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Author*Unverified author*
R Software Modulerwasp_multipleregression.wasp
Title produced by softwareMultiple Regression
Date of computationFri, 16 Nov 2007 09:33:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/16/t1195230571jh907c36pq2mpa6.htm/, Retrieved Mon, 06 May 2024 05:10:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5500, Retrieved Mon, 06 May 2024 05:10:06 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact257
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Multiple Regression] [Paper 20] [2007-11-16 16:33:57] [640491d00f3c9cca22cbf779aa38ac16] [Current]
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Dataseries X:
100,70	99,20	100,80	99,20	101,30	99,80
97,90	95,80	100,80	98,10	97,60	103,50
96,50	93,80	100,80	96,10	96,40	103,10
96,60	94,40	90,10	95,50	97,00	105,60
96,60	94,80	95,70	95,70	96,40	105,70
95,50	96,90	88,60	95,90	94,70	106,60
91,80	93,10	93,30	96,20	89,30	107,00
89,30	92,20	93,30	95,70	85,90	105,20
87,00	90,80	93,30	93,40	83,30	105,70
85,90	92,40	93,30	93,40	81,50	105,00
88,00	91,20	93,30	91,90	85,00	105,10
87,90	89,80	93,30	92,80	84,80	105,90
89,20	85,80	88,60	93,20	87,50	105,30
90,90	88,20	97,40	93,80	89,00	104,90
91,60	89,90	97,40	93,80	90,00	103,20
90,20	91,80	102,90	85,10	89,60	103,40
89,10	93,40	102,90	86,10	87,40	104,40
87,50	93,80	102,90	86,50	84,80	104,50
86,30	95,00	105,10	90,00	81,90	105,90
86,00	97,30	105,10	89,10	81,10	110,60
84,40	95,30	105,10	88,40	79,10	112,40
86,10	97,90	105,10	91,40	80,50	111,80
91,00	97,00	105,10	88,00	88,50	111,00
92,70	97,00	105,10	87,80	90,90	111,00
88,00	65,20	96,90	87,40	84,90	109,10
84,30	64,10	96,90	86,20	80,00	107,80
82,20	65,60	96,90	87,80	76,50	107,20
80,80	66,50	96,90	84,60	75,40	108,40
79,40	65,60	96,90	85,00	73,50	107,50
80,20	66,10	96,90	85,70	74,30	106,40
82,20	65,90	96,50	83,90	77,70	106,20
82,20	65,80	96,50	83,60	77,90	104,90
81,20	64,10	96,50	82,60	76,70	106,20
82,10	63,50	96,00	84,90	77,20	107,60
88,10	64,40	96,00	84,20	86,00	107,00
88,50	66,00	96,00	83,80	86,90	104,50
92,10	67,70	96,00	84,20	92,00	105,10
98,60	70,40	96,00	84,40	101,70	104,70
100,90	74,10	96,00	86,00	104,50	103,70
100,60	75,50	105,80	89,70	101,70	104,90
101,10	80,80	105,80	93,90	100,60	105,90
102,10	83,90	105,80	98,40	100,30	106,10
103,60	83,60	105,80	98,30	102,50	106,10
102,80	88,70	105,80	99,30	101,00	106,80
108,30	87,00	105,80	100,50	108,60	106,40
104,00	86,90	105,80	96,90	103,40	107,80
106,10	88,60	105,80	97,50	106,40	107,60
106,30	88,60	105,80	97,50	106,60	107,60
109,00	86,90	123,60	98,90	108,90	108,40
111,00	86,10	142,20	99,30	110,50	109,50
113,70	86,60	142,20	100,60	114,00	109,20
112,70	83,90	141,20	99,90	112,80	109,10
110,30	84,20	141,20	98,80	109,60	110,00
114,50	83,20	141,20	98,60	116,00	109,00
119,30	78,40	124,70	98,20	124,60	109,00
121,80	77,60	124,70	96,30	129,00	111,90
125,40	77,10	124,70	103,40	131,50	109,30
129,70	76,80	122,70	102,70	138,60	112,10
129,40	76,80	122,70	102,70	138,10	112,10
134,50	76,80	122,70	102,60	146,30	112,50
141,20	76,80	123,30	101,60	157,60	113,60
141,40	78,70	123,30	100,90	158,40	112,90
152,20	78,70	123,30	101,10	176,30	114,00
167,70	78,70	127,20	105,60	199,90	116,10
173,30	78,70	127,20	104,70	210,40	116,50
168,70	78,70	127,20	103,80	202,60	117,10
172,60	83,70	140,00	105,40	207,10	117,10
169,80	83,70	140,00	105,60	202,00	117,10
172,00	87,90	140,00	109,20	203,40	116,50
179,40	87,90	140,00	109,50	216,30	116,50
174,60	84,50	140,00	110,10	207,30	116,30
172,50	84,50	140,00	110,00	203,50	116,50
