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*Unverified author*

R Software Module

rwasp_multipleregression.wasp

Title produced by software

Multiple Regression

Date of computation

Tue, 20 Nov 2007 12:06:45 -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/2007/Nov/20/t1195585220jalwtyy8k7jmvlw.htm/, Retrieved Sun, 05 May 2024 13:00:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5806, Retrieved Sun, 05 May 2024 13:00:12 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

paper, multiple regression

Estimated Impact

243

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

-       [Multiple Regression] [Q3,W6, multiple r...] [2007-11-20 19:06:45] [bd7b8d7754bcf95ad80b21f541dc6b78] [Current]

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Dataseries X:

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88,74	88,95
88,92	88,81
88,77	88,9
89,17	90,15
89,61	90,92
89,52	90,78
89,74	90,81
89,4	89,46
89,36	89,22
89,38	88,89
89,36	89,41
89,29	89,59
89,59	90,25
89,79	90,2
89,86	90,27
90,21	90,71
90,37	91,18
90,19	90,66
90,33	89,72
90,22	88,72
90,42	88,91
90,54	89,15
90,73	89,15
91,02	89,08
91,19	89,28
91,53	89,47
91,88	89,53
92,06	90,72
92,32	90,91
92,67	91,38
92,85	91,49
92,82	90,9
93,46	90,93
93,23	90,57
93,54	91,28
93,29	90,83
93,2	91,5
93,6	91,58
93,81	92,49
94,62	94,16
95,22	95,46
95,38	95,8
95,31	95,32
95,3	95,41
95,57	95,35
95,42	95,68
95,53	95,59
95,33	94,96
95.90	96.92
96.06	96.06
96.31	96.59
96.34	96.67
96.49	97.27
96.22	96.38
96.53	96.47
96.50	96.05
96.77	96.76
96.66	96.51
96.58	96.55
96.63	95.97
97.06	97.00
97.73	97.46
98.01	97.90
97.76	98.42
97.49	98.54
97.77	99.00
97.96	98.94
98.23	99.02
98.51	100.07
98.19	98.72
98.37	98.73
98.31	98.04
98.60	99.08
98.97	99.22
99.11	99.57
99.64	100.44
100.03	100.84
99.98	100.75
100.32	100.49
100.44	99.98
100.51	99.96
101.00	99.76
100.88	100.11
100.55	99.79
100.83	100.29
101.51	101.12
102.16	102.65
102.39	102.71
102.54	103.39
102.85	102.80
103.47	102.07
103.57	102.15
103.69	101.21
103.50	101.27
103.47	101.86
103.45	101.65
103.48	101.94
103.93	102.62
103.89	102.71
104.40	103.39
104.79	104.51
104.77	104.09
105.13	104.29
105.26	104.57
104.96	105.39
104.75	105.15
105.01	106.13
105.15	105.46
105.20	106.47
105.77	106.62
105.78	106.52
106.26	108.04
106.13	107.15
106.12	107.32
106.57	107.76
106.44	107.26
106.54	107.89

Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5806&T=0

[TABLE]
[ROW][C]Summary of compuational 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]4 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=5806&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5806&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Multiple Linear Regression - Estimated Regression Equation
Y[t] = + 71.192346155451 + 0.189215809505315X[t] + 0.130691870654899t + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
Y[t] =  +  71.192346155451 +  0.189215809505315X[t] +  0.130691870654899t  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5806&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]Y[t] =  +  71.192346155451 +  0.189215809505315X[t] +  0.130691870654899t  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5806&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5806&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
Y[t] = + 71.192346155451 + 0.189215809505315X[t] + 0.130691870654899t + 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)	71.192346155451	3.104658	22.9308	0	0
X	0.189215809505315	0.035615	5.3129	1e-06	0
t	0.130691870654899	0.006099	21.4278	0	0

\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) & 71.192346155451 & 3.104658 & 22.9308 & 0 & 0 \tabularnewline
X & 0.189215809505315 & 0.035615 & 5.3129 & 1e-06 & 0 \tabularnewline
t & 0.130691870654899 & 0.006099 & 21.4278 & 0 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5806&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]71.192346155451[/C][C]3.104658[/C][C]22.9308[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]X[/C][C]0.189215809505315[/C][C]0.035615[/C][C]5.3129[/C][C]1e-06[/C][C]0[/C][/ROW]
[ROW][C]t[/C][C]0.130691870654899[/C][C]0.006099[/C][C]21.4278[/C][C]0[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5806&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5806&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)	71.192346155451	3.104658	22.9308	0	0
X	0.189215809505315	0.035615	5.3129	1e-06	0
t	0.130691870654899	0.006099	21.4278	0	0

Multiple Linear Regression - Regression Statistics
Multiple R	0.996691571344112
R-squared	0.993394088388395
Adjusted R-squared	0.993278195202227
F-TEST (value)	8571.63497898886
F-TEST (DF numerator)	2
F-TEST (DF denominator)	114
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.453540662683154
Sum Squared Residuals	23.4497011286064

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.996691571344112 \tabularnewline
R-squared & 0.993394088388395 \tabularnewline
Adjusted R-squared & 0.993278195202227 \tabularnewline
F-TEST (value) & 8571.63497898886 \tabularnewline
F-TEST (DF numerator) & 2 \tabularnewline
F-TEST (DF denominator) & 114 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 0.453540662683154 \tabularnewline
Sum Squared Residuals & 23.4497011286064 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5806&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.996691571344112[/C][/ROW]
[ROW][C]R-squared[/C][C]0.993394088388395[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.993278195202227[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]8571.63497898886[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]2[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]114[/C][/ROW]
[ROW][C]p-value[/C][C]0[/C][/ROW]
[ROW][C]Multiple Linear Regression - Residual Statistics[/C][/ROW]
[ROW][C]Residual Standard Deviation[/C][C]0.453540662683154[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]23.4497011286064[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5806&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5806&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	0.996691571344112
R-squared	0.993394088388395
Adjusted R-squared	0.993278195202227
F-TEST (value)	8571.63497898886
F-TEST (DF numerator)	2
F-TEST (DF denominator)	114
p-value	0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation	0.453540662683154
Sum Squared Residuals	23.4497011286064

Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or Index	Actuals	InterpolationForecast	ResidualsPrediction Error
1	88.74	88.1537842816038	0.586215718396221
2	88.92	88.2579859389278	0.662014061072154
3	88.77	88.4057072324382	0.364292767561744
4	89.17	88.7729188649748	0.397081135025204
5	89.61	89.0493069089488	0.560693091051211
6	89.52	89.153508566273	0.366491433727052
7	89.74	89.289876911213	0.450123088786993
8	89.4	89.1651274390357	0.234872560964283
9	89.36	89.2504075154093	0.109592484590652
10	89.38	89.3186581689275	0.0613418310725031
11	89.36	89.5477422605252	-0.187742260525154
12	89.29	89.712492976891	-0.422492976891004
13	89.59	89.9680672818194	-0.378067281819413
14	89.79	90.089298361999	-0.299298361999043
15	89.86	90.2332353393193	-0.37323533931932
16	90.21	90.4471821661566	-0.237182166156562
17	90.37	90.666805467279	-0.296805467278951
18	90.19	90.6991051169911	-0.50910511699109
19	90.33	90.651934126711	-0.321934126710993
20	90.22	90.5934101878606	-0.373410187860576
21	90.42	90.7600530623215	-0.34005306232148
22	90.54	90.9361567272577	-0.396156727257652
23	90.73	91.0668485979126	-0.336848597912553
24	91.02	91.1842953619021	-0.164295361902086
25	91.19	91.352830394458	-0.162830394458047
26	91.53	91.519473268919	0.0105267310810493
27	91.88	91.6615180881442	0.218481911855825
28	92.06	92.0173767721104	0.0426232278896090
29	92.32	92.1840196465713	0.135980353428692
30	92.67	92.4036429476937	0.266357052306304
31	92.85	92.5551485573942	0.294851442605812
32	92.82	92.574203100441	0.245796899559047
33	93.46	92.710571445381	0.749428554618989
34	93.23	92.773145624614	0.456854375386017
35	93.54	93.0381807200177	0.501819279982345
36	93.29	93.0837254763952	0.206274523604838
37	93.2	93.3411919394186	-0.141191939418625
38	93.6	93.487021074834	0.112978925166043
39	93.81	93.7898993321387	0.0201006678613164
40	94.62	94.2365816046675	0.383418395332543
41	95.22	94.6132540276793	0.606745972320729
42	95.38	94.808279273566	0.57172072643402
43	95.31	94.8481475556583	0.461852444341679
44	95.3	94.9958688491687	0.304131150831297
45	95.57	95.1152077712533	0.454792228746713
46	95.42	95.308340859045	0.111659140955067
47	95.53	95.4220033068444	0.107996693155647
48	95.33	95.433489217511	-0.103489217510904
49	95.9	95.9350440747962	-0.0350440747962152
50	96.06	95.9030103492765	0.156989650723454
51	96.31	96.1339865989693	0.176013401030738
52	96.34	96.2798157343846	0.0601842656154157
53	96.49	96.5240370907427	-0.0340370907426796
54	96.22	96.4863268909378	-0.266326890937844
55	96.53	96.6340481844482	-0.104048184448219
56	96.5	96.685269415111	-0.185269415110886
57	96.77	96.9503045105146	-0.180304510514564
58	96.66	97.0336924287931	-0.373692428793133
59	96.58	97.1719529318282	-0.591952931828241
60	96.63	97.19289963297	-0.56289963297006
61	97.06	97.5184837874154	-0.458483787415427
62	97.73	97.7362149304428	-0.00621493044276782
63	98.01	97.95016175728	0.0598382427199937
64	97.76	98.1792458488777	-0.419245848877668
65	97.49	98.3326436166732	-0.842643616673216
66	97.77	98.5503747597006	-0.780374759700557
67	97.96	98.6697136817851	-0.709713681785139
68	98.23	98.8155428172005	-0.585542817200452
69	98.51	99.144911287836	-0.63491128783593
70	98.19	99.0201618156587	-0.830161815658661
71	98.37	99.1527458444086	-0.782745844408607
72	98.31	99.1528788065048	-0.842878806504841
73	98.6	99.4803551190453	-0.880355119045274
74	98.97	99.637537203031	-0.667537203030912
75	99.11	99.8344546070127	-0.72445460701267
76	99.64	100.129764231937	-0.489764231937193
77	100.03	100.336142426394	-0.306142426394218
78	99.98	100.449804874194	-0.469804874193634
79	100.32	100.531300634377	-0.211300634377161
80	100.44	100.565492442184	-0.125492442184346
81	100.51	100.692399996649	-0.182399996649129
82	101	100.785248705403	0.214751294597028
83	100.88	100.982166109385	-0.102166109384734
84	100.55	101.052308920998	-0.502308920997932
85	100.83	101.277608696405	-0.447608696405487
86	101.51	101.565349688950	-0.0553496889497899
87	102.16	101.985541748148	0.174458251852170
88	102.39	102.127586567373	0.262413432626959
89	102.54	102.386945188492	0.15305481150845
90	102.85	102.405999731538	0.444000268461676
91	103.47	102.398564061254	1.07143593874566
92	103.57	102.544393196670	1.02560680333033
93	103.69	102.497222206390	1.19277779361044
94	103.5	102.639267025615	0.86073297438522
95	103.47	102.881596223878	0.588403776122183
96	103.45	102.972552774537	0.477447225463404
97	103.48	103.158117229948	0.321882770051967
98	103.93	103.417475851067	0.512524148933455
99	103.89	103.565197144577	0.324802855423074
100	104.4	103.824555765695	0.575444234304564
101	104.79	104.167169342996	0.622830657003712
102	104.77	104.218390573659	0.551609426341036
103	105.13	104.386925606215	0.743074393785074
104	105.26	104.570597903531	0.689402096468699
105	104.96	104.856446737981	0.103553262019429
106	104.75	104.941726814354	-0.191726814354188
107	105.01	105.257850178324	-0.247850178324289
108	105.15	105.261767456611	-0.111767456610626
109	105.2	105.583567294866	-0.383567294865896
110	105.77	105.742641536947	0.0273584630534
111	105.78	105.854411826651	-0.0744118266509604
112	106.26	106.272711727754	-0.0127117277539372
113	106.13	106.235001527949	-0.105001527949114
114	106.12	106.397860086220	-0.277860086219905
115	106.57	106.611806913057	-0.0418069130571564
116	106.44	106.647890878959	-0.207890878959393
117	106.54	106.897788709603	-0.35778870960263

