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R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 24 Nov 2009 04:57:53 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Nov/24/t1259064129e5isj8s7anepl3u.htm/, Retrieved Wed, 13 Aug 2025 20:49:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59015, Retrieved Wed, 13 Aug 2025 20:49:42 +0000

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User-defined keywords

Estimated Impact

318

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Multiple Regression] [] [2009-11-24 11:34:57] [f57b281e621ed7dff28b90886f5aa97c]
-   P     [Multiple Regression] [] [2009-11-24 11:57:53] [4d89445a8ea4b299af2ee123046cffa6] [Current]

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Dataseries X:

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Boxplots

97.4	116.7
97	109
105.4	119.5
102.7	115.1
98.1	107.1
104.5	109.7
87.4	110.4
89.9	105
109.8	115.8
111.7	116.4
98.6	111.1
96.9	119.5
95.1	110.9
97	115.1
112.7	125.2
102.9	116
97.4	112.9
111.4	121.7
87.4	123.2
96.8	116.6
114.1	136.2
110.3	120.9
103.9	119.6
101.6	125.9
94.6	116.1
95.9	107.5
104.7	116.7
102.8	112.5
98.1	113
113.9	126.4
80.9	114.1
95.7	112.5
113.2	112.4
105.9	113.1
108.8	116.3
102.3	111.7
99	118.8
100.7	116.5
115.5	125.1
100.7	113.1
109.9	119.6
114.6	114.4
85.4	114
100.5	117.8
114.8	117
116.5	120.9
112.9	115
102	117.3
106	119.4
105.3	114.9
118.8	125.8
106.1	117.6
109.3	117.6
117.2	114.9
92.5	121.9
104.2	117
112.5	106.4
122.4	110.5
113.3	113.6
100	114.2

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 6 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
ipchn[t] = + 46.4146793383104 + 0.746503234894817Tip[t] -0.892302272677017M1[t] -5.13511571343774M2[t] -4.30778629079102M3[t] -5.54756016461321M4[t] -5.90470959410443M5[t] -9.70605214891858M6[t] + 8.80895968214796M7[t] -2.01409591346731M8[t] -9.6705069071819M9[t] -11.1242994421722M10[t] -7.88526146792929M11[t] -0.104529017759257t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
ipchn[t] =  +  46.4146793383104 +  0.746503234894817Tip[t] -0.892302272677017M1[t] -5.13511571343774M2[t] -4.30778629079102M3[t] -5.54756016461321M4[t] -5.90470959410443M5[t] -9.70605214891858M6[t] +  8.80895968214796M7[t] -2.01409591346731M8[t] -9.6705069071819M9[t] -11.1242994421722M10[t] -7.88526146792929M11[t] -0.104529017759257t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]ipchn[t] =  +  46.4146793383104 +  0.746503234894817Tip[t] -0.892302272677017M1[t] -5.13511571343774M2[t] -4.30778629079102M3[t] -5.54756016461321M4[t] -5.90470959410443M5[t] -9.70605214891858M6[t] +  8.80895968214796M7[t] -2.01409591346731M8[t] -9.6705069071819M9[t] -11.1242994421722M10[t] -7.88526146792929M11[t] -0.104529017759257t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Estimated Regression Equation
ipchn[t] = + 46.4146793383104 + 0.746503234894817Tip[t] -0.892302272677017M1[t] -5.13511571343774M2[t] -4.30778629079102M3[t] -5.54756016461321M4[t] -5.90470959410443M5[t] -9.70605214891858M6[t] + 8.80895968214796M7[t] -2.01409591346731M8[t] -9.6705069071819M9[t] -11.1242994421722M10[t] -7.88526146792929M11[t] -0.104529017759257t + e[t]

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	46.4146793383104	19.953483	2.3261	0.024472	0.012236
Tip	0.746503234894817	0.210242	3.5507	0.000899	0.00045
M1	-0.892302272677017	3.154317	-0.2829	0.778536	0.389268
M2	-5.13511571343774	3.15061	-1.6299	0.109957	0.054978
M3	-4.30778629079102	4.095137	-1.0519	0.298328	0.149164
M4	-5.54756016461321	3.24736	-1.7083	0.094316	0.047158
M5	-5.90470959410443	3.211719	-1.8385	0.072452	0.036226
M6	-9.70605214891858	4.136587	-2.3464	0.02332	0.01166
M7	8.80895968214796	4.149407	2.1229	0.039171	0.019586
M8	-2.01409591346731	3.171649	-0.635	0.528554	0.264277
M9	-9.6705069071819	4.134973	-2.3387	0.023751	0.011875
M10	-11.1242994421722	4.175721	-2.664	0.010609	0.005305
M11	-7.88526146792929	3.466862	-2.2745	0.027648	0.013824
t	-0.104529017759257	0.053261	-1.9626	0.055761	0.02788