172,60	84,40	139,00	110,30	204,40	119,20
176,30	87,50	139,00	109,30	203,70	118,60
178,90	89,20	139,00	110,20	205,70	117,50
179,60	88,90	147,00	113,00	208,00	117,10
179,90	88,80	147,00	113,60	209,30	117,60
180,30	89,50	147,00	111,20	208,70	118,30
180,90	90,40	147,10	111,30	206,50	118,60
177,70	87,90	147,10	115,00	204,50	116,70




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5500&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]3 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=5500&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5500&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Multiple Linear Regression - Estimated Regression Equation
TM[t] = -7.79895678054507 -0.0335405225086837EGKS[t] + 0.0994588527017785BUIZEN[t] + 0.338478881529632NEGKS[t] + 0.624837353466008NF[t] + 0.0535379228849357`GM `[t] + e[t]

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Estimated Regression Equation \tabularnewline
TM[t] =  -7.79895678054507 -0.0335405225086837EGKS[t] +  0.0994588527017785BUIZEN[t] +  0.338478881529632NEGKS[t] +  0.624837353466008NF[t] +  0.0535379228849357`GM
`[t]  + e[t] \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5500&T=1

[TABLE]
[ROW][C]Multiple Linear Regression - Estimated Regression Equation[/C][/ROW]
[ROW][C]TM[t] =  -7.79895678054507 -0.0335405225086837EGKS[t] +  0.0994588527017785BUIZEN[t] +  0.338478881529632NEGKS[t] +  0.624837353466008NF[t] +  0.0535379228849357`GM
`[t]  + e[t][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5500&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5500&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
TM[t] = -7.79895678054507 -0.0335405225086837EGKS[t] + 0.0994588527017785BUIZEN[t] + 0.338478881529632NEGKS[t] + 0.624837353466008NF[t] + 0.0535379228849357`GM `[t] + e[t]







Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-7.798956780545077.161466-1.0890.279680.13984
EGKS-0.03354052250868370.016356-2.05060.0438430.021922
BUIZEN0.09945885270177850.0153236.490700
NEGKS0.3384788815296320.0430357.865200
NF0.6248373534660080.00905369.017400
`GM `0.05353792288493570.0649020.82490.4120760.206038

\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) & -7.79895678054507 & 7.161466 & -1.089 & 0.27968 & 0.13984 \tabularnewline
EGKS & -0.0335405225086837 & 0.016356 & -2.0506 & 0.043843 & 0.021922 \tabularnewline
BUIZEN & 0.0994588527017785 & 0.015323 & 6.4907 & 0 & 0 \tabularnewline
NEGKS & 0.338478881529632 & 0.043035 & 7.8652 & 0 & 0 \tabularnewline
NF & 0.624837353466008 & 0.009053 & 69.0174 & 0 & 0 \tabularnewline
`GM
` & 0.0535379228849357 & 0.064902 & 0.8249 & 0.412076 & 0.206038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5500&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]-7.79895678054507[/C][C]7.161466[/C][C]-1.089[/C][C]0.27968[/C][C]0.13984[/C][/ROW]
[ROW][C]EGKS[/C][C]-0.0335405225086837[/C][C]0.016356[/C][C]-2.0506[/C][C]0.043843[/C][C]0.021922[/C][/ROW]
[ROW][C]BUIZEN[/C][C]0.0994588527017785[/C][C]0.015323[/C][C]6.4907[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]NEGKS[/C][C]0.338478881529632[/C][C]0.043035[/C][C]7.8652[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]NF[/C][C]0.624837353466008[/C][C]0.009053[/C][C]69.0174[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]`GM
`[/C][C]0.0535379228849357[/C][C]0.064902[/C][C]0.8249[/C][C]0.412076[/C][C]0.206038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5500&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5500&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
