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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_linear_regression.wasp
Title produced by softwareLinear Regression Graphical Model Validation
Date of computationTue, 15 Nov 2011 17:38:28 -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/2011/Nov/15/t1321396778c6yvj8n1e1f801d.htm/, Retrieved Fri, 19 Apr 2024 05:52:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=143634, Retrieved Fri, 19 Apr 2024 05:52:31 +0000
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IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Linear Regression Graphical Model Validation] [Colombia Coffee -...] [2008-02-26 10:22:06] [74be16979710d4c4e7c6647856088456]
- RM D    [Linear Regression Graphical Model Validation] [Tutorial] [2011-11-15 22:38:28] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-    D      [Linear Regression Graphical Model Validation] [ws6 tutorial] [2011-11-15 22:50:40] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
93,09
94,84
93,53
95,5
94,52
95,33
97,45
98,2
97,7
98,68
97,43
97,8
98,1
96,86
97,72
96,63
95,27
97,66
97,72
99,42
101,59
101,93
102,01
103,13
102,2
99,08
100,52
102,01
101,7
101
103,06
101,45
103,24
102,24
102,71
105,74
106,06
110,89
112,06
111,78
111,88
114,88
116,65
114,53
115,89
115,53
113,3
115,7
115,79
113,71
113,67
108,52
111,05
114,9
113,93
114,96
114,96
115,7
115,72
115,59
115,1
115,27
115,17
115,17
115,27
115,17
115,27
115,17
122,3
122,67
126,65
123,98
122,88
122,36
123,45
121,61
121,33
123,85
123,99
124,04
123,66
124,14
125,13
125,02
125,89
125,12
122,45
121,19
110,8
109,13
115,9
117,63
112,57
112,98
113,83
112,73
109,99
112,3
111,42
112,39
110,1
112,53
114,93
115,05
115,03
114,68
116,63
114,53
115,54
115,84
114,48
116,78
117,85
119,57
118,78
119,1
120,16
113,01
114,02
113,21
111,69
112,1
114,21
107,26
105,12
105,99
108,78
112,4
112,48
117,77
111,39
113,61
113,62
118,59
118,33
117,03
117,75
118,78
118,32
117,26
116,05
117,06
118,15
117,51
118,67
117,94
118,28
117,43
117,36
116,74
116,81
116,46
113,23
107,25
109,37
103,74
102,57
106,68
108,02
108,03
109,91
109,47
110,6
106,99
108,62
108,11
108,36
109,31
110,69
111,36
111,88
114,02
114,85
114,29
112,33
110,08
112,89
115,69
114,55
112,77
112,25
111,89
112,4
115,34
112,22
109,14
110,54
110,36
105,49
103,97
103,94
107,14
103,81
103,95
102,76
101,71
99,79
102,73
105,73
105,88
108,95
111,12
111,36
111,11
114,68
110,16
111,15
108,39
109,76
109,56
109,56
111,45
108,91
112,08
109,91
109,56
Dataseries Y:
Download CSV
Histogram 
3035
2932
2852
2830
2850
2881
2934
2959
2952
3019
3019
3036
3100
3178
3184
3312
3335
3352
3358
3277
3352
3313
3352
3358
3251
3223
3239
3272
3397
3374
3400
3410
3463
3482
3546
3546
3633
3661
3684
3698
3757
3660
3701
3774
3697
3721
3703
3585
3490
3460
3431
3294
3233
3282
3127
3189
3263
3251
3203
3242
3248
3057
2987
2952
3011
3020
2975
2999
2987
2974
3022
3053
3066
3125
3239
3127
3117
3131
3130
3130
3128
3131
3206
3330
3390
3353
3271
3236
3087
3137
3143
3135
3115
3035
3000
3006
2980
2995
2979
2902
2865
2884
2962
3010
3010
2973
2999
2953
2904
2878
2863
2891
2927
2980
2997
3001
3014
2987
2914
2917
2967
3027
3040
2986
2967
2995
3018
3114
3170
3170
3142
3228
3202
3194
3099
3058
3076
3180
3166
3168
3186
3187
3207
3194
3093
3025
3047
3073
3011
3008
2989
2965
2952
2941
2975
2945
2943
2871
2871
2943
2871
2943
2871
2871
2943
2871
2943
2871
2871
2943
2871
2943
2871
3060
3067
3092
3067
3092
3092
3067
3092
3067
3092
3092
2792
2716
2730
2727
2680
2634
2678
2721
2664
2694
2608
2575
2592
2622
2660
2562
2684
2632
2659
2658
2700
2650
2610
2644
2607
2611
2670
2683
2727
2779
2770
2723