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 88.74 & 88.1537842816038 & 0.586215718396221 \tabularnewline
2 & 88.92 & 88.2579859389278 & 0.662014061072154 \tabularnewline
3 & 88.77 & 88.4057072324382 & 0.364292767561744 \tabularnewline
4 & 89.17 & 88.7729188649748 & 0.397081135025204 \tabularnewline
5 & 89.61 & 89.0493069089488 & 0.560693091051211 \tabularnewline
6 & 89.52 & 89.153508566273 & 0.366491433727052 \tabularnewline
7 & 89.74 & 89.289876911213 & 0.450123088786993 \tabularnewline
8 & 89.4 & 89.1651274390357 & 0.234872560964283 \tabularnewline
9 & 89.36 & 89.2504075154093 & 0.109592484590652 \tabularnewline
10 & 89.38 & 89.3186581689275 & 0.0613418310725031 \tabularnewline
11 & 89.36 & 89.5477422605252 & -0.187742260525154 \tabularnewline
12 & 89.29 & 89.712492976891 & -0.422492976891004 \tabularnewline
13 & 89.59 & 89.9680672818194 & -0.378067281819413 \tabularnewline
14 & 89.79 & 90.089298361999 & -0.299298361999043 \tabularnewline
15 & 89.86 & 90.2332353393193 & -0.37323533931932 \tabularnewline
16 & 90.21 & 90.4471821661566 & -0.237182166156562 \tabularnewline
17 & 90.37 & 90.666805467279 & -0.296805467278951 \tabularnewline
18 & 90.19 & 90.6991051169911 & -0.50910511699109 \tabularnewline
19 & 90.33 & 90.651934126711 & -0.321934126710993 \tabularnewline
20 & 90.22 & 90.5934101878606 & -0.373410187860576 \tabularnewline
21 & 90.42 & 90.7600530623215 & -0.34005306232148 \tabularnewline
22 & 90.54 & 90.9361567272577 & -0.396156727257652 \tabularnewline
23 & 90.73 & 91.0668485979126 & -0.336848597912553 \tabularnewline
24 & 91.02 & 91.1842953619021 & -0.164295361902086 \tabularnewline
25 & 91.19 & 91.352830394458 & -0.162830394458047 \tabularnewline
26 & 91.53 & 91.519473268919 & 0.0105267310810493 \tabularnewline
27 & 91.88 & 91.6615180881442 & 0.218481911855825 \tabularnewline
28 & 92.06 & 92.0173767721104 & 0.0426232278896090 \tabularnewline
29 & 92.32 & 92.1840196465713 & 0.135980353428692 \tabularnewline
30 & 92.67 & 92.4036429476937 & 0.266357052306304 \tabularnewline
31 & 92.85 & 92.5551485573942 & 0.294851442605812 \tabularnewline
32 & 92.82 & 92.574203100441 & 0.245796899559047 \tabularnewline
33 & 93.46 & 92.710571445381 & 0.749428554618989 \tabularnewline
34 & 93.23 & 92.773145624614 & 0.456854375386017 \tabularnewline
35 & 93.54 & 93.0381807200177 & 0.501819279982345 \tabularnewline
36 & 93.29 & 93.0837254763952 & 0.206274523604838 \tabularnewline
37 & 93.2 & 93.3411919394186 & -0.141191939418625 \tabularnewline
38 & 93.6 & 93.487021074834 & 0.112978925166043 \tabularnewline
39 & 93.81 & 93.7898993321387 & 0.0201006678613164 \tabularnewline
40 & 94.62 & 94.2365816046675 & 0.383418395332543 \tabularnewline
41 & 95.22 & 94.6132540276793 & 0.606745972320729 \tabularnewline
42 & 95.38 & 94.808279273566 & 0.57172072643402 \tabularnewline
43 & 95.31 & 94.8481475556583 & 0.461852444341679 \tabularnewline
44 & 95.3 & 94.9958688491687 & 0.304131150831297 \tabularnewline
45 & 95.57 & 95.1152077712533 & 0.454792228746713 \tabularnewline
46 & 95.42 & 95.308340859045 & 0.111659140955067 \tabularnewline
47 & 95.53 & 95.4220033068444 & 0.107996693155647 \tabularnewline
48 & 95.33 & 95.433489217511 & -0.103489217510904 \tabularnewline
49 & 95.9 & 95.9350440747962 & -0.0350440747962152 \tabularnewline
50 & 96.06 & 95.9030103492765 & 0.156989650723454 \tabularnewline
51 & 96.31 & 96.1339865989693 & 0.176013401030738 \tabularnewline
52 & 96.34 & 96.2798157343846 & 0.0601842656154157 \tabularnewline
53 & 96.49 & 96.5240370907427 & -0.0340370907426796 \tabularnewline
54 & 96.22 & 96.4863268909378 & -0.266326890937844 \tabularnewline
55 & 96.53 & 96.6340481844482 & -0.104048184448219 \tabularnewline
56 & 96.5 & 96.685269415111 & -0.185269415110886 \tabularnewline
57 & 96.77 & 96.9503045105146 & -0.180304510514564 \tabularnewline
58 & 96.66 & 97.0336924287931 & -0.373692428793133 \tabularnewline