VariableParameterS.D.T-STATH0: parameter = 02-tail p-value1-tail p-value
(Intercept)-7.798956780545077.161466-1.0890.279680.13984
EGKS-0.03354052250868370.016356-2.05060.0438430.021922
BUIZEN0.09945885270177850.0153236.490700
NEGKS0.3384788815296320.0430357.865200
NF0.6248373534660080.00905369.017400
`GM `0.05353792288493570.0649020.82490.4120760.206038







Multiple Linear Regression - Regression Statistics
Multiple R0.99943890991353
R-squared0.998878134649145
Adjusted R-squared0.99880233293625
F-TEST (value)13177.5140230020
F-TEST (DF numerator)5
F-TEST (DF denominator)74
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.19634092346888
Sum Squared Residuals105.911138782311

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Regression Statistics \tabularnewline
Multiple R & 0.99943890991353 \tabularnewline
R-squared & 0.998878134649145 \tabularnewline
Adjusted R-squared & 0.99880233293625 \tabularnewline
F-TEST (value) & 13177.5140230020 \tabularnewline
F-TEST (DF numerator) & 5 \tabularnewline
F-TEST (DF denominator) & 74 \tabularnewline
p-value & 0 \tabularnewline
Multiple Linear Regression - Residual Statistics \tabularnewline
Residual Standard Deviation & 1.19634092346888 \tabularnewline
Sum Squared Residuals & 105.911138782311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5500&T=3

[TABLE]
[ROW][C]Multiple Linear Regression - Regression Statistics[/C][/ROW]
[ROW][C]Multiple R[/C][C]0.99943890991353[/C][/ROW]
[ROW][C]R-squared[/C][C]0.998878134649145[/C][/ROW]
[ROW][C]Adjusted R-squared[/C][C]0.99880233293625[/C][/ROW]
[ROW][C]F-TEST (value)[/C][C]13177.5140230020[/C][/ROW]
[ROW][C]F-TEST (DF numerator)[/C][C]5[/C][/ROW]
[ROW][C]F-TEST (DF denominator)[/C][C]74[/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]1.19634092346888[/C][/ROW]
[ROW][C]Sum Squared Residuals[/C][C]105.911138782311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5500&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5500&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 R0.99943890991353
R-squared0.998878134649145
Adjusted R-squared0.99880233293625
F-TEST (value)13177.5140230020
F-TEST (DF numerator)5
F-TEST (DF denominator)74
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.19634092346888
Sum Squared Residuals105.911138782311







Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolationForecastResidualsPrediction Error
1100.7101.115489396696-0.415489396695537
297.998.7433925103924-0.843392510392405
396.597.3622957990373-0.862295799037326
496.696.58362165199730.0163783480026958
596.696.8253221746386-0.225322174638585
695.595.10238562919790.397614370802138
791.892.4461333473256-0.646133347325636
889.390.0862651138413-0.786265113841327
98787.7569122602662-0.756912260266172
1085.986.541063641994-0.641063641994005
118888.2658784761295-0.265878476129506
1287.988.5353290686331-0.63532906863307
1389.289.9923642042086-0.792364204208559
1490.991.9060330439262-1.00603304392619
1591.692.382837040223-0.782837040223049
1690.289.68214011119910.517859888800899
1789.188.64584990197460.454150098025423
1887.587.14860191885980.351398081140185
1986.386.7747636201345-0.474763620134514
208686.1447477797742-0.144747779774249
2184.484.8215871619818-0.421587161981748
2286.186.5924679891695-0.492467989169524
239190.42769475164670.572305248353299
2492.791.85960862365920.840391376340807
258888.1244969203915-0.124496920391489
2684.384.6239145055816-0.323914505581620
2782.282.896116441404-0.696116441404008
