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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_Simple Regression Y ~ X.wasp
Title produced by softwareSimple Linear Regression
Date of computationFri, 21 Dec 2012 07:31:01 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356093238en5hgzmyww5i68g.htm/, Retrieved Thu, 28 Mar 2024 22:15:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203556, Retrieved Thu, 28 Mar 2024 22:15:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [simple regression] [2012-12-21 12:31:01] [fb932d62b365c77ae1a4ae64527e1257] [Current]
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Dataseries X:
112285	210907
84786	120982
83123	176508
101193	179321
38361	123185
68504	52746
119182	385534
22807	33170
17140	101645
116174	149061
57635	165446
66198	237213
71701	173326
57793	133131
80444	258873
53855	180083
97668	324799
133824	230964
101481	236785
99645	135473
114789	202925
99052	215147
67654	344297
65553	153935
97500	132943
69112	174724
82753	174415
85323	225548
72654	223632
30727	124817
77873	221698
117478	210767
74007	170266
90183	260561
61542	84853
101494	294424
27570	101011
55813	215641
79215	325107
1423	7176
55461	167542
31081	106408
22996	96560
83122	265769
70106	269651
60578	149112
39992	175824
79892	152871
49810	111665
71570	116408
100708	362301
33032	78800
82875	183167
139077	277965
71595	150629
72260	168809
5950	24188
115762	329267
32551	65029
31701	101097
80670	218946
143558	244052
117105	341570
23789	103597
120733	233328
105195	256462
73107	206161
132068	311473
149193	235800
46821	177939
87011	207176
95260	196553
55183	174184
106671	143246
73511	187559
92945	187681
78664	119016
70054	182192
22618	73566
74011	194979
83737	167488
69094	143756
93133	275541
95536	243199
225920	182999
62133	135649
61370	152299
43836	120221
106117	346485
38692	145790
84651	193339
56622	80953
15986	122774
95364	130585
26706	112611
89691	286468
67267	241066
126846	148446
41140	204713
102860	182079
51715	140344
55801	220516
111813	243060
120293	162765
138599	182613
161647	232138
115929	265318
24266	85574
162901	310839
109825	225060
129838	232317
37510	144966
43750	43287
40652	155754
87771	164709
85872	201940
89275	235454
44418	220801
192565	99466
35232	92661
40909	133328
13294	61361
32387	125930
140867	100750
120662	224549
21233	82316
44332	102010
61056	101523
101338	243511
1168	22938
13497	41566
65567	152474
25162	61857
32334	99923
40735	132487
91413	317394
855	21054
97068	209641
44339	22648
14116	31414
10288	46698
65622	131698
16563	91735
76643	244749
110681	184510
29011	79863
92696	128423
94785	97839
8773	38214
83209	151101
93815	272458
86687	172494
34553	108043
105547	328107
103487	250579
213688	351067
71220	158015
23517	98866
56926	85439
91721	229242
115168	351619
111194	84207
51009	120445
135777	324598
51513	131069
74163	204271
51633	165543
75345	141722
33416	116048
83305	250047
98952	299775
102372	195838
37238	173260
103772	254488
123969	104389
27142	136084
135400	199476
21399	92499
130115	224330
24874	135781
34988	74408
45549	81240
6023	14688
64466	181633
54990	271856
1644	7199
6179	46660
3926	17547
32755	133368
34777	95227
73224	152601
27114	98146
20760	79619
37636	59194
65461	139942
30080	118612
24094	72880
69008	65475
54968	99643
46090	71965
27507	77272
10672	49289
34029	135131
46300	108446
24760	89746
18779	44296
21280	77648
40662	181528
28987	134019
22827	124064
18513	92630
30594	121848
24006	52915
27913	81872
42744	58981
12934	53515
22574	60812
41385	56375
18653	65490
18472	80949
30976	76302
63339	104011
25568	98104
33747	67989
4154	30989
19474	135458
35130	73504
39067	63123
13310	61254
65892	74914
4143	31774
28579	81437
51776	87186
21152	50090
38084	65745
27717	56653
32928	158399
11342	46455
19499	73624
16380	38395
36874	91899
48259	139526
16734	52164
28207	51567
30143	70551
41369	84856
45833	102538
29156	86678
35944	85709
36278	34662
45588	150580
45097	99611
3895	19349
28394	99373
18632	86230
2325	30837
25139	31706
27975	89806
14483	62088
13127	40151
5839	27634
24069	76990
3738	37460
18625	54157
36341	49862
24548	84337
21792	64175
26263	59382
23686	119308
49303	76702
25659	103425
28904	70344
2781	43410
29236	104838
19546	62215
22818	69304
32689	53117
5752	19764
22197	86680
20055	84105
25272	77945
82206	89113
32073	91005
5444	40248
20154	64187
36944	50857
8019	56613
30884	62792