59 & 96.58 & 97.1719529318282 & -0.591952931828241 \tabularnewline
60 & 96.63 & 97.19289963297 & -0.56289963297006 \tabularnewline
61 & 97.06 & 97.5184837874154 & -0.458483787415427 \tabularnewline
62 & 97.73 & 97.7362149304428 & -0.00621493044276782 \tabularnewline
63 & 98.01 & 97.95016175728 & 0.0598382427199937 \tabularnewline
64 & 97.76 & 98.1792458488777 & -0.419245848877668 \tabularnewline
65 & 97.49 & 98.3326436166732 & -0.842643616673216 \tabularnewline
66 & 97.77 & 98.5503747597006 & -0.780374759700557 \tabularnewline
67 & 97.96 & 98.6697136817851 & -0.709713681785139 \tabularnewline
68 & 98.23 & 98.8155428172005 & -0.585542817200452 \tabularnewline
69 & 98.51 & 99.144911287836 & -0.63491128783593 \tabularnewline
70 & 98.19 & 99.0201618156587 & -0.830161815658661 \tabularnewline
71 & 98.37 & 99.1527458444086 & -0.782745844408607 \tabularnewline
72 & 98.31 & 99.1528788065048 & -0.842878806504841 \tabularnewline
73 & 98.6 & 99.4803551190453 & -0.880355119045274 \tabularnewline
74 & 98.97 & 99.637537203031 & -0.667537203030912 \tabularnewline
75 & 99.11 & 99.8344546070127 & -0.72445460701267 \tabularnewline
76 & 99.64 & 100.129764231937 & -0.489764231937193 \tabularnewline
77 & 100.03 & 100.336142426394 & -0.306142426394218 \tabularnewline
78 & 99.98 & 100.449804874194 & -0.469804874193634 \tabularnewline
79 & 100.32 & 100.531300634377 & -0.211300634377161 \tabularnewline
80 & 100.44 & 100.565492442184 & -0.125492442184346 \tabularnewline
81 & 100.51 & 100.692399996649 & -0.182399996649129 \tabularnewline
82 & 101 & 100.785248705403 & 0.214751294597028 \tabularnewline
83 & 100.88 & 100.982166109385 & -0.102166109384734 \tabularnewline
84 & 100.55 & 101.052308920998 & -0.502308920997932 \tabularnewline
85 & 100.83 & 101.277608696405 & -0.447608696405487 \tabularnewline
86 & 101.51 & 101.565349688950 & -0.0553496889497899 \tabularnewline
87 & 102.16 & 101.985541748148 & 0.174458251852170 \tabularnewline
88 & 102.39 & 102.127586567373 & 0.262413432626959 \tabularnewline
89 & 102.54 & 102.386945188492 & 0.15305481150845 \tabularnewline
90 & 102.85 & 102.405999731538 & 0.444000268461676 \tabularnewline
91 & 103.47 & 102.398564061254 & 1.07143593874566 \tabularnewline
92 & 103.57 & 102.544393196670 & 1.02560680333033 \tabularnewline
93 & 103.69 & 102.497222206390 & 1.19277779361044 \tabularnewline
94 & 103.5 & 102.639267025615 & 0.86073297438522 \tabularnewline
95 & 103.47 & 102.881596223878 & 0.588403776122183 \tabularnewline
96 & 103.45 & 102.972552774537 & 0.477447225463404 \tabularnewline
97 & 103.48 & 103.158117229948 & 0.321882770051967 \tabularnewline
98 & 103.93 & 103.417475851067 & 0.512524148933455 \tabularnewline
99 & 103.89 & 103.565197144577 & 0.324802855423074 \tabularnewline
100 & 104.4 & 103.824555765695 & 0.575444234304564 \tabularnewline
101 & 104.79 & 104.167169342996 & 0.622830657003712 \tabularnewline
102 & 104.77 & 104.218390573659 & 0.551609426341036 \tabularnewline
103 & 105.13 & 104.386925606215 & 0.743074393785074 \tabularnewline
104 & 105.26 & 104.570597903531 & 0.689402096468699 \tabularnewline
105 & 104.96 & 104.856446737981 & 0.103553262019429 \tabularnewline
106 & 104.75 & 104.941726814354 & -0.191726814354188 \tabularnewline
107 & 105.01 & 105.257850178324 & -0.247850178324289 \tabularnewline
108 & 105.15 & 105.261767456611 & -0.111767456610626 \tabularnewline
109 & 105.2 & 105.583567294866 & -0.383567294865896 \tabularnewline
110 & 105.77 & 105.742641536947 & 0.0273584630534 \tabularnewline
111 & 105.78 & 105.854411826651 & -0.0744118266509604 \tabularnewline
112 & 106.26 & 106.272711727754 & -0.0127117277539372 \tabularnewline
113 & 106.13 & 106.235001527949 & -0.105001527949114 \tabularnewline
114 & 106.12 & 106.397860086220 & -0.277860086219905 \tabularnewline
115 & 106.57 & 106.611806913057 & -0.0418069130571564 \tabularnewline
116 & 106.44 & 106.647890878959 & -0.207890878959393 \tabularnewline