2880.881.1597219689007-0.359721968900693
2979.480.0899248895885-0.689924889588492
3080.280.7510680130043-0.551068013004276
3182.282.2224700068794-0.022470006879401
3282.282.17964856561420.0203514343858335
3381.281.2179830479405-0.0179830479405009
3482.182.3542511313849-0.254251131384905
3588.187.55357540082620.546424599173750
3688.587.79302782310760.706972176892433
3792.191.09019374386231.00980625613773
3898.697.1068372688611.49316273113894
39100.999.22031021284621.67968978715379
40100.699.71512301722820.884876982771768
41101.1100.3251863844290.774813615571013
42102.1101.5676221100730.532377889927401
43103.6102.9184785562970.681521443702544
44102.8102.1861212888530.613878711146758
45108.3107.3766635521410.923336447858752
46104102.9872924849011.01270751509888
47106.1104.9971654013751.10283459862483
48106.3105.1221328720681.17786712793164
49109108.9033460238460.0966539761539607
50111111.974136135437-0.97413613543695
51113.7114.568257780437-0.868257780436668
52112.7113.567264504990-0.867264504989893
53110.3111.23358017806-0.933580178059907
54114.5115.144846063560-0.644846063560175
55119.3118.9029791892180.397020810781655
56121.8121.1912460639360.608753936064255
57125.4125.0341111682150.365888831785339
58129.7129.1945717961790.50542820382055
59129.4128.8821531194460.51784688055357
60134.5133.9933866988690.506613301131277
61141.2140.8341369382990.365863061700521
62141.4140.9958680652160.404131934784417
63152.2152.307044183736-0.107044183736498
64167.7169.076679856013-1.37667985601293
65173.3175.354256243183-2.05425624318331
66168.7170.208016646503-1.50801664650274
67172.6174.666721649587-2.06672164958653
68169.8171.547746923216-1.74774692321580
69172173.468050243307-1.46805024330748
70179.4181.629995767478-2.22999576747787
71174.6176.312877107154-1.71287710715413
72172.5173.915354860407-1.41535486040731
73172.6174.627699734324-2.02769973432402
74176.3173.7157363318602.58426366813971
75178.9175.1541314287313.74586857126923
76179.6178.3233160191981.27668398080155
77179.9179.3688149213150.531185078684633
78180.3178.1955613738282.104438626172
79180.9176.8505878762344.0494121237664
80177.7176.8354142837520.864585716248428

\begin{tabular}{lllllllll}
\hline
Multiple Linear Regression - Actuals, Interpolation, and Residuals \tabularnewline
Time or Index & Actuals & InterpolationForecast & ResidualsPrediction Error \tabularnewline
1 & 100.7 & 101.115489396696 & -0.415489396695537 \tabularnewline
2 & 97.9 & 98.7433925103924 & -0.843392510392405 \tabularnewline
3 & 96.5 & 97.3622957990373 & -0.862295799037326 \tabularnewline
4 & 96.6 & 96.5836216519973 & 0.0163783480026958 \tabularnewline
5 & 96.6 & 96.8253221746386 & -0.225322174638585 \tabularnewline
6 & 95.5 & 95.1023856291979 & 0.397614370802138 \tabularnewline
7 & 91.8 & 92.4461333473256 & -0.646133347325636 \tabularnewline
8 & 89.3 & 90.0862651138413 & -0.786265113841327 \tabularnewline
9 & 87 & 87.7569122602662 & -0.756912260266172 \tabularnewline
10 & 85.9 & 86.541063641994 & -0.641063641994005 \tabularnewline
11 & 88 & 88.2658784761295 & -0.265878476129506 \tabularnewline
12 & 87.9 & 88.5353290686331 & -0.63532906863307 \tabularnewline
13 & 89.2 & 89.9923642042086 & -0.792364204208559 \tabularnewline
14 & 90.9 & 91.9060330439262 & -1.00603304392619 \tabularnewline
15 & 91.6 & 92.382837040223 & -0.782837040223049 \tabularnewline
16 & 90.2 & 89.6821401111991 & 0.517859888800899 \tabularnewline
17 & 89.1 & 88.6458499019746 & 0.454150098025423 \tabularnewline
18 & 87.5 & 87.1486019188598 & 0.351398081140185 \tabularnewline
