−29 , ANOVATable →
In[97]:=
In[98]:=
Model
DF 1
SumOfSq 50.8333
MeanSq 50.8333
Error Total
4 5
3.66031 × 10−28 50.8333
9.15079 × 10−29
FRatio 5.55508 × 1029
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
PValue 0.
=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
11
regression.nb Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[99]:=
In[100]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
26
24
22
20
22
24
26
Out[100]=
Graphics
ü4 data = 88−4, 0.5<, 8−4, −.6<, 8−3, −.5<, 83, .5<, 84, .5<, 84, −.6<<;
In[101]:=
In[102]:=
dplot = ListPlot@dataD; 0.4 0.2
-4
-2
2 -0.2 -0.4 -0.6
func = Fit@data, 81, x<, xD
In[103]:=
Out[103]=
−0.0333333 + 0.0365854 x
4
12
regression.nb
regress = Regress@data, 81, x<, xD
In[104]:=
Out[104]=
9ParameterTable → 1 x
Estimate −0.0333333 0.0365854
SE 0.258487 0.0699211
TStat −0.128955 0.523238
PValue 0.903617, 0.628456
RSquared → 0.06406, AdjustedRSquared → −0.169925, EstimatedVariance → 0.400894, DF 1 4 5
Model ANOVATable → Error Total
SumOfSq 0.109756 1.60358 1.71333
MeanSq 0.109756 0.400894
FRatio 0.273778
PValue 0.628456
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[105]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[106]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[107]:=
In[108]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
1
-4
-2
2 -1
-2 Out[108]=
Graphics
4
13
regression.nb
ü B In[109]:=
data = data ê. 8x_, y_< → 9 99−
Out[109]=
x 10
, 10 y=
2 2 3 3 2 2 , 5.=, 9− , −6.=, 9− , −5.=, 9 , 5.=, 9 , 5.=, 9 , −6.== 5 5 10 10 5 5
In[110]:=
dplot = ListPlot@dataD;
4 2
-0.4
-0.2
0.2
0.4
-2 -4 -6
func = Fit@data, 81, x<, xD
In[111]:=
Out[111]=
−0.333333 + 3.65854 x regress = Regress@data, 81, x<, xD
In[112]:=
Out[112]=
9ParameterTable → 1 x
Estimate −0.333333 3.65854
SE 2.58487 6.99211
TStat −0.128955 0.523238
PValue 0.903617, 0.628456
RSquared → 0.06406, AdjustedRSquared → −0.169925, EstimatedVariance → 40.0894, Model ANOVATable → Error Total
DF 1 4 5
SumOfSq 10.9756 160.358 171.333
MeanSq 10.9756 40.0894
FRatio 0.273778
PValue 0.628456
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[113]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[114]:=
14
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[115]:=
In[116]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
10
-0.4
-0.2
0.2
0.4
-10
-20 Out[116]=
Graphics
ü C r1=0.06405997912119195` r2 =0.06405997912119195` ﺗﻐﻴﻴﺮهﻤﺎهﻨﮓ ﻃﻮر ﺑﻪ دادﻩهﺎ
آﺮدﻩاﻧﺪ
ü5 ü A data = 881.30, 0.11<, 82.40, .38<, 82.60, .41<, 82.80, .45<, 82.40, .39<, 83.00, .48<, 84.10, .61<<;
In[131]:=
15
regression.nb
In[132]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
1.5
2.5
3
3.5
4
func = Fit@data, 81, x<, xD
In[133]:=
Out[133]=
−0.063111 + 0.175902 x regress = Regress@data, 81, x<, xD
In[134]:=
Out[134]=
9ParameterTable → 1 x
Estimate −0.063111 0.175902
SE 0.0530339 0.0191619
TStat −1.19001 9.17977
PValue 0.28746 , 0.000257308
RSquared → 0.943989, AdjustedRSquared → 0.932787, EstimatedVariance → 0.0015411, Model ANOVATable → Error Total
DF 1 5 6
SumOfSq 0.129866 0.00770551 0.137571
MeanSq 0.129866 0.0015411
FRatio 84.2682
PValue 0.000257308
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[135]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[136]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[137]:=