117 & 106.54 & 106.897788709603 & -0.35778870960263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5806&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]88.74[/C][C]88.1537842816038[/C][C]0.586215718396221[/C][/ROW]
[ROW][C]2[/C][C]88.92[/C][C]88.2579859389278[/C][C]0.662014061072154[/C][/ROW]
[ROW][C]3[/C][C]88.77[/C][C]88.4057072324382[/C][C]0.364292767561744[/C][/ROW]
[ROW][C]4[/C][C]89.17[/C][C]88.7729188649748[/C][C]0.397081135025204[/C][/ROW]
[ROW][C]5[/C][C]89.61[/C][C]89.0493069089488[/C][C]0.560693091051211[/C][/ROW]
[ROW][C]6[/C][C]89.52[/C][C]89.153508566273[/C][C]0.366491433727052[/C][/ROW]
[ROW][C]7[/C][C]89.74[/C][C]89.289876911213[/C][C]0.450123088786993[/C][/ROW]
[ROW][C]8[/C][C]89.4[/C][C]89.1651274390357[/C][C]0.234872560964283[/C][/ROW]
[ROW][C]9[/C][C]89.36[/C][C]89.2504075154093[/C][C]0.109592484590652[/C][/ROW]
[ROW][C]10[/C][C]89.38[/C][C]89.3186581689275[/C][C]0.0613418310725031[/C][/ROW]
[ROW][C]11[/C][C]89.36[/C][C]89.5477422605252[/C][C]-0.187742260525154[/C][/ROW]
[ROW][C]12[/C][C]89.29[/C][C]89.712492976891[/C][C]-0.422492976891004[/C][/ROW]
[ROW][C]13[/C][C]89.59[/C][C]89.9680672818194[/C][C]-0.378067281819413[/C][/ROW]
[ROW][C]14[/C][C]89.79[/C][C]90.089298361999[/C][C]-0.299298361999043[/C][/ROW]
[ROW][C]15[/C][C]89.86[/C][C]90.2332353393193[/C][C]-0.37323533931932[/C][/ROW]
[ROW][C]16[/C][C]90.21[/C][C]90.4471821661566[/C][C]-0.237182166156562[/C][/ROW]
[ROW][C]17[/C][C]90.37[/C][C]90.666805467279[/C][C]-0.296805467278951[/C][/ROW]
[ROW][C]18[/C][C]90.19[/C][C]90.6991051169911[/C][C]-0.50910511699109[/C][/ROW]
[ROW][C]19[/C][C]90.33[/C][C]90.651934126711[/C][C]-0.321934126710993[/C][/ROW]
[ROW][C]20[/C][C]90.22[/C][C]90.5934101878606[/C][C]-0.373410187860576[/C][/ROW]
[ROW][C]21[/C][C]90.42[/C][C]90.7600530623215[/C][C]-0.34005306232148[/C][/ROW]
[ROW][C]22[/C][C]90.54[/C][C]90.9361567272577[/C][C]-0.396156727257652[/C][/ROW]
[ROW][C]23[/C][C]90.73[/C][C]91.0668485979126[/C][C]-0.336848597912553[/C][/ROW]
[ROW][C]24[/C][C]91.02[/C][C]91.1842953619021[/C][C]-0.164295361902086[/C][/ROW]
[ROW][C]25[/C][C]91.19[/C][C]91.352830394458[/C][C]-0.162830394458047[/C][/ROW]
[ROW][C]26[/C][C]91.53[/C][C]91.519473268919[/C][C]0.0105267310810493[/C][/ROW]
[ROW][C]27[/C][C]91.88[/C][C]91.6615180881442[/C][C]0.218481911855825[/C][/ROW]
[ROW][C]28[/C][C]92.06[/C][C]92.0173767721104[/C][C]0.0426232278896090[/C][/ROW]
[ROW][C]29[/C][C]92.32[/C][C]92.1840196465713[/C][C]0.135980353428692[/C][/ROW]
[ROW][C]30[/C][C]92.67[/C][C]92.4036429476937[/C][C]0.266357052306304[/C][/ROW]
[ROW][C]31[/C][C]92.85[/C][C]92.5551485573942[/C][C]0.294851442605812[/C][/ROW]
[ROW][C]32[/C][C]92.82[/C][C]92.574203100441[/C][C]0.245796899559047[/C][/ROW]
[ROW][C]33[/C][C]93.46[/C][C]92.710571445381[/C][C]0.749428554618989[/C][/ROW]
[ROW][C]34[/C][C]93.23[/C][C]92.773145624614[/C][C]0.456854375386017[/C][/ROW]
[ROW][C]35[/C][C]93.54[/C][C]93.0381807200177[/C][C]0.501819279982345[/C][/ROW]
[ROW][C]36[/C][C]93.29[/C][C]93.0837254763952[/C][C]0.206274523604838[/C][/ROW]
[ROW][C]37[/C][C]93.2[/C][C]93.3411919394186[/C][C]-0.141191939418625[/C][/ROW]
[ROW][C]38[/C][C]93.6[/C][C]93.487021074834[/C][C]0.112978925166043[/C][/ROW]
[ROW][C]39[/C][C]93.81[/C][C]93.7898993321387[/C][C]0.0201006678613164[/C][/ROW]
[ROW][C]40[/C][C]94.62[/C][C]94.2365816046675[/C][C]0.383418395332543[/C][/ROW]
[ROW][C]41[/C][C]95.22[/C][C]94.6132540276793[/C][C]0.606745972320729[/C][/ROW]
[ROW][C]42[/C][C]95.38[/C][C]94.808279273566[/C][C]0.57172072643402[/C][/ROW]
[ROW][C]43[/C][C]95.31[/C][C]94.8481475556583[/C][C]0.461852444341679[/C][/ROW]
[ROW][C]44[/C][C]95.3[/C][C]94.9958688491687[/C][C]0.304131150831297[/C][/ROW]
[ROW][C]45[/C][C]95.57[/C][C]95.1152077712533[/C][C]0.454792228746713[/C][/ROW]
[ROW][C]46[/C][C]95.42[/C][C]95.308340859045[/C][C]0.111659140955067[/C][/ROW]
[ROW][C]47[/C][C]95.53[/C][C]95.4220033068444[/C][C]0.107996693155647[/C][/ROW]