19 & 86.3 & 86.7747636201345 & -0.474763620134514 \tabularnewline
20 & 86 & 86.1447477797742 & -0.144747779774249 \tabularnewline
21 & 84.4 & 84.8215871619818 & -0.421587161981748 \tabularnewline
22 & 86.1 & 86.5924679891695 & -0.492467989169524 \tabularnewline
23 & 91 & 90.4276947516467 & 0.572305248353299 \tabularnewline
24 & 92.7 & 91.8596086236592 & 0.840391376340807 \tabularnewline
25 & 88 & 88.1244969203915 & -0.124496920391489 \tabularnewline
26 & 84.3 & 84.6239145055816 & -0.323914505581620 \tabularnewline
27 & 82.2 & 82.896116441404 & -0.696116441404008 \tabularnewline
28 & 80.8 & 81.1597219689007 & -0.359721968900693 \tabularnewline
29 & 79.4 & 80.0899248895885 & -0.689924889588492 \tabularnewline
30 & 80.2 & 80.7510680130043 & -0.551068013004276 \tabularnewline
31 & 82.2 & 82.2224700068794 & -0.022470006879401 \tabularnewline
32 & 82.2 & 82.1796485656142 & 0.0203514343858335 \tabularnewline
33 & 81.2 & 81.2179830479405 & -0.0179830479405009 \tabularnewline
34 & 82.1 & 82.3542511313849 & -0.254251131384905 \tabularnewline
35 & 88.1 & 87.5535754008262 & 0.546424599173750 \tabularnewline
36 & 88.5 & 87.7930278231076 & 0.706972176892433 \tabularnewline
37 & 92.1 & 91.0901937438623 & 1.00980625613773 \tabularnewline
38 & 98.6 & 97.106837268861 & 1.49316273113894 \tabularnewline
39 & 100.9 & 99.2203102128462 & 1.67968978715379 \tabularnewline
40 & 100.6 & 99.7151230172282 & 0.884876982771768 \tabularnewline
41 & 101.1 & 100.325186384429 & 0.774813615571013 \tabularnewline
42 & 102.1 & 101.567622110073 & 0.532377889927401 \tabularnewline
43 & 103.6 & 102.918478556297 & 0.681521443702544 \tabularnewline
44 & 102.8 & 102.186121288853 & 0.613878711146758 \tabularnewline
45 & 108.3 & 107.376663552141 & 0.923336447858752 \tabularnewline
46 & 104 & 102.987292484901 & 1.01270751509888 \tabularnewline
47 & 106.1 & 104.997165401375 & 1.10283459862483 \tabularnewline
48 & 106.3 & 105.122132872068 & 1.17786712793164 \tabularnewline
49 & 109 & 108.903346023846 & 0.0966539761539607 \tabularnewline
50 & 111 & 111.974136135437 & -0.97413613543695 \tabularnewline
51 & 113.7 & 114.568257780437 & -0.868257780436668 \tabularnewline
52 & 112.7 & 113.567264504990 & -0.867264504989893 \tabularnewline
53 & 110.3 & 111.23358017806 & -0.933580178059907 \tabularnewline
54 & 114.5 & 115.144846063560 & -0.644846063560175 \tabularnewline
55 & 119.3 & 118.902979189218 & 0.397020810781655 \tabularnewline
56 & 121.8 & 121.191246063936 & 0.608753936064255 \tabularnewline
57 & 125.4 & 125.034111168215 & 0.365888831785339 \tabularnewline
58 & 129.7 & 129.194571796179 & 0.50542820382055 \tabularnewline
59 & 129.4 & 128.882153119446 & 0.51784688055357 \tabularnewline
60 & 134.5 & 133.993386698869 & 0.506613301131277 \tabularnewline
61 & 141.2 & 140.834136938299 & 0.365863061700521 \tabularnewline
62 & 141.4 & 140.995868065216 & 0.404131934784417 \tabularnewline
63 & 152.2 & 152.307044183736 & -0.107044183736498 \tabularnewline
64 & 167.7 & 169.076679856013 & -1.37667985601293 \tabularnewline
65 & 173.3 & 175.354256243183 & -2.05425624318331 \tabularnewline
66 & 168.7 & 170.208016646503 & -1.50801664650274 \tabularnewline
67 & 172.6 & 174.666721649587 & -2.06672164958653 \tabularnewline
68 & 169.8 & 171.547746923216 & -1.74774692321580 \tabularnewline
69 & 172 & 173.468050243307 & -1.46805024330748 \tabularnewline
70 & 179.4 & 181.629995767478 & -2.22999576747787 \tabularnewline
71 & 174.6 & 176.312877107154 & -1.71287710715413 \tabularnewline