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Ordinary Least Squares \tabularnewline
Variable & Parameter & S.D. & T-STATH0: parameter = 0 & 2-tail p-value & 1-tail p-value \tabularnewline
(Intercept) & 46.4146793383104 & 19.953483 & 2.3261 & 0.024472 & 0.012236 \tabularnewline
Tip & 0.746503234894817 & 0.210242 & 3.5507 & 0.000899 & 0.00045 \tabularnewline
M1 & -0.892302272677017 & 3.154317 & -0.2829 & 0.778536 & 0.389268 \tabularnewline
M2 & -5.13511571343774 & 3.15061 & -1.6299 & 0.109957 & 0.054978 \tabularnewline
M3 & -4.30778629079102 & 4.095137 & -1.0519 & 0.298328 & 0.149164 \tabularnewline
M4 & -5.54756016461321 & 3.24736 & -1.7083 & 0.094316 & 0.047158 \tabularnewline
M5 & -5.90470959410443 & 3.211719 & -1.8385 & 0.072452 & 0.036226 \tabularnewline
M6 & -9.70605214891858 & 4.136587 & -2.3464 & 0.02332 & 0.01166 \tabularnewline
M7 & 8.80895968214796 & 4.149407 & 2.1229 & 0.039171 & 0.019586 \tabularnewline
M8 & -2.01409591346731 & 3.171649 & -0.635 & 0.528554 & 0.264277 \tabularnewline
M9 & -9.6705069071819 & 4.134973 & -2.3387 & 0.023751 & 0.011875 \tabularnewline
M10 & -11.1242994421722 & 4.175721 & -2.664 & 0.010609 & 0.005305 \tabularnewline
M11 & -7.88526146792929 & 3.466862 & -2.2745 & 0.027648 & 0.013824 \tabularnewline
t & -0.104529017759257 & 0.053261 & -1.9626 & 0.055761 & 0.02788 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=2

[TABLE]
[ROW][C]Multiple Linear Regression - Ordinary Least Squares[/C][/ROW]
[ROW][C]Variable[/C][C]Parameter[/C][C]S.D.[/C][C]T-STATH0: parameter = 0[/C][C]2-tail p-value[/C][C]1-tail p-value[/C][/ROW]
[ROW][C](Intercept)[/C][C]46.4146793383104[/C][C]19.953483[/C][C]2.3261[/C][C]0.024472[/C][C]0.012236[/C][/ROW]
[ROW][C]Tip[/C][C]0.746503234894817[/C][C]0.210242[/C][C]3.5507[/C][C]0.000899[/C][C]0.00045[/C][/ROW]
[ROW][C]M1[/C][C]-0.892302272677017[/C][C]3.154317[/C][C]-0.2829[/C][C]0.778536[/C][C]0.389268[/C][/ROW]
[ROW][C]M2[/C][C]-5.13511571343774[/C][C]3.15061[/C][C]-1.6299[/C][C]0.109957[/C][C]0.054978[/C][/ROW]
[ROW][C]M3[/C][C]-4.30778629079102[/C][C]4.095137[/C][C]-1.0519[/C][C]0.298328[/C][C]0.149164[/C][/ROW]
[ROW][C]M4[/C][C]-5.54756016461321[/C][C]3.24736[/C][C]-1.7083[/C][C]0.094316[/C][C]0.047158[/C][/ROW]
[ROW][C]M5[/C][C]-5.90470959410443[/C][C]3.211719[/C][C]-1.8385[/C][C]0.072452[/C][C]0.036226[/C][/ROW]
[ROW][C]M6[/C][C]-9.70605214891858[/C][C]4.136587[/C][C]-2.3464[/C][C]0.02332[/C][C]0.01166[/C][/ROW]
[ROW][C]M7[/C][C]8.80895968214796[/C][C]4.149407[/C][C]2.1229[/C][C]0.039171[/C][C]0.019586[/C][/ROW]
[ROW][C]M8[/C][C]-2.01409591346731[/C][C]3.171649[/C][C]-0.635[/C][C]0.528554[/C][C]0.264277[/C][/ROW]
[ROW][C]M9[/C][C]-9.6705069071819[/C][C]4.134973[/C][C]-2.3387[/C][C]0.023751[/C][C]0.011875[/C][/ROW]
[ROW][C]M10[/C][C]-11.1242994421722[/C][C]4.175721[/C][C]-2.664[/C][C]0.010609[/C][C]0.005305[/C][/ROW]
[ROW][C]M11[/C][C]-7.88526146792929[/C][C]3.466862[/C][C]-2.2745[/C][C]0.027648[/C][C]0.013824[/C][/ROW]
[ROW][C]t[/C][C]-0.104529017759257[/C][C]0.053261[/C][C]-1.9626[/C][C]0.055761[/C][C]0.02788[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Ordinary Least Squares
Variable	Parameter	S.D.	T-STATH0: parameter = 0	2-tail p-value	1-tail p-value
(Intercept)	46.4146793383104	19.953483	2.3261	0.024472	0.012236
Tip	0.746503234894817	0.210242	3.5507	0.000899	0.00045
M1	-0.892302272677017	3.154317	-0.2829	0.778536	0.389268
M2	-5.13511571343774	3.15061	-1.6299	0.109957	0.054978
M3	-4.30778629079102	4.095137	-1.0519	0.298328	0.149164
M4	-5.54756016461321	3.24736	-1.7083	0.094316	0.047158
M5	-5.90470959410443	3.211719	-1.8385	0.072452	0.036226
M6	-9.70605214891858	4.136587	-2.3464	0.02332	0.01166
M7	8.80895968214796	4.149407	2.1229	0.039171	0.019586
M8	-2.01409591346731	3.171649	-0.635	0.528554	0.264277
M9	-9.6705069071819	4.134973	-2.3387	0.023751	0.011875
M10	-11.1242994421722	4.175721	-2.664	0.010609	0.005305
M11	-7.88526146792929	3.466862	-2.2745	0.027648	0.013824
t	-0.104529017759257	0.053261	-1.9626	0.055761	0.02788