[ROW][C]48[/C][C]95.33[/C][C]95.433489217511[/C][C]-0.103489217510904[/C][/ROW]
[ROW][C]49[/C][C]95.9[/C][C]95.9350440747962[/C][C]-0.0350440747962152[/C][/ROW]
[ROW][C]50[/C][C]96.06[/C][C]95.9030103492765[/C][C]0.156989650723454[/C][/ROW]
[ROW][C]51[/C][C]96.31[/C][C]96.1339865989693[/C][C]0.176013401030738[/C][/ROW]
[ROW][C]52[/C][C]96.34[/C][C]96.2798157343846[/C][C]0.0601842656154157[/C][/ROW]
[ROW][C]53[/C][C]96.49[/C][C]96.5240370907427[/C][C]-0.0340370907426796[/C][/ROW]
[ROW][C]54[/C][C]96.22[/C][C]96.4863268909378[/C][C]-0.266326890937844[/C][/ROW]
[ROW][C]55[/C][C]96.53[/C][C]96.6340481844482[/C][C]-0.104048184448219[/C][/ROW]
[ROW][C]56[/C][C]96.5[/C][C]96.685269415111[/C][C]-0.185269415110886[/C][/ROW]
[ROW][C]57[/C][C]96.77[/C][C]96.9503045105146[/C][C]-0.180304510514564[/C][/ROW]
[ROW][C]58[/C][C]96.66[/C][C]97.0336924287931[/C][C]-0.373692428793133[/C][/ROW]
[ROW][C]59[/C][C]96.58[/C][C]97.1719529318282[/C][C]-0.591952931828241[/C][/ROW]
[ROW][C]60[/C][C]96.63[/C][C]97.19289963297[/C][C]-0.56289963297006[/C][/ROW]
[ROW][C]61[/C][C]97.06[/C][C]97.5184837874154[/C][C]-0.458483787415427[/C][/ROW]
[ROW][C]62[/C][C]97.73[/C][C]97.7362149304428[/C][C]-0.00621493044276782[/C][/ROW]
[ROW][C]63[/C][C]98.01[/C][C]97.95016175728[/C][C]0.0598382427199937[/C][/ROW]
[ROW][C]64[/C][C]97.76[/C][C]98.1792458488777[/C][C]-0.419245848877668[/C][/ROW]
[ROW][C]65[/C][C]97.49[/C][C]98.3326436166732[/C][C]-0.842643616673216[/C][/ROW]
[ROW][C]66[/C][C]97.77[/C][C]98.5503747597006[/C][C]-0.780374759700557[/C][/ROW]
[ROW][C]67[/C][C]97.96[/C][C]98.6697136817851[/C][C]-0.709713681785139[/C][/ROW]
[ROW][C]68[/C][C]98.23[/C][C]98.8155428172005[/C][C]-0.585542817200452[/C][/ROW]
[ROW][C]69[/C][C]98.51[/C][C]99.144911287836[/C][C]-0.63491128783593[/C][/ROW]
[ROW][C]70[/C][C]98.19[/C][C]99.0201618156587[/C][C]-0.830161815658661[/C][/ROW]
[ROW][C]71[/C][C]98.37[/C][C]99.1527458444086[/C][C]-0.782745844408607[/C][/ROW]
[ROW][C]72[/C][C]98.31[/C][C]99.1528788065048[/C][C]-0.842878806504841[/C][/ROW]
[ROW][C]73[/C][C]98.6[/C][C]99.4803551190453[/C][C]-0.880355119045274[/C][/ROW]
[ROW][C]74[/C][C]98.97[/C][C]99.637537203031[/C][C]-0.667537203030912[/C][/ROW]
[ROW][C]75[/C][C]99.11[/C][C]99.8344546070127[/C][C]-0.72445460701267[/C][/ROW]
[ROW][C]76[/C][C]99.64[/C][C]100.129764231937[/C][C]-0.489764231937193[/C][/ROW]
[ROW][C]77[/C][C]100.03[/C][C]100.336142426394[/C][C]-0.306142426394218[/C][/ROW]
[ROW][C]78[/C][C]99.98[/C][C]100.449804874194[/C][C]-0.469804874193634[/C][/ROW]
[ROW][C]79[/C][C]100.32[/C][C]100.531300634377[/C][C]-0.211300634377161[/C][/ROW]
[ROW][C]80[/C][C]100.44[/C][C]100.565492442184[/C][C]-0.125492442184346[/C][/ROW]
[ROW][C]81[/C][C]100.51[/C][C]100.692399996649[/C][C]-0.182399996649129[/C][/ROW]
[ROW][C]82[/C][C]101[/C][C]100.785248705403[/C][C]0.214751294597028[/C][/ROW]
[ROW][C]83[/C][C]100.88[/C][C]100.982166109385[/C][C]-0.102166109384734[/C][/ROW]
[ROW][C]84[/C][C]100.55[/C][C]101.052308920998[/C][C]-0.502308920997932[/C][/ROW]
[ROW][C]85[/C][C]100.83[/C][C]101.277608696405[/C][C]-0.447608696405487[/C][/ROW]
[ROW][C]86[/C][C]101.51[/C][C]101.565349688950[/C][C]-0.0553496889497899[/C][/ROW]
[ROW][C]87[/C][C]102.16[/C][C]101.985541748148[/C][C]0.174458251852170[/C][/ROW]
[ROW][C]88[/C][C]102.39[/C][C]102.127586567373[/C][C]0.262413432626959[/C][/ROW]
[ROW][C]89[/C][C]102.54[/C][C]102.386945188492[/C][C]0.15305481150845[/C][/ROW]
[ROW][C]90[/C][C]102.85[/C][C]102.405999731538[/C][C]0.444000268461676[/C][/ROW]
[ROW][C]91[/C][C]103.47[/C][C]102.398564061254[/C][C]1.07143593874566[/C][/ROW]
[ROW][C]92[/C][C]103.57[/C][C]102.544393196670[/C][C]1.02560680333033[/C][/ROW]
[ROW][C]93[/C][C]103.69[/C][C]102.497222206390[/C][C]1.19277779361044[/C][/ROW]
[ROW][C]94[/C][C]103.5[/C][C]102.639267025615[/C][C]0.86073297438522[/C][/ROW]
[ROW][C]95[/C][C]103.47[/C][C]102.881596223878[/C][C]0.588403776122183[/C][/ROW]
