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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 computationFri, 17 Dec 2010 16:29:12 +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/Dec/17/t12926032660jkm9745o4xoiqd.htm/, Retrieved Mon, 06 May 2024 20:44:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111566, Retrieved Mon, 06 May 2024 20:44:40 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122

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] [] [2010-11-12 14:29:30] [0175b38674e1402e67841c9c82e4a5a3]
-   PD      [Linear Regression Graphical Model Validation] [] [2010-12-17 16:29:12] [c2e23af56713b360851e64c7775b3f2b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13.193
15.234
14.718
16.961
13.945
15.876
16.226
18.316
16.748
17.904
17.209
18.950
17.225
18.710
17.236
18.687
17.580
19.568
17.381
19.580
17.260
18.661
15.658
18.674
15.908
17.475
17.725
19.562
16.368
19.555
17.743
19.867
15.703
19.324
18.162
19.074
15.323
19.704
18.375
18.352
13.927
17.795
16.761
18.902
16.239
19.158
18.279
15.698
16.239
18.431
18.414
19.801
14.995
18.706
18.232
19.409
16.263
19.017
20.298
19.891
15.203
17.845
17.502
18.532
15.737
17.770
17.224
17.601
14.940
18.507
17.635
19.392
15.699
17.661
18.243
19.643
15.770
17.344
17.229
17.322
16.152
17.919
16.918
18.114
16.308
17.759
16.021
17.952
15.954
17.762
16.610
17.751
15.458
18.106
15.990
15.349
13.185
15.409
16.007
16.633
14.800
15.974
15.693
Dataseries Y:
Download CSV
Histogram 
45,42946715
47,30890126
46,45641863
47,3698655
47,21193993
50,36128845
48,46762714
48,98376976
52,05486602
54,4900144
53,78154258
50,39349266
53,42125278
56,37086815
54,65045802
56,30443403
61,62567836
64,47747993
62,62799233
63,95944303
67,29379922
66,17531557
63,35044548
64,73553232
69,02983248
65,38533723
74,25980235
70,6765517
74,00536331
79,69624895
74,29508517
75,23141734
78,12084346
79,89684672
81,10600518
81,90173907
83,26140877
87,63561055
82,34316058
82,17568328
87,5273976
85,7646506
89,44224465
91,02960423
88,65177953
98,73311222
93,21265556
90,78122563
88,65177953
102,0613232
97,62922224
104,8501774
107,4114354
104,0886408
108,3004803
112,2068344
112,5130961
115,9068912
116,137225
113,1145975
119,8591079
122,9852011
125,6783881
125,9717097
132,2688646
132,2177364
128,8320534
138,9298575
144,3433282
150,1766286
151,8766262
154,2529855
158,998195
164,9009977
162,8670286
162,4671806
166,2743851
175,6203913
168,1232692
175,2475017
216,570789
225,7245312
233,5111144
228,3567392
244,7747817
260,8077061
268,5485339
254,6309481
285,0569791
280,3959709
298,8097542
275,6544121
301,8949699
309,0113243
303,0490807
296,4917526
297,3047194
298,0350867
303,5097269
289,5155581
316,2819921
307,684349
323,6859879

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111566&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111566&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111566&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'George Udny Yule' @ 72.249.76.132






Simple Linear Regression
StatisticsEstimateS.D.T-STAT (H0: coeff=0)P-value (two-sided)
constant term375.02507243156489.5291663475494.188859203443616.00880758931943e-05
slope-13.85448940004495.1567322221961-2.686680014217350.00843952492041833

\begin{tabular}{lllllllll}
\hline
Simple Linear Regression \tabularnewline
Statistics & Estimate & S.D. & T-STAT (H0: coeff=0) & P-value (two-sided) \tabularnewline
constant term & 375.025072431564 & 89.529166347549 & 4.18885920344361 & 6.00880758931943e-05 \tabularnewline
slope & -13.8544894000449 & 5.1567322221961 & -2.68668001421735 & 0.00843952492041833 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111566&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]375.025072431564[/C][C]89.529166347549[/C][C]4.18885920344361[/C][C]6.00880758931943e-05[/C][/ROW]
[ROW][C]slope[/C][C]-13.8544894000449[/C][C]5.1567322221961[/C][C]-2.68668001421735[/C][C]0.00843952492041833[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111566&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111566&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 term375.02507243156489.5291663475494.188859203443616.00880758931943e-05
slope-13.85448940004495.1567322221961-2.686680014217350.00843952492041833


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 = 1 ; par2 = 2 ; par3 = FALSE ;
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')