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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_linear_regression.wasp
Title produced by softwareLinear Regression Graphical Model Validation
Date of computationThu, 25 Nov 2010 18:35:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/25/t12907100901scg9u5g93ei0hg.htm/, Retrieved Tue, 23 Apr 2024 23:09:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101334, Retrieved Tue, 23 Apr 2024 23:09:19 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120

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]
-  M D  [Linear Regression Graphical Model Validation] [] [2010-11-25 09:23:05] [4dfa50539945b119a90a7606969443b9]
-    D      [Linear Regression Graphical Model Validation] [] [2010-11-25 18:35:56] [cf84dc108eae081aed36d3d050e63ee7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,3898
1,3067
1,2894
1,277
1,2208
1,2565
1,3406
1,3569
1,3686
1,4272
1,4614
1,4914
1,4816
1,4562
1,4268
1,4088
1,4016
1,365
1,319
1,305
1,2785
1,3239
1,3449
1,2732
1,3322
1,4369
1,4975
1,577
1,5553
1,5557
1,575
1,5527
1,4748
1,4718
1,457
1,4684
1,4227
1,3896
1,3622
1,3716
1,3419
1,3511
1,3516
1,3242
1,3074
1,2999
1,3213
1,2881
1,2611
1,2727
1,2811
1,2684
1,265
1,277
1,2271
1,202
1,1938
1,2103
1,1856
1,1786
1,2015
1,2256
1,2292
1,2037
1,2165
1,2694
1,2938
1,3201
1,3014
1,3119
1,3408
1,2991
1,249
1,2218
1,2176
1,2266
1,2138
1,2007
1,1985
1,2262
1,2646
1,2613
1,2286
1,1702
1,1692
1,1222
1,1139
1,1372
1,1663
1,1582
1,0848
1,0807
1,0773
1,0622
1,0183
1,0014
0,9811
0,9808
0,9778
0,9922
0,9554
0,917
0,8858
0,8758
0,87
0,8833
0,8924
0,8883
0,9059
0,9111
0,9005
0,8607
0,8532
0,8742
0,892
0,9095
0,9217
0,9383
0,8973
0,8564
Dataseries Y:
Download CSV
Histogram 
31,077
31,293
30,236
30,160
32,436
30,695
27,525
26,434
25,739
25,204
24,977
24,320
22,680
22,052
21,467
21,383
21,777
21,928
21,814
22,937
23,595
20,830
19,650
19,195
19,644
18,483
18,079
19,178
18,391
18,441
18,584
20,108
20,148
19,394
17,745
17,696
17,032
16,438
15,683
15,594
15,713
15,937
16,171
15,928
16,348
15,579
15,305
15,648
14,954
15,137
15,839
16,050
15,168
17,064
16,005
14,886
14,931
14,544
13,812
13,031
12,574
11,964
11,451
11,346
11,353
10,702
10,646
10,556
10,463
10,407
10,625
10,872
10,805
10,653
10,574
10,431
10,383
10,296
10,872
10,635
10,297
10,570
10,662
10,709
10,413
10,846
10,371
9,924
9,828
9,897
9,721
10,171
10,738
10,812
10,511
10,244
10,368
10,457
10,186
10,166
10,827
10,997
10,940
10,756
10,893
10,236
9,960
10,018
10,063
10,002
9,728
10,002
10,177
9,948
9,394
9,308
9,155
9,103
9,732
9,984

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 5 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101334&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101334&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101334&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 time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term-8.392263708036762.76378641457984-3.036509501517540.00294605099205825
slope19.33880373951752.238209064885078.640302661141523.19744231092045e-14

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & -8.39226370803676 & 2.76378641457984 & -3.03650950151754 & 0.00294605099205825 \tabularnewline
slope & 19.3388037395175 & 2.23820906488507 & 8.64030266114152 & 3.19744231092045e-14 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101334&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]-8.39226370803676[/C][C]2.76378641457984[/C][C]-3.03650950151754[/C][C]0.00294605099205825[/C][/ROW]
[ROW][C]slope[/C][C]19.3388037395175[/C][C]2.23820906488507[/C][C]8.64030266114152[/C][C]3.19744231092045e-14[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101334&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101334&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 term-8.392263708036762.76378641457984-3.036509501517540.00294605099205825
slope19.33880373951752.238209064885078.640302661141523.19744231092045e-14


Figures (Output of Computation)

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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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')