Multiple Linear Regression - Regression Statistics
Multiple R	0.61415688381946
R-squared	0.377188677942829
Adjusted R-squared	0.201176782578846
F-TEST (value)	2.14297265058605
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.0291661287439557
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.94401772121584
Sum Squared Residuals	1124.39231647403

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.61415688381946 \tabularnewline
R-squared & 0.377188677942829 \tabularnewline
Adjusted R-squared & 0.201176782578846 \tabularnewline
F-TEST (value) & 2.14297265058605 \tabularnewline
F-TEST (DF numerator) & 13 \tabularnewline
F-TEST (DF denominator) & 46 \tabularnewline
p-value & 0.0291661287439557 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 4.94401772121584 \tabularnewline
Sum Squared Residuals & 1124.39231647403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.61415688381946[/C][/ROW]
[ROW][C]R-squared[/C][C]0.377188677942829[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.201176782578846[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]2.14297265058605[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]13[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]46[/C][/ROW]
[ROW][C]p-value[/C][C]0.0291661287439557[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]4.94401772121584[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]1124.39231647403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Regression Statistics
Multiple R	0.61415688381946
R-squared	0.377188677942829
Adjusted R-squared	0.201176782578846
F-TEST (value)	2.14297265058605
F-TEST (DF numerator)	13
F-TEST (DF denominator)	46
p-value	0.0291661287439557
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	4.94401772121584
Sum Squared Residuals	1124.39231647403

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	116.7	118.127263126630	-1.42726312662984
2	109	113.481319374152	-4.48131937415151
3	119.5	120.474746952155	-0.974746952155375
4	115.1	117.114885326358	-2.01488532635793
5	107.1	113.219291998591	-6.11929199859128
6	109.7	114.091041129345	-4.3910411293447
7	110.4	119.736318625951	-9.33631862595064
8	105	110.674992099813	-5.67499209981315
9	115.8	117.769466462746	-1.96946646274613
10	116.4	117.629501056297	-1.22950105629677
11	111.1	110.984817635658	0.115182364341702
12	119.5	117.496494586507	2.00350541349286
13	110.9	115.155957473260	-4.25595747326019
14	115.1	112.226971161040	2.87302883895962
15	125.2	124.669872353776	0.530127646223556
16	116	116.009837760226	-0.00983776022580646
17	112.9	111.442391521054	1.45760847894617
18	121.7	117.987565237008	3.71243476299214
19	123.2	118.481970412840	4.71802958716045
20	116.6	114.571516207476	2.02848379252370
21	136.2	119.725082159683	16.4749178403172
22	120.9	115.330048314333	5.56995168566706
23	119.6	113.686936567490	5.91306343251025
24	125.9	119.750711577402	6.14928842259831
25	116.1	113.528357642702	2.57164235729829
26	107.5	110.151469389545	-2.65146938954499
27	116.7	117.443498261507	-0.743498261506833
28	112.5	114.680839223625	-2.18083922362524
29	113	110.710595572369	2.28940442763088
30	126.4	118.599475111134	7.80052488886619
31	114.1	112.375351172912	1.72464882708782
32	112.5	112.496014435981	0.00398556401908479
33	112.4	117.798881035166	-5.39888103516634
34	113.1	110.791085867685	2.30891413231532
35	116.3	116.090454205363	0.209545794636744
36	111.7	119.018915628717	-7.31891562871698
37	118.8	115.558623663128	3.24137633687218
38	116.5	112.480336703929	4.01966329607097
39	125.1	124.251384985260	0.848615014740228
40	113.1	111.858834217235	1.24116578276495
41	119.6	118.264985531017	1.33501446898312
42	114.4	117.867679162449	-3.46767916244909
43	114	114.480267516828	-0.480267516827762
44	117.8	114.824881750365	2.97511824963505
45	117	117.738937997887	-0.738937997886962
46	120.9	117.449671944459	3.45032805554136
47	115	117.896769255321	-2.89676925532093
48	117.3	117.540616445137	-0.24061644513746
49	119.4	119.529798094280	-0.129798094280441
50	114.9	114.659903371334	0.240096628665911
51	125.8	125.460497447302	0.339502552698423
52	117.6	114.635603472556	2.96439652744403
53	117.6	116.562735376969	1.03726462303110
54	114.9	118.554239360065	-3.65423936006454
55	121.9	118.52609227147	3.37390772853014
56	117	116.332595506365	0.66740449363531
57	106.4	114.767632344518	-8.3676323445178
58	110.5	120.599692817227	-10.0996928172270
59	113.6	116.941022336168	-3.34102233616777
60	114.2	114.793261762237	-0.59326176223674