[ROW][C]96[/C][C]103.45[/C][C]102.972552774537[/C][C]0.477447225463404[/C][/ROW]
[ROW][C]97[/C][C]103.48[/C][C]103.158117229948[/C][C]0.321882770051967[/C][/ROW]
[ROW][C]98[/C][C]103.93[/C][C]103.417475851067[/C][C]0.512524148933455[/C][/ROW]
[ROW][C]99[/C][C]103.89[/C][C]103.565197144577[/C][C]0.324802855423074[/C][/ROW]
[ROW][C]100[/C][C]104.4[/C][C]103.824555765695[/C][C]0.575444234304564[/C][/ROW]
[ROW][C]101[/C][C]104.79[/C][C]104.167169342996[/C][C]0.622830657003712[/C][/ROW]
[ROW][C]102[/C][C]104.77[/C][C]104.218390573659[/C][C]0.551609426341036[/C][/ROW]
[ROW][C]103[/C][C]105.13[/C][C]104.386925606215[/C][C]0.743074393785074[/C][/ROW]
[ROW][C]104[/C][C]105.26[/C][C]104.570597903531[/C][C]0.689402096468699[/C][/ROW]
[ROW][C]105[/C][C]104.96[/C][C]104.856446737981[/C][C]0.103553262019429[/C][/ROW]
[ROW][C]106[/C][C]104.75[/C][C]104.941726814354[/C][C]-0.191726814354188[/C][/ROW]
[ROW][C]107[/C][C]105.01[/C][C]105.257850178324[/C][C]-0.247850178324289[/C][/ROW]
[ROW][C]108[/C][C]105.15[/C][C]105.261767456611[/C][C]-0.111767456610626[/C][/ROW]
[ROW][C]109[/C][C]105.2[/C][C]105.583567294866[/C][C]-0.383567294865896[/C][/ROW]
[ROW][C]110[/C][C]105.77[/C][C]105.742641536947[/C][C]0.0273584630534[/C][/ROW]
[ROW][C]111[/C][C]105.78[/C][C]105.854411826651[/C][C]-0.0744118266509604[/C][/ROW]
[ROW][C]112[/C][C]106.26[/C][C]106.272711727754[/C][C]-0.0127117277539372[/C][/ROW]
[ROW][C]113[/C][C]106.13[/C][C]106.235001527949[/C][C]-0.105001527949114[/C][/ROW]
[ROW][C]114[/C][C]106.12[/C][C]106.397860086220[/C][C]-0.277860086219905[/C][/ROW]
[ROW][C]115[/C][C]106.57[/C][C]106.611806913057[/C][C]-0.0418069130571564[/C][/ROW]
[ROW][C]116[/C][C]106.44[/C][C]106.647890878959[/C][C]-0.207890878959393[/C][/ROW]
[ROW][C]117[/C][C]106.54[/C][C]106.897788709603[/C][C]-0.35778870960263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5806&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5806&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	88.74	88.1537842816038	0.586215718396221
2	88.92	88.2579859389278	0.662014061072154
3	88.77	88.4057072324382	0.364292767561744
4	89.17	88.7729188649748	0.397081135025204
5	89.61	89.0493069089488	0.560693091051211
6	89.52	89.153508566273	0.366491433727052
7	89.74	89.289876911213	0.450123088786993
8	89.4	89.1651274390357	0.234872560964283
9	89.36	89.2504075154093	0.109592484590652
10	89.38	89.3186581689275	0.0613418310725031
11	89.36	89.5477422605252	-0.187742260525154
12	89.29	89.712492976891	-0.422492976891004
13	89.59	89.9680672818194	-0.378067281819413
14	89.79	90.089298361999	-0.299298361999043
15	89.86	90.2332353393193	-0.37323533931932
16	90.21	90.4471821661566	-0.237182166156562
17	90.37	90.666805467279	-0.296805467278951
18	90.19	90.6991051169911	-0.50910511699109
19	90.33	90.651934126711	-0.321934126710993
20	90.22	90.5934101878606	-0.373410187860576
21	90.42	90.7600530623215	-0.34005306232148
22	90.54	90.9361567272577	-0.396156727257652
23	90.73	91.0668485979126	-0.336848597912553
24	91.02	91.1842953619021	-0.164295361902086
25	91.19	91.352830394458	-0.162830394458047
26	91.53	91.519473268919	0.0105267310810493
27	91.88	91.6615180881442	0.218481911855825
28	92.06	92.0173767721104	0.0426232278896090
29	92.32	92.1840196465713	0.135980353428692
30	92.67	92.4036429476937	0.266357052306304
31	92.85	92.5551485573942	0.294851442605812
32	92.82	92.574203100441	0.245796899559047
33	93.46	92.710571445381	0.749428554618989
34	93.23	92.773145624614	0.456854375386017
35	93.54	93.0381807200177	0.501819279982345
36	93.29	93.0837254763952	0.206274523604838
37	93.2	93.3411919394186	-0.141191939418625
38	93.6	93.487021074834	0.112978925166043
39	93.81	93.7898993321387	0.0201006678613164
40	94.62	94.2365816046675	0.383418395332543
41	95.22	94.6132540276793	0.606745972320729
42	95.38	94.808279273566	0.57172072643402
43	95.31	94.8481475556583	0.461852444341679