=
16
regression.nb
In[138]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.6
0.4
0.2
1.5
2.5
3
3.5
4
Out[138]=
Graphics
ü B data = data ê. 8x_, y_< → 8x2 , y<
In[139]:=
881.69, 0.11<, 85.76, 0.38<, 86.76, 0.41<, 87.84, 0.45<, 85.76, 0.39<, 89., 0.48<, 816.81, 0.61<<
Out[139]=
In[140]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
4
6
8
10
func = Fit@data, 81, x<, xD
In[141]:=
Out[141]=
0.178021 + 0.0295385 x
12
14
16
17
regression.nb
regress = Regress@data, 81, x<, xD
In[142]:=
Out[142]=
9ParameterTable → 1 x
SE 0.0544383 0.00619835
Estimate 0.178021 0.0295385
TStat 3.27015 4.76553
PValue 0.0221949 , 0.00503469
RSquared → 0.819562, AdjustedRSquared → 0.783474, EstimatedVariance → 0.00496463, Model ANOVATable → Error Total
DF 1 5 6
SumOfSq 0.112748 0.0248232 0.137571
MeanSq 0.112748 0.00496463
FRatio 22.7103
PValue 0.00503469
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[143]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[144]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[145]:=
In[146]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.8
0.6
0.4
0.2
2.5 Out[146]=
Graphics
5
7.5
10
12.5
15
=
18
regression.nb
ü C data = data ê. 8x_, y_< → 8Log@xD, y<
In[148]:=
880.262364, 0.11<, 80.875469, 0.38<, 80.955511, 0.41<, 81.02962, 0.45<, 80.875469, 0.39<, 81.09861, 0.48<, 81.41099, 0.61<<
Out[148]=
In[149]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
0.4
0.6
0.8
1.2
1.4
func = Fit@data, 81, x<, xD
In[150]:=
Out[150]=
−0.00130688 + 0.436253 x regress = Regress@data, 81, x<, xD
In[151]:=
Out[151]=
9ParameterTable → 1 x
Estimate −0.00130688
SE 0.00645851
TStat −0.202349
PValue 0.847619
0.436253
0.006566
66.4412
1.46239 × 10−8
,
RSquared → 0.998869, AdjustedRSquared → 0.998642, EstimatedVariance → 0.0000311288, ANOVATable → Model Error Total
DF 1 5 6
SumOfSq 0.137416 0.000155644 0.137571
MeanSq 0.137416 0.0000311288
FRatio 4414.43
PValue 1.46239 × 10−8
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[152]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[153]:=
19
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[154]:=
In[155]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.6
0.8
1.2
1.4
Out[155]=
Graphics
ü D è!!!! data = data ê. 8x_, y_< → 9 x , y=
In[157]:=
881.14018, 0.11<, 81.54919, 0.38<, 81.61245, 0.41<, 81.67332, 0.45<, 81.54919, 0.39<, 81.73205, 0.48<, 82.02485, 0.61<<
Out[157]=
In[158]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
1.2
1.4
1.6
1.8
20
regression.nb
func = Fit@data, 81, x<, xD
In[159]:=
Out[159]=
−0.511247 + 0.568088 x regress = Regress@data, 81, x<, xD
In[160]:=
Out[160]=
9ParameterTable → 1 x
SE 0.0541346 0.0332099
Estimate −0.511247 0.568088
TStat −9.44399 17.106
PValue 0.00022476 , 0.0000124966
RSquared → 0.9832, AdjustedRSquared → 0.97984, EstimatedVariance → 0.000462247, ANOVATable → Model Error Total
DF 1 5 6
SumOfSq 0.13526 0.00231124 0.137571
MeanSq 0.13526 0.000462247
FRatio 292.614
PValue 0.0000124966
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[161]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[162]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[163]:=