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 116.7 & 118.127263126630 & -1.42726312662984 \tabularnewline
2 & 109 & 113.481319374152 & -4.48131937415151 \tabularnewline
3 & 119.5 & 120.474746952155 & -0.974746952155375 \tabularnewline
4 & 115.1 & 117.114885326358 & -2.01488532635793 \tabularnewline
5 & 107.1 & 113.219291998591 & -6.11929199859128 \tabularnewline
6 & 109.7 & 114.091041129345 & -4.3910411293447 \tabularnewline
7 & 110.4 & 119.736318625951 & -9.33631862595064 \tabularnewline
8 & 105 & 110.674992099813 & -5.67499209981315 \tabularnewline
9 & 115.8 & 117.769466462746 & -1.96946646274613 \tabularnewline
10 & 116.4 & 117.629501056297 & -1.22950105629677 \tabularnewline
11 & 111.1 & 110.984817635658 & 0.115182364341702 \tabularnewline
12 & 119.5 & 117.496494586507 & 2.00350541349286 \tabularnewline
13 & 110.9 & 115.155957473260 & -4.25595747326019 \tabularnewline
14 & 115.1 & 112.226971161040 & 2.87302883895962 \tabularnewline
15 & 125.2 & 124.669872353776 & 0.530127646223556 \tabularnewline
16 & 116 & 116.009837760226 & -0.00983776022580646 \tabularnewline
17 & 112.9 & 111.442391521054 & 1.45760847894617 \tabularnewline
18 & 121.7 & 117.987565237008 & 3.71243476299214 \tabularnewline
19 & 123.2 & 118.481970412840 & 4.71802958716045 \tabularnewline
20 & 116.6 & 114.571516207476 & 2.02848379252370 \tabularnewline
21 & 136.2 & 119.725082159683 & 16.4749178403172 \tabularnewline
22 & 120.9 & 115.330048314333 & 5.56995168566706 \tabularnewline
23 & 119.6 & 113.686936567490 & 5.91306343251025 \tabularnewline
24 & 125.9 & 119.750711577402 & 6.14928842259831 \tabularnewline
25 & 116.1 & 113.528357642702 & 2.57164235729829 \tabularnewline
26 & 107.5 & 110.151469389545 & -2.65146938954499 \tabularnewline
27 & 116.7 & 117.443498261507 & -0.743498261506833 \tabularnewline
28 & 112.5 & 114.680839223625 & -2.18083922362524 \tabularnewline
29 & 113 & 110.710595572369 & 2.28940442763088 \tabularnewline
30 & 126.4 & 118.599475111134 & 7.80052488886619 \tabularnewline
31 & 114.1 & 112.375351172912 & 1.72464882708782 \tabularnewline
32 & 112.5 & 112.496014435981 & 0.00398556401908479 \tabularnewline
33 & 112.4 & 117.798881035166 & -5.39888103516634 \tabularnewline
34 & 113.1 & 110.791085867685 & 2.30891413231532 \tabularnewline
35 & 116.3 & 116.090454205363 & 0.209545794636744 \tabularnewline
36 & 111.7 & 119.018915628717 & -7.31891562871698 \tabularnewline
37 & 118.8 & 115.558623663128 & 3.24137633687218 \tabularnewline
38 & 116.5 & 112.480336703929 & 4.01966329607097 \tabularnewline
39 & 125.1 & 124.251384985260 & 0.848615014740228 \tabularnewline
40 & 113.1 & 111.858834217235 & 1.24116578276495 \tabularnewline
41 & 119.6 & 118.264985531017 & 1.33501446898312 \tabularnewline
42 & 114.4 & 117.867679162449 & -3.46767916244909 \tabularnewline
43 & 114 & 114.480267516828 & -0.480267516827762 \tabularnewline
44 & 117.8 & 114.824881750365 & 2.97511824963505 \tabularnewline
45 & 117 & 117.738937997887 & -0.738937997886962 \tabularnewline
46 & 120.9 & 117.449671944459 & 3.45032805554136 \tabularnewline
47 & 115 & 117.896769255321 & -2.89676925532093 \tabularnewline
48 & 117.3 & 117.540616445137 & -0.24061644513746 \tabularnewline
49 & 119.4 & 119.529798094280 & -0.129798094280441 \tabularnewline
50 & 114.9 & 114.659903371334 & 0.240096628665911 \tabularnewline
51 & 125.8 & 125.460497447302 & 0.339502552698423 \tabularnewline
52 & 117.6 & 114.635603472556 & 2.96439652744403 \tabularnewline
53 & 117.6 & 116.562735376969 & 1.03726462303110 \tabularnewline
54 & 114.9 & 118.554239360065 & -3.65423936006454 \tabularnewline
55 & 121.9 & 118.52609227147 & 3.37390772853014 \tabularnewline
56 & 117 & 116.332595506365 & 0.66740449363531 \tabularnewline
57 & 106.4 & 114.767632344518 & -8.3676323445178 \tabularnewline
58 & 110.5 & 120.599692817227 & -10.0996928172270 \tabularnewline
59 & 113.6 & 116.941022336168 & -3.34102233616777 \tabularnewline
60 & 114.2 & 114.793261762237 & -0.59326176223674 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=4