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203556&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203556&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)7199.1713112.0052.3130.021
X0.3660.01918.9190
- - -
Residual Std. Err. 26992.778 on 286 df
Multiple R-sq. 0.556
Adjusted R-sq. 0.554

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 7199.171 & 3112.005 & 2.313 & 0.021 \tabularnewline
X & 0.366 & 0.019 & 18.919 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 26992.778  on  286 df \tabularnewline
Multiple R-sq.  & 0.556 \tabularnewline
Adjusted R-sq.  & 0.554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203556&T=1

[TABLE]
[ROW][C]Linear Regression Model[/C][/ROW]
[ROW][C]Y ~ X[/C][/ROW]
[ROW][C]coefficients:[/C][C] [/C][/ROW]
[ROW][C] [/C][C]Estimate[/C][C]Std. Error[/C][C]t value[/C][C]Pr(>|t|)[/C][/ROW]
[C](Intercept)[/C][C]7199.171[/C][C]3112.005[/C][C]2.313[/C][C]0.021[/C][/ROW]
[C]X[/C][C]0.366[/C][C]0.019[/C][C]18.919[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]26992.778  on  286 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.556[/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203556&T=1

As an alternative you can also use a QR Code:  

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

Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)7199.1713112.0052.3130.021
X0.3660.01918.9190
- - -
Residual Std. Err. 26992.778 on 286 df
Multiple R-sq. 0.556
Adjusted R-sq. 0.554







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Timerfc1260789168190.575260789168190.575357.9270
Residuals286208382472419.077728610043.423

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Timerfc & 1 & 260789168190.575 & 260789168190.575 & 357.927 & 0 \tabularnewline
Residuals & 286 & 208382472419.077 & 728610043.423 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203556&T=2

[TABLE]
[ROW][C]ANOVA Statistics[/C][/ROW]
[ROW][C] [/C][C]Df[/C][C]Sum Sq[/C][C]Mean Sq[/C][C]F value[/C][C]Pr(>F)[/C][/ROW]
[ROW][C]Timerfc[/C][C]1[/C][C]260789168190.575[/C][C]260789168190.575[/C][C]357.927[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]286[/C][C]208382472419.077[/C][C]728610043.423[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203556&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203556&T=2

As an alternative you can also use a QR Code:  

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

ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Timerfc1260789168190.575260789168190.575357.9270
Residuals286208382472419.077728610043.423



Parameters (Session):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
Parameters (R input):
par1 = 1 ; par2 = 2 ; par3 = TRUE ;
R code (references can be found in the software module):
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- t(x)
xdf<-data.frame(t(y))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'coefficients')
nr <- nrow(sumlmxdf$'coefficients')
a<-table.row.start(a)
a<-table.element(a,'Linear Regression Model', nc+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, lmxdf$call['formula'],nc+1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'coefficients:',1,TRUE)
a<-table.element(a, ' ',nc,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
for(i in 1 : nc){
a<-table.element(a, dimnames(sumlmxdf$'coefficients')[[2]][i],1,TRUE)
}#end header
a<-table.row.end(a)
for(i in 1: nr){
a<-table.element(a,dimnames(sumlmxdf$'coefficients')[[1]][i] ,1,TRUE)
for(j in 1 : nc){
a<-table.element(a, round(sumlmxdf$coefficients[i, j], digits=3), 1 ,FALSE)
}
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a, '- - - ',1,TRUE)
a<-table.element(a, ' ',nc,FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Std. Err. ',1,TRUE)
a<-table.element(a, paste(round(sumlmxdf$'sigma', digits=3), ' on ', sumlmxdf$'df'[2], 'df') ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-sq. ',1,TRUE)
a<-table.element(a, round(sumlmxdf$'adj.r.squared', digits=3) ,nc, FALSE)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ANOVA Statistics', 5+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, ' ',1,TRUE)
a<-table.element(a, 'Df',1,TRUE)
a<-table.element(a, 'Sum Sq',1,TRUE)
a<-table.element(a, 'Mean Sq',1,TRUE)
a<-table.element(a, 'F value',1,TRUE)
a<-table.element(a, 'Pr(>F)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, V2,1,TRUE)
a<-table.element(a, anova.xdf$Df[1])
a<-table.element(a, round(anova.xdf$'Sum Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[1], digits=3))
a<-table.element(a, round(anova.xdf$'F value'[1], digits=3))
a<-table.element(a, round(anova.xdf$'Pr(>F)'[1], digits=3))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residuals',1,TRUE)
a<-table.element(a, anova.xdf$Df[2])
a<-table.element(a, round(anova.xdf$'Sum Sq'[2], digits=3))
a<-table.element(a, round(anova.xdf$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qq.plot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot.lm(lmxdf, which=4)
dev.off()