In[164]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
Graphics
1.4
1.6
1.8
21
regression.nb
ü E In[166]:=
data = data ê. 8x_, y_< → 9
1 x
, y=
880.769231, 0.11<, 80.416667, 0.38<, 80.384615, 0.41<, 80.357143, 0.45<, 80.416667, 0.39<, 80.333333, 0.48<, 80.243902, 0.61<<
Out[166]=
In[167]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
0.4
0.5
0.6
0.7
func = Fit@data, 81, x<, xD
In[168]:=
Out[168]=
0.778439 − 0.896463 x regress = Regress@data, 81, x<, xD
In[169]:=
Out[169]=
9ParameterTable → 1 x
Estimate 0.778439 −0.896463
SE 0.0325635 0.0732069
TStat 23.9053 −12.2456
PValue 2.38631 × 10−6 , 0.0000642482
RSquared → 0.967733, AdjustedRSquared → 0.961279, EstimatedVariance → 0.000887815, ANOVATable → Model Error Total
DF 1 5 6
SumOfSq 0.133132 0.00443908 0.137571
MeanSq 0.133132 0.000887815
FRatio 149.955
PValue 0.0000642482
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[170]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[171]:=
22
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[172]:=
In[173]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
0.25
0.35
0.4
0.45
0.5
Out[173]=
Graphics
Page 406 ü7 data = 881, 8.1<, 81.1, 7.5<, 81.2, 8.5<, 81.3, 9.5<, 81.4, 9.5<, 81.5, 8.9<, 81.6, 8.6<, 81.7, 10.2<, 81.8, 9.3<, 81.9, 9.1<, 82, 10.5<<;
In[175]:=
23
regression.nb
ü A In[167]:=
dplot = ListPlot@dataD; 0.6 0.5 0.4 0.3 0.2
0.4
0.5
0.6
0.7
ü B func = Fit@data, 81, x<, xD
In[168]:=
Out[168]=
0.778439 − 0.896463 x
ü C a = 0.778438553758127` b = −0.8964633841626545`
ü D 0.778438553758127` − 0.8964633841626545` x ê. x → 1.75
In[176]:=
Out[176]=
−0.790372
24
regression.nb
ü E&F regress = Regress@data, 81, x<, xD
In[177]:=
Out[177]=
9ParameterTable → 1 x
Estimate 6.15909 1.93636
SE 0.924545 0.603106
TStat 6.66176 3.21065
PValue 0.0000924862 , 0.0106478
RSquared → 0.533879, AdjustedRSquared → 0.482087, EstimatedVariance → 0.400111, Model ANOVATable → Error Total
DF 1 9 10
SumOfSq 4.12445 3.601 7.72545
MeanSq 4.12445 0.400111
FRatio 10.3083
PValue 0.0106478
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[178]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[179]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[180]:=
In[181]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
11 10 9 8
1.2 Out[181]=
Graphics
1.4
1.6
1.8
2
25
regression.nb
ü8 data = 880, 8 + 5 + 8<, 815, 12 + 10 + 14<, 830, 25 + 21 + 24<, 845, 31 + 33 + 28<, 860, 44 + 39 + 42<, 875, 48 + 51 + 44<<;
In[182]:=
In[183]:=
dplot = ListPlot@dataD; 140 120 100 80 60 40
10
20
30
40
50
60
70
50
60
70
ü A func = Fit@data, 81, x<, xD
In[184]:=
Out[184]=
16.9524 + 1.71238 x pl = Plot@func, 8x, 0, 75
In[186]:=
140 120 100 80 60 40 20 10 Out[186]=
Graphics
20
30
40
26
regression.nb
ü B In[187]:=
Show@dplot, plD 140 120 100 80 60 40 20 10
20
30
40
50
60
70
Out[187]=
Graphics
ü C func ê. x → 50
In[188]:=
Out[188]=
102.571
ü D regress = Regress@data, 81, x<, xD
In[194]:=
Out[194]=
9ParameterTable → 1 x
Estimate 16.9524 1.71238
SE 3.63867 0.0801208
TStat 4.65895 21.3725
PValue 0.00959707 , 0.0000283413
RSquared → 0.991319, AdjustedRSquared → 0.989149, EstimatedVariance → 25.2762, Model ANOVATable → Error Total
DF 1 4 5
SumOfSq 11545.7 101.105 11646.8
MeanSq 11545.7 25.2762
FRatio 456.783