[TABLE]
[ROW][C]Multiple Linear Regression - Actuals, Interpolation, and Residuals[/C][/ROW]
[ROW][C]Time or Index[/C][C]Actuals[/C][C]InterpolationForecast[/C][C]ResidualsPrediction Error[/C][/ROW]
[ROW][C]1[/C][C]116.7[/C][C]118.127263126630[/C][C]-1.42726312662984[/C][/ROW]
[ROW][C]2[/C][C]109[/C][C]113.481319374152[/C][C]-4.48131937415151[/C][/ROW]
[ROW][C]3[/C][C]119.5[/C][C]120.474746952155[/C][C]-0.974746952155375[/C][/ROW]
[ROW][C]4[/C][C]115.1[/C][C]117.114885326358[/C][C]-2.01488532635793[/C][/ROW]
[ROW][C]5[/C][C]107.1[/C][C]113.219291998591[/C][C]-6.11929199859128[/C][/ROW]
[ROW][C]6[/C][C]109.7[/C][C]114.091041129345[/C][C]-4.3910411293447[/C][/ROW]
[ROW][C]7[/C][C]110.4[/C][C]119.736318625951[/C][C]-9.33631862595064[/C][/ROW]
[ROW][C]8[/C][C]105[/C][C]110.674992099813[/C][C]-5.67499209981315[/C][/ROW]
[ROW][C]9[/C][C]115.8[/C][C]117.769466462746[/C][C]-1.96946646274613[/C][/ROW]
[ROW][C]10[/C][C]116.4[/C][C]117.629501056297[/C][C]-1.22950105629677[/C][/ROW]
[ROW][C]11[/C][C]111.1[/C][C]110.984817635658[/C][C]0.115182364341702[/C][/ROW]
[ROW][C]12[/C][C]119.5[/C][C]117.496494586507[/C][C]2.00350541349286[/C][/ROW]
[ROW][C]13[/C][C]110.9[/C][C]115.155957473260[/C][C]-4.25595747326019[/C][/ROW]
[ROW][C]14[/C][C]115.1[/C][C]112.226971161040[/C][C]2.87302883895962[/C][/ROW]
[ROW][C]15[/C][C]125.2[/C][C]124.669872353776[/C][C]0.530127646223556[/C][/ROW]
[ROW][C]16[/C][C]116[/C][C]116.009837760226[/C][C]-0.00983776022580646[/C][/ROW]
[ROW][C]17[/C][C]112.9[/C][C]111.442391521054[/C][C]1.45760847894617[/C][/ROW]
[ROW][C]18[/C][C]121.7[/C][C]117.987565237008[/C][C]3.71243476299214[/C][/ROW]
[ROW][C]19[/C][C]123.2[/C][C]118.481970412840[/C][C]4.71802958716045[/C][/ROW]
[ROW][C]20[/C][C]116.6[/C][C]114.571516207476[/C][C]2.02848379252370[/C][/ROW]
[ROW][C]21[/C][C]136.2[/C][C]119.725082159683[/C][C]16.4749178403172[/C][/ROW]
[ROW][C]22[/C][C]120.9[/C][C]115.330048314333[/C][C]5.56995168566706[/C][/ROW]
[ROW][C]23[/C][C]119.6[/C][C]113.686936567490[/C][C]5.91306343251025[/C][/ROW]
[ROW][C]24[/C][C]125.9[/C][C]119.750711577402[/C][C]6.14928842259831[/C][/ROW]
[ROW][C]25[/C][C]116.1[/C][C]113.528357642702[/C][C]2.57164235729829[/C][/ROW]
[ROW][C]26[/C][C]107.5[/C][C]110.151469389545[/C][C]-2.65146938954499[/C][/ROW]
[ROW][C]27[/C][C]116.7[/C][C]117.443498261507[/C][C]-0.743498261506833[/C][/ROW]
[ROW][C]28[/C][C]112.5[/C][C]114.680839223625[/C][C]-2.18083922362524[/C][/ROW]
[ROW][C]29[/C][C]113[/C][C]110.710595572369[/C][C]2.28940442763088[/C][/ROW]
[ROW][C]30[/C][C]126.4[/C][C]118.599475111134[/C][C]7.80052488886619[/C][/ROW]
[ROW][C]31[/C][C]114.1[/C][C]112.375351172912[/C][C]1.72464882708782[/C][/ROW]
[ROW][C]32[/C][C]112.5[/C][C]112.496014435981[/C][C]0.00398556401908479[/C][/ROW]
[ROW][C]33[/C][C]112.4[/C][C]117.798881035166[/C][C]-5.39888103516634[/C][/ROW]
[ROW][C]34[/C][C]113.1[/C][C]110.791085867685[/C][C]2.30891413231532[/C][/ROW]
[ROW][C]35[/C][C]116.3[/C][C]116.090454205363[/C][C]0.209545794636744[/C][/ROW]
[ROW][C]36[/C][C]111.7[/C][C]119.018915628717[/C][C]-7.31891562871698[/C][/ROW]
[ROW][C]37[/C][C]118.8[/C][C]115.558623663128[/C][C]3.24137633687218[/C][/ROW]
[ROW][C]38[/C][C]116.5[/C][C]112.480336703929[/C][C]4.01966329607097[/C][/ROW]
[ROW][C]39[/C][C]125.1[/C][C]124.251384985260[/C][C]0.848615014740228[/C][/ROW]
[ROW][C]40[/C][C]113.1[/C][C]111.858834217235[/C][C]1.24116578276495[/C][/ROW]
[ROW][C]41[/C][C]119.6[/C][C]118.264985531017[/C][C]1.33501446898312[/C][/ROW]
[ROW][C]42[/C][C]114.4[/C][C]117.867679162449[/C][C]-3.46767916244909[/C][/ROW]
[ROW][C]43[/C][C]114[/C][C]114.480267516828[/C][C]-0.480267516827762[/C][/ROW]
[ROW][C]44[/C][C]117.8[/C][C]114.824881750365[/C][C]2.97511824963505[/C][/ROW]
[ROW][C]45[/C][C]117[/C][C]117.738937997887[/C][C]-0.738937997886962[/C][/ROW]
[ROW][C]46[/C][C]120.9[/C][C]117.449671944459[/C][C]3.45032805554136[/C][/ROW]
[ROW][C]47[/C][C]115[/C][C]117.896769255321[/C][C]-2.89676925532093[/C][/ROW]
[ROW][C]48[/C][C]117.3[/C][C]117.540616445137[/C][C]-0.24061644513746[/C][/ROW]
[ROW][C]49[/C][C]119.4[/C][C]119.529798094280[/C][C]-0.129798094280441[/C][/ROW]
[ROW][C]50[/C][C]114.9[/C][C]114.659903371334[/C][C]0.240096628665911[/C][/ROW]
[ROW][C]51[/C][C]125.8[/C][C]125.460497447302[/C][C]0.339502552698423[/C][/ROW]
[ROW][C]52[/C][C]117.6[/C][C]114.635603472556[/C][C]2.96439652744403[/C][/ROW]
[ROW][C]53[/C][C]117.6[/C][C]116.562735376969[/C][C]1.03726462303110[/C][/ROW]
[ROW][C]54[/C][C]114.9[/C][C]118.554239360065[/C][C]-3.65423936006454[/C][/ROW]
[ROW][C]55[/C][C]121.9[/C][C]118.52609227147[/C][C]3.37390772853014[/C][/ROW]
[ROW][C]56[/C][C]117[/C][C]116.332595506365[/C][C]0.66740449363531[/C][/ROW]
[ROW][C]57[/C][C]106.4[/C][C]114.767632344518[/C][C]-8.3676323445178[/C][/ROW]
[ROW][C]58[/C][C]110.5[/C][C]120.599692817227[/C][C]-10.0996928172270[/C][/ROW]
[ROW][C]59[/C][C]113.6[/C][C]116.941022336168[/C][C]-3.34102233616777[/C][/ROW]
[ROW][C]60[/C][C]114.2[/C][C]114.793261762237[/C][C]-0.59326176223674[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=4