72 & 172.5 & 173.915354860407 & -1.41535486040731 \tabularnewline
73 & 172.6 & 174.627699734324 & -2.02769973432402 \tabularnewline
74 & 176.3 & 173.715736331860 & 2.58426366813971 \tabularnewline
75 & 178.9 & 175.154131428731 & 3.74586857126923 \tabularnewline
76 & 179.6 & 178.323316019198 & 1.27668398080155 \tabularnewline
77 & 179.9 & 179.368814921315 & 0.531185078684633 \tabularnewline
78 & 180.3 & 178.195561373828 & 2.104438626172 \tabularnewline
79 & 180.9 & 176.850587876234 & 4.0494121237664 \tabularnewline
80 & 177.7 & 176.835414283752 & 0.864585716248428 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5500&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]100.7[/C][C]101.115489396696[/C][C]-0.415489396695537[/C][/ROW]
[ROW][C]2[/C][C]97.9[/C][C]98.7433925103924[/C][C]-0.843392510392405[/C][/ROW]
[ROW][C]3[/C][C]96.5[/C][C]97.3622957990373[/C][C]-0.862295799037326[/C][/ROW]
[ROW][C]4[/C][C]96.6[/C][C]96.5836216519973[/C][C]0.0163783480026958[/C][/ROW]
[ROW][C]5[/C][C]96.6[/C][C]96.8253221746386[/C][C]-0.225322174638585[/C][/ROW]
[ROW][C]6[/C][C]95.5[/C][C]95.1023856291979[/C][C]0.397614370802138[/C][/ROW]
[ROW][C]7[/C][C]91.8[/C][C]92.4461333473256[/C][C]-0.646133347325636[/C][/ROW]
[ROW][C]8[/C][C]89.3[/C][C]90.0862651138413[/C][C]-0.786265113841327[/C][/ROW]
[ROW][C]9[/C][C]87[/C][C]87.7569122602662[/C][C]-0.756912260266172[/C][/ROW]
[ROW][C]10[/C][C]85.9[/C][C]86.541063641994[/C][C]-0.641063641994005[/C][/ROW]
[ROW][C]11[/C][C]88[/C][C]88.2658784761295[/C][C]-0.265878476129506[/C][/ROW]
[ROW][C]12[/C][C]87.9[/C][C]88.5353290686331[/C][C]-0.63532906863307[/C][/ROW]
[ROW][C]13[/C][C]89.2[/C][C]89.9923642042086[/C][C]-0.792364204208559[/C][/ROW]
[ROW][C]14[/C][C]90.9[/C][C]91.9060330439262[/C][C]-1.00603304392619[/C][/ROW]
[ROW][C]15[/C][C]91.6[/C][C]92.382837040223[/C][C]-0.782837040223049[/C][/ROW]
[ROW][C]16[/C][C]90.2[/C][C]89.6821401111991[/C][C]0.517859888800899[/C][/ROW]
[ROW][C]17[/C][C]89.1[/C][C]88.6458499019746[/C][C]0.454150098025423[/C][/ROW]
[ROW][C]18[/C][C]87.5[/C][C]87.1486019188598[/C][C]0.351398081140185[/C][/ROW]
[ROW][C]19[/C][C]86.3[/C][C]86.7747636201345[/C][C]-0.474763620134514[/C][/ROW]
[ROW][C]20[/C][C]86[/C][C]86.1447477797742[/C][C]-0.144747779774249[/C][/ROW]
[ROW][C]21[/C][C]84.4[/C][C]84.8215871619818[/C][C]-0.421587161981748[/C][/ROW]
[ROW][C]22[/C][C]86.1[/C][C]86.5924679891695[/C][C]-0.492467989169524[/C][/ROW]
[ROW][C]23[/C][C]91[/C][C]90.4276947516467[/C][C]0.572305248353299[/C][/ROW]
[ROW][C]24[/C][C]92.7[/C][C]91.8596086236592[/C][C]0.840391376340807[/C][/ROW]
[ROW][C]25[/C][C]88[/C][C]88.1244969203915[/C][C]-0.124496920391489[/C][/ROW]
[ROW][C]26[/C][C]84.3[/C][C]84.6239145055816[/C][C]-0.323914505581620[/C][/ROW]
[ROW][C]27[/C][C]82.2[/C][C]82.896116441404[/C][C]-0.696116441404008[/C][/ROW]
[ROW][C]28[/C][C]80.8[/C][C]81.1597219689007[/C][C]-0.359721968900693[/C][/ROW]
[ROW][C]29[/C][C]79.4[/C][C]80.0899248895885[/C][C]-0.689924889588492[/C][/ROW]
[ROW][C]30[/C][C]80.2[/C][C]80.7510680130043[/C][C]-0.551068013004276[/C][/ROW]
[ROW][C]31[/C][C]82.2[/C][C]82.2224700068794[/C][C]-0.022470006879401[/C][/ROW]
[ROW][C]32[/C][C]82.2[/C][C]82.1796485656142[/C][C]0.0203514343858335[/C][/ROW]
[ROW][C]33[/C][C]81.2[/C][C]81.2179830479405[/C][C]-0.0179830479405009[/C][/ROW]
[ROW][C]34[/C][C]82.1[/C][C]82.3542511313849[/C][C]-0.254251131384905[/C][/ROW]
[ROW][C]35[/C][C]88.1[/C][C]87.5535754008262[/C][C]0.546424599173750[/C][/ROW]
[ROW][C]36[/C][C]88.5[/C][C]87.7930278231076[/C][C]0.706972176892433[/C][/ROW]