PValue 0.0000283413
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[195]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[196]:=
27
regression.nb
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[197]:=
In[198]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
10
20
30
40
50
60
70
Out[198]=
Graphics
ü E regress = Regress@data, 81, x<, x, RegressionReport → 8AdjustedRSquared
In[200]:=
8AdjustedRSquared → 0.989149<
Out[200]=
ü 11 data = 881, 0.1<, 82, 0.2<, 83, 0.25<, 84, 0.4<, 85, 0.4<, 86, 0.5<, 87, 1<, 88, 1<<;
In[203]:=
ﺑﻴﻦ راﺑﻄﻪ
ln(x) , -ln(y) اﺳﺖ ﺧﻄﻲ data = data ê. 8x_, y_< → 8Log@xD, −Log@yD< êê N
In[204]:=
880., 2.30259<, 80.693147, 1.60944<, 81.09861, 1.38629<, 81.38629, 0.916291<, 81.60944, 0.916291<, 81.79176, 0.693147<, 81.94591, 0.<, 82.07944, 0.<<
Out[204]=
28
regression.nb
In[205]:=
dplot = ListPlot@dataD;
2
1.5
1
0.5
0.5
1
1.5
2
func = Fit@data, 81, x<, xD
In[206]:=
Out[206]=
2.41171 − 1.08157 x regress = Regress@data, 81, x<, xD
In[207]:=
Out[207]=
9ParameterTable → 1 x
Estimate 2.41171 −1.08157
SE 0.168761 0.114036
TStat 14.2907 −9.48446
PValue 7.34449 × 10−6 , 0.0000782631
RSquared → 0.937471, AdjustedRSquared → 0.927049, EstimatedVariance → 0.0450385, Model ANOVATable → Error Total
DF 1 6 7
SumOfSq 4.05144 0.270231 4.32167
MeanSq 4.05144 0.0450385
FRatio 89.955
PValue 0.0000782631
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[208]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[209]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[210]:=
=
29
regression.nb
In[211]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
1
1.5
2
-0.5 Out[211]=
Graphics
ü 12 data = 881280, 5<, 81300, 10<, 81320, 31<, 81340, 31<, 81360, 50<, 81380, 70<<;
In[212]:=
In[213]:=
dplot = ListPlot@dataD; 70 60 50 40 30 20 10 1300
1320
1340
func = Fit@data, 81, x<, xD
In[214]:=
Out[214]=
−812.667 + 0.635714 x
1360
1380
30
regression.nb
regress = Regress@data, 81, x<, xD
In[215]:=
Out[215]=
9ParameterTable → 1 x
Estimate −812.667 0.635714
SE 97.3472 0.0731693
TStat −8.34812 8.68827
PValue 0.00112552 , 0.00096606
RSquared → 0.949677, AdjustedRSquared → 0.937096, EstimatedVariance → 37.4762, Model ANOVATable → Error Total
DF 1 4 5
SumOfSq 2828.93 149.905 2978.83
MeanSq 2828.93 37.4762
FRatio 75.486
PValue 0.00096606
=
regress = Regress@data, 81, x<, x, RegressionReport → 8FitResiduals, SinglePredictionCITable, ParameterConfidenceRegion
In[216]:=
8observed, predicted, se, ci< = Transpose@HSinglePredictionCITable ê. regressL@@1DDD;
In[217]:=
Hxval = Map@First, dataD; predicted = Transpose@8xval, predicted
In[218]:=
In[219]:=
MultipleListPlot@data, predicted, lowerCI, upperCI, SymbolShape → 8PlotSymbol@DiamondD, None, None, None<, PlotJoined → 8False, True, True, True<, PlotStyle → 8Automatic, Automatic, [email protected], .05
1300 -20 Out[219]=
Graphics func ê. x → 1400
In[220]:=
Out[220]=
77.3333
1320
1340
1360
1380
Related Documents
Regression With Mathematica
December 2019 14
Heat Equation With Mathematica
December 2019 10
Mathematica
May 2020 9
Mathematica
October 2019 15
Getting Started With Mathematica & Maple
June 2020 5
Simple Regression With Spss
June 2020 14More Documents from ""
Wakoopa-the State Of Apps Q2
May 2020 8