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	116.7	118.127263126630	-1.42726312662984
2	109	113.481319374152	-4.48131937415151
3	119.5	120.474746952155	-0.974746952155375
4	115.1	117.114885326358	-2.01488532635793
5	107.1	113.219291998591	-6.11929199859128
6	109.7	114.091041129345	-4.3910411293447
7	110.4	119.736318625951	-9.33631862595064
8	105	110.674992099813	-5.67499209981315
9	115.8	117.769466462746	-1.96946646274613
10	116.4	117.629501056297	-1.22950105629677
11	111.1	110.984817635658	0.115182364341702
12	119.5	117.496494586507	2.00350541349286
13	110.9	115.155957473260	-4.25595747326019
14	115.1	112.226971161040	2.87302883895962
15	125.2	124.669872353776	0.530127646223556
16	116	116.009837760226	-0.00983776022580646
17	112.9	111.442391521054	1.45760847894617
18	121.7	117.987565237008	3.71243476299214
19	123.2	118.481970412840	4.71802958716045
20	116.6	114.571516207476	2.02848379252370
21	136.2	119.725082159683	16.4749178403172
22	120.9	115.330048314333	5.56995168566706
23	119.6	113.686936567490	5.91306343251025
24	125.9	119.750711577402	6.14928842259831
25	116.1	113.528357642702	2.57164235729829
26	107.5	110.151469389545	-2.65146938954499
27	116.7	117.443498261507	-0.743498261506833
28	112.5	114.680839223625	-2.18083922362524
29	113	110.710595572369	2.28940442763088
30	126.4	118.599475111134	7.80052488886619
31	114.1	112.375351172912	1.72464882708782
32	112.5	112.496014435981	0.00398556401908479
33	112.4	117.798881035166	-5.39888103516634
34	113.1	110.791085867685	2.30891413231532
35	116.3	116.090454205363	0.209545794636744
36	111.7	119.018915628717	-7.31891562871698
37	118.8	115.558623663128	3.24137633687218
38	116.5	112.480336703929	4.01966329607097
39	125.1	124.251384985260	0.848615014740228
40	113.1	111.858834217235	1.24116578276495
41	119.6	118.264985531017	1.33501446898312
42	114.4	117.867679162449	-3.46767916244909
43	114	114.480267516828	-0.480267516827762
44	117.8	114.824881750365	2.97511824963505
45	117	117.738937997887	-0.738937997886962
46	120.9	117.449671944459	3.45032805554136
47	115	117.896769255321	-2.89676925532093
48	117.3	117.540616445137	-0.24061644513746
49	119.4	119.529798094280	-0.129798094280441
50	114.9	114.659903371334	0.240096628665911
51	125.8	125.460497447302	0.339502552698423
52	117.6	114.635603472556	2.96439652744403
53	117.6	116.562735376969	1.03726462303110
54	114.9	118.554239360065	-3.65423936006454
55	121.9	118.52609227147	3.37390772853014
56	117	116.332595506365	0.66740449363531
57	106.4	114.767632344518	-8.3676323445178
58	110.5	120.599692817227	-10.0996928172270
59	113.6	116.941022336168	-3.34102233616777
60	114.2	114.793261762237	-0.59326176223674