[ROW][C]37[/C][C]92.1[/C][C]91.0901937438623[/C][C]1.00980625613773[/C][/ROW]
[ROW][C]38[/C][C]98.6[/C][C]97.106837268861[/C][C]1.49316273113894[/C][/ROW]
[ROW][C]39[/C][C]100.9[/C][C]99.2203102128462[/C][C]1.67968978715379[/C][/ROW]
[ROW][C]40[/C][C]100.6[/C][C]99.7151230172282[/C][C]0.884876982771768[/C][/ROW]
[ROW][C]41[/C][C]101.1[/C][C]100.325186384429[/C][C]0.774813615571013[/C][/ROW]
[ROW][C]42[/C][C]102.1[/C][C]101.567622110073[/C][C]0.532377889927401[/C][/ROW]
[ROW][C]43[/C][C]103.6[/C][C]102.918478556297[/C][C]0.681521443702544[/C][/ROW]
[ROW][C]44[/C][C]102.8[/C][C]102.186121288853[/C][C]0.613878711146758[/C][/ROW]
[ROW][C]45[/C][C]108.3[/C][C]107.376663552141[/C][C]0.923336447858752[/C][/ROW]
[ROW][C]46[/C][C]104[/C][C]102.987292484901[/C][C]1.01270751509888[/C][/ROW]
[ROW][C]47[/C][C]106.1[/C][C]104.997165401375[/C][C]1.10283459862483[/C][/ROW]
[ROW][C]48[/C][C]106.3[/C][C]105.122132872068[/C][C]1.17786712793164[/C][/ROW]
[ROW][C]49[/C][C]109[/C][C]108.903346023846[/C][C]0.0966539761539607[/C][/ROW]
[ROW][C]50[/C][C]111[/C][C]111.974136135437[/C][C]-0.97413613543695[/C][/ROW]
[ROW][C]51[/C][C]113.7[/C][C]114.568257780437[/C][C]-0.868257780436668[/C][/ROW]
[ROW][C]52[/C][C]112.7[/C][C]113.567264504990[/C][C]-0.867264504989893[/C][/ROW]
[ROW][C]53[/C][C]110.3[/C][C]111.23358017806[/C][C]-0.933580178059907[/C][/ROW]
[ROW][C]54[/C][C]114.5[/C][C]115.144846063560[/C][C]-0.644846063560175[/C][/ROW]
[ROW][C]55[/C][C]119.3[/C][C]118.902979189218[/C][C]0.397020810781655[/C][/ROW]
[ROW][C]56[/C][C]121.8[/C][C]121.191246063936[/C][C]0.608753936064255[/C][/ROW]
[ROW][C]57[/C][C]125.4[/C][C]125.034111168215[/C][C]0.365888831785339[/C][/ROW]
[ROW][C]58[/C][C]129.7[/C][C]129.194571796179[/C][C]0.50542820382055[/C][/ROW]
[ROW][C]59[/C][C]129.4[/C][C]128.882153119446[/C][C]0.51784688055357[/C][/ROW]
[ROW][C]60[/C][C]134.5[/C][C]133.993386698869[/C][C]0.506613301131277[/C][/ROW]
[ROW][C]61[/C][C]141.2[/C][C]140.834136938299[/C][C]0.365863061700521[/C][/ROW]
[ROW][C]62[/C][C]141.4[/C][C]140.995868065216[/C][C]0.404131934784417[/C][/ROW]
[ROW][C]63[/C][C]152.2[/C][C]152.307044183736[/C][C]-0.107044183736498[/C][/ROW]
[ROW][C]64[/C][C]167.7[/C][C]169.076679856013[/C][C]-1.37667985601293[/C][/ROW]
[ROW][C]65[/C][C]173.3[/C][C]175.354256243183[/C][C]-2.05425624318331[/C][/ROW]
[ROW][C]66[/C][C]168.7[/C][C]170.208016646503[/C][C]-1.50801664650274[/C][/ROW]
[ROW][C]67[/C][C]172.6[/C][C]174.666721649587[/C][C]-2.06672164958653[/C][/ROW]
[ROW][C]68[/C][C]169.8[/C][C]171.547746923216[/C][C]-1.74774692321580[/C][/ROW]
[ROW][C]69[/C][C]172[/C][C]173.468050243307[/C][C]-1.46805024330748[/C][/ROW]
[ROW][C]70[/C][C]179.4[/C][C]181.629995767478[/C][C]-2.22999576747787[/C][/ROW]
[ROW][C]71[/C][C]174.6[/C][C]176.312877107154[/C][C]-1.71287710715413[/C][/ROW]
[ROW][C]72[/C][C]172.5[/C][C]173.915354860407[/C][C]-1.41535486040731[/C][/ROW]
[ROW][C]73[/C][C]172.6[/C][C]174.627699734324[/C][C]-2.02769973432402[/C][/ROW]
[ROW][C]74[/C][C]176.3[/C][C]173.715736331860[/C][C]2.58426366813971[/C][/ROW]
[ROW][C]75[/C][C]178.9[/C][C]175.154131428731[/C][C]3.74586857126923[/C][/ROW]
[ROW][C]76[/C][C]179.6[/C][C]178.323316019198[/C][C]1.27668398080155[/C][/ROW]
[ROW][C]77[/C][C]179.9[/C][C]179.368814921315[/C][C]0.531185078684633[/C][/ROW]
[ROW][C]78[/C][C]180.3[/C][C]178.195561373828[/C][C]2.104438626172[/C][/ROW]
[ROW][C]79[/C][C]180.9[/C][C]176.850587876234[/C][C]4.0494121237664[/C][/ROW]