44	95.3	94.9958688491687	0.304131150831297
45	95.57	95.1152077712533	0.454792228746713
46	95.42	95.308340859045	0.111659140955067
47	95.53	95.4220033068444	0.107996693155647
48	95.33	95.433489217511	-0.103489217510904
49	95.9	95.9350440747962	-0.0350440747962152
50	96.06	95.9030103492765	0.156989650723454
51	96.31	96.1339865989693	0.176013401030738
52	96.34	96.2798157343846	0.0601842656154157
53	96.49	96.5240370907427	-0.0340370907426796
54	96.22	96.4863268909378	-0.266326890937844
55	96.53	96.6340481844482	-0.104048184448219
56	96.5	96.685269415111	-0.185269415110886
57	96.77	96.9503045105146	-0.180304510514564
58	96.66	97.0336924287931	-0.373692428793133
59	96.58	97.1719529318282	-0.591952931828241
60	96.63	97.19289963297	-0.56289963297006
61	97.06	97.5184837874154	-0.458483787415427
62	97.73	97.7362149304428	-0.00621493044276782
63	98.01	97.95016175728	0.0598382427199937
64	97.76	98.1792458488777	-0.419245848877668
65	97.49	98.3326436166732	-0.842643616673216
66	97.77	98.5503747597006	-0.780374759700557
67	97.96	98.6697136817851	-0.709713681785139
68	98.23	98.8155428172005	-0.585542817200452
69	98.51	99.144911287836	-0.63491128783593
70	98.19	99.0201618156587	-0.830161815658661
71	98.37	99.1527458444086	-0.782745844408607
72	98.31	99.1528788065048	-0.842878806504841
73	98.6	99.4803551190453	-0.880355119045274
74	98.97	99.637537203031	-0.667537203030912
75	99.11	99.8344546070127	-0.72445460701267
76	99.64	100.129764231937	-0.489764231937193
77	100.03	100.336142426394	-0.306142426394218
78	99.98	100.449804874194	-0.469804874193634
79	100.32	100.531300634377	-0.211300634377161
80	100.44	100.565492442184	-0.125492442184346
81	100.51	100.692399996649	-0.182399996649129
82	101	100.785248705403	0.214751294597028
83	100.88	100.982166109385	-0.102166109384734
84	100.55	101.052308920998	-0.502308920997932
85	100.83	101.277608696405	-0.447608696405487
86	101.51	101.565349688950	-0.0553496889497899
87	102.16	101.985541748148	0.174458251852170
88	102.39	102.127586567373	0.262413432626959
89	102.54	102.386945188492	0.15305481150845
90	102.85	102.405999731538	0.444000268461676
91	103.47	102.398564061254	1.07143593874566
92	103.57	102.544393196670	1.02560680333033
93	103.69	102.497222206390	1.19277779361044
94	103.5	102.639267025615	0.86073297438522
95	103.47	102.881596223878	0.588403776122183
96	103.45	102.972552774537	0.477447225463404
97	103.48	103.158117229948	0.321882770051967
98	103.93	103.417475851067	0.512524148933455
99	103.89	103.565197144577	0.324802855423074
100	104.4	103.824555765695	0.575444234304564
101	104.79	104.167169342996	0.622830657003712
102	104.77	104.218390573659	0.551609426341036
103	105.13	104.386925606215	0.743074393785074
104	105.26	104.570597903531	0.689402096468699
105	104.96	104.856446737981	0.103553262019429
106	104.75	104.941726814354	-0.191726814354188
107	105.01	105.257850178324	-0.247850178324289
108	105.15	105.261767456611	-0.111767456610626
109	105.2	105.583567294866	-0.383567294865896
110	105.77	105.742641536947	0.0273584630534
111	105.78	105.854411826651	-0.0744118266509604
112	106.26	106.272711727754	-0.0127117277539372
113	106.13	106.235001527949	-0.105001527949114
114	106.12	106.397860086220	-0.277860086219905
115	106.57	106.611806913057	-0.0418069130571564
116	106.44	106.647890878959	-0.207890878959393
117	106.54	106.897788709603	-0.35778870960263

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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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

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

library(lattice)
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))
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$resid, main='Residual Normal Q-Q Plot')
grid()
dev.off()
(myerror <- as.ts(mysum$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()
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code