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.389795845757798	0.779591691515597	0.610204154242202
18	0.284967720196960	0.569935440393921	0.71503227980304
19	0.463585088333979	0.927170176667957	0.536414911666021
20	0.345186358345715	0.69037271669143	0.654813641654285
21	0.781373830157016	0.437252339685968	0.218626169842984
22	0.704886627253679	0.590226745492642	0.295113372746321
23	0.649876198640993	0.700247602718013	0.350123801359007
24	0.652358730631309	0.695282538737383	0.347641269368691
25	0.56962651514332	0.86074696971336	0.43037348485668
26	0.705078012925797	0.589843974148406	0.294921987074203
27	0.668281441578158	0.663437116843685	0.331718558421842
28	0.696391261764448	0.607217476471104	0.303608738235552
29	0.612418219039953	0.775163561920095	0.387581780960047
30	0.756392854043642	0.487214291912717	0.243607145956358
31	0.704575685542324	0.590848628915351	0.295424314457676
32	0.694255067648684	0.611489864702633	0.305744932351316
33	0.897561076075207	0.204877847849586	0.102438923924793
34	0.840486365284154	0.319027269431692	0.159513634715846
35	0.824233129634122	0.351533740731755	0.175766870365878
36	0.942451523328138	0.115096953343723	0.0575484766718617
37	0.900720116254906	0.198559767490188	0.0992798837450942
38	0.84164291648119	0.316714167037621	0.158357083518810
39	0.760610798707863	0.478778402584273	0.239389201292137
40	0.682366302026535	0.63526739594693	0.317633697973465
41	0.564571212117743	0.870857575764514	0.435428787882257
42	0.473624382985058	0.947248765970117	0.526375617014942
43	0.614279227124504	0.771441545750993	0.385720772875496

\begin{tabular}{lllllllll}
\hline
Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
p-values & Alternative Hypothesis \tabularnewline
breakpoint index & greater & 2-sided & less \tabularnewline
17 & 0.389795845757798 & 0.779591691515597 & 0.610204154242202 \tabularnewline
18 & 0.284967720196960 & 0.569935440393921 & 0.71503227980304 \tabularnewline
19 & 0.463585088333979 & 0.927170176667957 & 0.536414911666021 \tabularnewline
20 & 0.345186358345715 & 0.69037271669143 & 0.654813641654285 \tabularnewline
21 & 0.781373830157016 & 0.437252339685968 & 0.218626169842984 \tabularnewline
22 & 0.704886627253679 & 0.590226745492642 & 0.295113372746321 \tabularnewline
23 & 0.649876198640993 & 0.700247602718013 & 0.350123801359007 \tabularnewline
24 & 0.652358730631309 & 0.695282538737383 & 0.347641269368691 \tabularnewline
25 & 0.56962651514332 & 0.86074696971336 & 0.43037348485668 \tabularnewline
26 & 0.705078012925797 & 0.589843974148406 & 0.294921987074203 \tabularnewline
27 & 0.668281441578158 & 0.663437116843685 & 0.331718558421842 \tabularnewline
28 & 0.696391261764448 & 0.607217476471104 & 0.303608738235552 \tabularnewline
29 & 0.612418219039953 & 0.775163561920095 & 0.387581780960047 \tabularnewline
30 & 0.756392854043642 & 0.487214291912717 & 0.243607145956358 \tabularnewline
31 & 0.704575685542324 & 0.590848628915351 & 0.295424314457676 \tabularnewline
32 & 0.694255067648684 & 0.611489864702633 & 0.305744932351316 \tabularnewline
33 & 0.897561076075207 & 0.204877847849586 & 0.102438923924793 \tabularnewline
34 & 0.840486365284154 & 0.319027269431692 & 0.159513634715846 \tabularnewline
35 & 0.824233129634122 & 0.351533740731755 & 0.175766870365878 \tabularnewline
36 & 0.942451523328138 & 0.115096953343723 & 0.0575484766718617 \tabularnewline
37 & 0.900720116254906 & 0.198559767490188 & 0.0992798837450942 \tabularnewline
38 & 0.84164291648119 & 0.316714167037621 & 0.158357083518810 \tabularnewline
39 & 0.760610798707863 & 0.478778402584273 & 0.239389201292137 \tabularnewline
40 & 0.682366302026535 & 0.63526739594693 & 0.317633697973465 \tabularnewline
41 & 0.564571212117743 & 0.870857575764514 & 0.435428787882257 \tabularnewline
42 & 0.473624382985058 & 0.947248765970117 & 0.526375617014942 \tabularnewline
43 & 0.614279227124504 & 0.771441545750993 & 0.385720772875496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=5