[ROW][C]80[/C][C]177.7[/C][C]176.835414283752[/C][C]0.864585716248428[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5500&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5500&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 IndexActualsInterpolationForecastResidualsPrediction Error
1100.7101.115489396696-0.415489396695537
297.998.7433925103924-0.843392510392405
396.597.3622957990373-0.862295799037326
496.696.58362165199730.0163783480026958
596.696.8253221746386-0.225322174638585
695.595.10238562919790.397614370802138
791.892.4461333473256-0.646133347325636
889.390.0862651138413-0.786265113841327
98787.7569122602662-0.756912260266172
1085.986.541063641994-0.641063641994005
118888.2658784761295-0.265878476129506
1287.988.5353290686331-0.63532906863307
1389.289.9923642042086-0.792364204208559
1490.991.9060330439262-1.00603304392619
1591.692.382837040223-0.782837040223049
1690.289.68214011119910.517859888800899
1789.188.64584990197460.454150098025423
1887.587.14860191885980.351398081140185
1986.386.7747636201345-0.474763620134514
208686.1447477797742-0.144747779774249
2184.484.8215871619818-0.421587161981748
2286.186.5924679891695-0.492467989169524
239190.42769475164670.572305248353299
2492.791.85960862365920.840391376340807
258888.1244969203915-0.124496920391489
2684.384.6239145055816-0.323914505581620
2782.282.896116441404-0.696116441404008
2880.881.1597219689007-0.359721968900693
2979.480.0899248895885-0.689924889588492
3080.280.7510680130043-0.551068013004276
3182.282.2224700068794-0.022470006879401
3282.282.17964856561420.0203514343858335
3381.281.2179830479405-0.0179830479405009
3482.182.3542511313849-0.254251131384905
3588.187.55357540082620.546424599173750
3688.587.79302782310760.706972176892433
3792.191.09019374386231.00980625613773
3898.697.1068372688611.49316273113894
39100.999.22031021284621.67968978715379
40100.699.71512301722820.884876982771768
41101.1100.3251863844290.774813615571013
42102.1101.5676221100730.532377889927401
43103.6102.9184785562970.681521443702544
44102.8102.1861212888530.613878711146758
45108.3107.3766635521410.923336447858752
46104102.9872924849011.01270751509888
47106.1104.9971654013751.10283459862483
48106.3105.1221328720681.17786712793164
49109108.9033460238460.0966539761539607
50111111.974136135437-0.97413613543695
51113.7114.568257780437-0.868257780436668
52112.7113.567264504990-0.867264504989893
53110.3111.23358017806-0.933580178059907
54114.5115.144846063560-0.644846063560175
55119.3118.9029791892180.397020810781655
56121.8121.1912460639360.608753936064255
57125.4125.0341111682150.365888831785339
58129.7129.1945717961790.50542820382055
59129.4128.8821531194460.51784688055357
60134.5133.9933866988690.506613301131277
61141.2140.8341369382990.365863061700521
62141.4140.9958680652160.404131934784417
63152.2152.307044183736-0.107044183736498
64167.7169.076679856013-1.37667985601293
65173.3175.354256243183-2.05425624318331
66168.7170.208016646503-1.50801664650274
67172.6174.666721649587-2.06672164958653
68169.8171.547746923216-1.74774692321580
69172173.468050243307-1.46805024330748
70179.4181.629995767478-2.22999576747787
71174.6176.312877107154-1.71287710715413
72172.5173.915354860407-1.41535486040731
73172.6174.627699734324-2.02769973432402
74176.3173.7157363318602.58426366813971
75178.9175.1541314287313.74586857126923
76179.6178.3233160191981.27668398080155
77179.9179.3688149213150.531185078684633
78180.3178.1955613738282.104438626172
79180.9176.8505878762344.0494121237664
80177.7176.8354142837520.864585716248428



Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')