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143634&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143634&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143634&T=0

As an alternative you can also use a QR Code:  
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'Gwilym Jenkins' @ jenkins.wessa.net






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term2566.58069330294265.3855163027919.671140795696650
slope4.452792199000882.380559130788321.870481661812930.0627821168587623

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 2566.58069330294 & 265.385516302791 & 9.67114079569665 & 0 \tabularnewline
slope & 4.45279219900088 & 2.38055913078832 & 1.87048166181293 & 0.0627821168587623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=143634&T=1

[TABLE]
[ROW][C]Simple Linear Regression[/C][/ROW]
[ROW][C]Statistics[/C][C]Estimate[/C][C]S.D.[/C][C]T-STAT (H0: coeff=0)[/C][C]P-value (two-sided)[/C][/ROW]
[ROW][C]constant term[/C][C]2566.58069330294[/C][C]265.385516302791[/C][C]9.67114079569665[/C][C]0[/C][/ROW]
[ROW][C]slope[/C][C]4.45279219900088[/C][C]2.38055913078832[/C][C]1.87048166181293[/C][C]0.0627821168587623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=143634&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=143634&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term2566.58069330294265.3855163027919.671140795696650
slope4.452792199000882.380559130788321.870481661812930.0627821168587623


Figures (Output of Computation)

Figure 1
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Figure 2
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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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Input Parameters & R Code

Parameters (Session):
par1 = 0 ;
Parameters (R input):
par1 = 0 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
library(lattice)
z <- as.data.frame(cbind(x,y))
m <- lm(y~x)
summary(m)
bitmap(file='test1.png')
plot(z,main='Scatterplot, lowess, and regression line')
lines(lowess(z),col='red')
abline(m)
grid()
dev.off()
bitmap(file='test2.png')
m2 <- lm(m$fitted.values ~ x)
summary(m2)
z2 <- as.data.frame(cbind(x,m$fitted.values))
names(z2) <- list('x','Fitted')
plot(z2,main='Scatterplot, lowess, and regression line')
lines(lowess(z2),col='red')
abline(m2)
grid()
dev.off()
bitmap(file='test3.png')
m3 <- lm(m$residuals ~ x)
summary(m3)
z3 <- as.data.frame(cbind(x,m$residuals))
names(z3) <- list('x','Residuals')
plot(z3,main='Scatterplot, lowess, and regression line')
lines(lowess(z3),col='red')
abline(m3)
grid()
dev.off()
bitmap(file='test4.png')
m4 <- lm(m$fitted.values ~ m$residuals)
summary(m4)
z4 <- as.data.frame(cbind(m$residuals,m$fitted.values))
names(z4) <- list('Residuals','Fitted')
plot(z4,main='Scatterplot, lowess, and regression line')
lines(lowess(z4),col='red')
abline(m4)
grid()
dev.off()
bitmap(file='test5.png')
myr <- as.ts(m$residuals)
z5 <- as.data.frame(cbind(lag(myr,1),myr))
names(z5) <- list('Lagged Residuals','Residuals')
plot(z5,main='Lag plot')
m5 <- lm(z5)
summary(m5)
abline(m5)
grid()
dev.off()
bitmap(file='test6.png')
hist(m$residuals,main='Residual Histogram',xlab='Residuals')
dev.off()
bitmap(file='test7.png')
if (par1 > 0)
{
densityplot(~m$residuals,col='black',main=paste('Density Plot   bw = ',par1),bw=par1)
} else {
densityplot(~m$residuals,col='black',main='Density Plot')
}
dev.off()
bitmap(file='test8.png')
acf(m$residuals,main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test9.png')
qqnorm(x)
qqline(x)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Simple Linear Regression',5,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Statistics',1,TRUE)
a<-table.element(a,'Estimate',1,TRUE)
a<-table.element(a,'S.D.',1,TRUE)
a<-table.element(a,'T-STAT (H0: coeff=0)',1,TRUE)
a<-table.element(a,'P-value (two-sided)',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'constant term',header=TRUE)
a<-table.element(a,m$coefficients[[1]])
sd <- sqrt(vcov(m)[1,1])
a<-table.element(a,sd)
tstat <- m$coefficients[[1]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'slope',header=TRUE)
a<-table.element(a,m$coefficients[[2]])
sd <- sqrt(vcov(m)[2,2])
a<-table.element(a,sd)
tstat <- m$coefficients[[2]]/sd
a<-table.element(a,tstat)
pval <- 2*(1-pt(abs(tstat),length(x)-2))
a<-table.element(a,pval)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')