[TABLE]
[ROW][C]Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]p-values[/C][C]Alternative Hypothesis[/C][/ROW]
[ROW][C]breakpoint index[/C][C]greater[/C][C]2-sided[/C][C]less[/C][/ROW]
[ROW][C]17[/C][C]0.389795845757798[/C][C]0.779591691515597[/C][C]0.610204154242202[/C][/ROW]
[ROW][C]18[/C][C]0.284967720196960[/C][C]0.569935440393921[/C][C]0.71503227980304[/C][/ROW]
[ROW][C]19[/C][C]0.463585088333979[/C][C]0.927170176667957[/C][C]0.536414911666021[/C][/ROW]
[ROW][C]20[/C][C]0.345186358345715[/C][C]0.69037271669143[/C][C]0.654813641654285[/C][/ROW]
[ROW][C]21[/C][C]0.781373830157016[/C][C]0.437252339685968[/C][C]0.218626169842984[/C][/ROW]
[ROW][C]22[/C][C]0.704886627253679[/C][C]0.590226745492642[/C][C]0.295113372746321[/C][/ROW]
[ROW][C]23[/C][C]0.649876198640993[/C][C]0.700247602718013[/C][C]0.350123801359007[/C][/ROW]
[ROW][C]24[/C][C]0.652358730631309[/C][C]0.695282538737383[/C][C]0.347641269368691[/C][/ROW]
[ROW][C]25[/C][C]0.56962651514332[/C][C]0.86074696971336[/C][C]0.43037348485668[/C][/ROW]
[ROW][C]26[/C][C]0.705078012925797[/C][C]0.589843974148406[/C][C]0.294921987074203[/C][/ROW]
[ROW][C]27[/C][C]0.668281441578158[/C][C]0.663437116843685[/C][C]0.331718558421842[/C][/ROW]
[ROW][C]28[/C][C]0.696391261764448[/C][C]0.607217476471104[/C][C]0.303608738235552[/C][/ROW]
[ROW][C]29[/C][C]0.612418219039953[/C][C]0.775163561920095[/C][C]0.387581780960047[/C][/ROW]
[ROW][C]30[/C][C]0.756392854043642[/C][C]0.487214291912717[/C][C]0.243607145956358[/C][/ROW]
[ROW][C]31[/C][C]0.704575685542324[/C][C]0.590848628915351[/C][C]0.295424314457676[/C][/ROW]
[ROW][C]32[/C][C]0.694255067648684[/C][C]0.611489864702633[/C][C]0.305744932351316[/C][/ROW]
[ROW][C]33[/C][C]0.897561076075207[/C][C]0.204877847849586[/C][C]0.102438923924793[/C][/ROW]
[ROW][C]34[/C][C]0.840486365284154[/C][C]0.319027269431692[/C][C]0.159513634715846[/C][/ROW]
[ROW][C]35[/C][C]0.824233129634122[/C][C]0.351533740731755[/C][C]0.175766870365878[/C][/ROW]
[ROW][C]36[/C][C]0.942451523328138[/C][C]0.115096953343723[/C][C]0.0575484766718617[/C][/ROW]
[ROW][C]37[/C][C]0.900720116254906[/C][C]0.198559767490188[/C][C]0.0992798837450942[/C][/ROW]
[ROW][C]38[/C][C]0.84164291648119[/C][C]0.316714167037621[/C][C]0.158357083518810[/C][/ROW]
[ROW][C]39[/C][C]0.760610798707863[/C][C]0.478778402584273[/C][C]0.239389201292137[/C][/ROW]
[ROW][C]40[/C][C]0.682366302026535[/C][C]0.63526739594693[/C][C]0.317633697973465[/C][/ROW]
[ROW][C]41[/C][C]0.564571212117743[/C][C]0.870857575764514[/C][C]0.435428787882257[/C][/ROW]
[ROW][C]42[/C][C]0.473624382985058[/C][C]0.947248765970117[/C][C]0.526375617014942[/C][/ROW]
[ROW][C]43[/C][C]0.614279227124504[/C][C]0.771441545750993[/C][C]0.385720772875496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=5

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=5

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Goldfeld-Quandt test for Heteroskedasticity
p-values	Alternative Hypothesis
breakpoint index	greater	2-sided	less
17	0.389795845757798	0.779591691515597	0.610204154242202
18	0.284967720196960	0.569935440393921	0.71503227980304
19	0.463585088333979	0.927170176667957	0.536414911666021
20	0.345186358345715	0.69037271669143	0.654813641654285
21	0.781373830157016	0.437252339685968	0.218626169842984
22	0.704886627253679	0.590226745492642	0.295113372746321
23	0.649876198640993	0.700247602718013	0.350123801359007
24	0.652358730631309	0.695282538737383	0.347641269368691
25	0.56962651514332	0.86074696971336	0.43037348485668
26	0.705078012925797	0.589843974148406	0.294921987074203
27	0.668281441578158	0.663437116843685	0.331718558421842
28	0.696391261764448	0.607217476471104	0.303608738235552
29	0.612418219039953	0.775163561920095	0.387581780960047
30	0.756392854043642	0.487214291912717	0.243607145956358
31	0.704575685542324	0.590848628915351	0.295424314457676
32	0.694255067648684	0.611489864702633	0.305744932351316
33	0.897561076075207	0.204877847849586	0.102438923924793
34	0.840486365284154	0.319027269431692	0.159513634715846
35	0.824233129634122	0.351533740731755	0.175766870365878
36	0.942451523328138	0.115096953343723	0.0575484766718617
37	0.900720116254906	0.198559767490188	0.0992798837450942
38	0.84164291648119	0.316714167037621	0.158357083518810
39	0.760610798707863	0.478778402584273	0.239389201292137
40	0.682366302026535	0.63526739594693	0.317633697973465
41	0.564571212117743	0.870857575764514	0.435428787882257
42	0.473624382985058	0.947248765970117	0.526375617014942
43	0.614279227124504	0.771441545750993	0.385720772875496

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

\begin{tabular}{lllllllll}
\hline
Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity \tabularnewline
Description & # significant tests & % significant tests & OK/NOK \tabularnewline
1% type I error level & 0 & 0 & OK \tabularnewline
5% type I error level & 0 & 0 & OK \tabularnewline
10% type I error level & 0 & 0 & OK \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59015&T=6

[TABLE]
[ROW][C]Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity[/C][/ROW]
[ROW][C]Description[/C][C]# significant tests[/C][C]% significant tests[/C][C]OK/NOK[/C][/ROW]
[ROW][C]1% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]5% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[ROW][C]10% type I error level[/C][C]0[/C][C]0[/C][C]OK[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59015&T=6

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59015&T=6

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description	# significant tests	% significant tests	OK/NOK
1% type I error level	0	0	OK
5% type I error level	0	0	OK
10% type I error level	0	0	OK

Figure 1

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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PDF link

Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT
H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation
Forecast', 1, TRUE)
a<-table.element(a, 'Residuals
Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code