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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 computationThu, 20 Dec 2018 14:37:49 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2018/Dec/20/t1545313361g4o3ovbdu4zruo7.htm/, Retrieved Sun, 19 May 2024 01:07:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=316129, Retrieved Sun, 19 May 2024 01:07:17 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Simple Linear Regression] [] [2018-12-20 13:37:49] [b533b184177b91add058bbf2204e0bf7] [Current]
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Dataseries X:
2007 30277
2007 30277
1987 47262
2002 110000
1996 101353
1991 70367
1998 70367
1990 70367
1994 70367
2007 110239
2003 110000
1985 46052
1995 70367
1996 70367
2002 86000
2005 110000
2004 88500
1998 70367
2001 88500
1993 70367
2001 88500
1999 101509
2004 110000
2000 101509
1995 70606
2002 91000
1996 77713
2001 91000
1997 77713
2000 91000
2008 122000
2001 91000
2001 2329
1992 47225
1992 28430
2000 85619
1991 52926
1986 53872
2003 105000
2004 105000
1990 25000
2003 86000
1993 53049
2007 112000
1996 75166
2003 68000
1995 51004
1969 70327
2003 151400
2007 90000
1998 83338
1999 83000
2000 61000
2008 86000
1993 55451
1984 33920
2003 81769
1988 38000
1997 59652
1994 55451
1993 55451
1996 55451
1999 63000
1986 53872
2000 63000
2002 85000
2001 58600
2008 133500
2003 58825
1982 35143
2006 89600
2004 59058
1977 16852
2002 58600
1988 34250
2002 90000
1992 50760
2007 93000
2005 91000
1992 38000
1999 77104
2004 81000
1988 42000
1998 75338
1973 28000
2001 77104
1993 50760
1998 30277
2000 30277
1998 30277
1965 22080
2004 85000
1984 45000
2000 76000
2003 77000
1995 69153
2008 115000
2004 116000
2002 91627
2006 116000
1997 77499
2004 113000
2007 113000
2001 108865
1998 108806
2003 91627
1999 30277
1991 69845
1984 44348
2004 113000
2005 77499
2002 108977
1995 77499
1999 30277
1986 12500
2001 50000
1999 33000
1997 19200
2003 46000
2001 138000
2002 90090
1990 48563
1997 74137
2000 138000
2006 158000
1996 74137
2008 160000
2004 90090
1995 70000
2007 158000
1992 73941
2003 138000
1991 73941
2002 138000
2009 220000
2001 90090
1997 78491
2003 90090
1988 73192
1996 70000
1998 78491
1999 138000
1992 10000
1986 10000
1989 10000
1994 16800
2000 25000
2001 25000
1994 16800
1991 3341
1992 19093
2001 42000
1989 40053
1991 3341
1999 76800
1988 5350
1986 5350
1990 14745




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time11 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time11 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316129&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]11 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=316129&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316129&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time11 seconds
R ServerBig Analytics Cloud Computing Center







Linear Regression Model
Y ~ X
coefficients:
EstimateStd. Errort valuePr(>|t|)
(Intercept)1988.4641.0461900.3410
X009.5310
- - -
Residual Std. Err. 6.074 on 156 df
Multiple R-sq. 0.368
95% CI Multiple R-sq. [0.247, 0.463]
Adjusted R-sq. 0.364

\begin{tabular}{lllllllll}
\hline
Linear Regression Model \tabularnewline
Y ~ X \tabularnewline
coefficients: &   \tabularnewline
  & Estimate & Std. Error & t value & Pr(>|t|) \tabularnewline
(Intercept) & 1988.464 & 1.046 & 1900.341 & 0 \tabularnewline
X & 0 & 0 & 9.531 & 0 \tabularnewline
- - -  &   \tabularnewline
Residual Std. Err.  & 6.074  on  156 df \tabularnewline
Multiple R-sq.  & 0.368 \tabularnewline
95% CI Multiple R-sq.  & [0.247, 0.463] \tabularnewline
Adjusted R-sq.  & 0.364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316129&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]1988.464[/C][C]1.046[/C][C]1900.341[/C][C]0[/C][/ROW]
[C]X[/C][C]0[/C][C]0[/C][C]9.531[/C][C]0[/C][/ROW]
[ROW][C]- - - [/C][C] [/C][/ROW]
[ROW][C]Residual Std. Err. [/C][C]6.074  on  156 df[/C][/ROW]
[ROW][C]Multiple R-sq. [/C][C]0.368[/C][/ROW]
[ROW][C]95% CI Multiple R-sq. [/C][C][0.247, 0.463][/C][/ROW]
[ROW][C]Adjusted R-sq. [/C][C]0.364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316129&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316129&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)1988.4641.0461900.3410
X009.5310
- - -
Residual Std. Err. 6.074 on 156 df
Multiple R-sq. 0.368
95% CI Multiple R-sq. [0.247, 0.463]
Adjusted R-sq. 0.364







ANOVA Statistics
DfSum SqMean SqF valuePr(>F)
Tonnage13351.1133351.11390.8430
Residuals1565754.69136.889

\begin{tabular}{lllllllll}
\hline
ANOVA Statistics \tabularnewline
  & Df & Sum Sq & Mean Sq & F value & Pr(>F) \tabularnewline
Tonnage & 1 & 3351.113 & 3351.113 & 90.843 & 0 \tabularnewline
Residuals & 156 & 5754.691 & 36.889 &   &   \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=316129&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]Tonnage[/C][C]1[/C][C]3351.113[/C][C]3351.113[/C][C]90.843[/C][C]0[/C][/ROW]
[ROW][C]Residuals[/C][C]156[/C][C]5754.691[/C][C]36.889[/C][C] [/C][C] [/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=316129&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=316129&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)
Tonnage13351.1133351.11390.8430
Residuals1565754.69136.889



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):
library(boot)
cat1 <- as.numeric(par1)
cat2<- as.numeric(par2)
intercept<-as.logical(par3)
x <- na.omit(t(x))
rsq <- function(formula, data, indices) {
d <- data[indices,] # allows boot to select sample
fit <- lm(formula, data=d)
return(summary(fit)$r.square)
}
xdf<-data.frame(na.omit(t(y)))
(V1<-dimnames(y)[[1]][cat1])
(V2<-dimnames(y)[[1]][cat2])
xdf <- data.frame(xdf[[cat1]], xdf[[cat2]])
names(xdf)<-c('Y', 'X')
if(intercept == FALSE) (lmxdf<-lm(Y~ X - 1, data = xdf) ) else (lmxdf<-lm(Y~ X, data = xdf) )
(results <- boot(data=xdf, statistic=rsq, R=1000, formula=Y~X))
sumlmxdf<-summary(lmxdf)
(aov.xdf<-aov(lmxdf) )
(anova.xdf<-anova(lmxdf) )
load(file='createtable')
a<-table.start()
nc <- ncol(sumlmxdf$'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, '95% CI Multiple R-sq. ',1,TRUE)
a<-table.element(a, paste('[',round(boot.ci(results,type='bca')$bca[1,4], digits=3),', ', round(boot.ci(results,type='bca')$bca[1,5], digits=3), ']',sep='') ,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$'Mean Sq'[2], digits=3))
a<-table.element(a, ' ')
a<-table.element(a, ' ')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
bitmap(file='regressionplot.png')
plot(Y~ X, data=xdf, xlab=V2, ylab=V1, main='Regression Solution')
if(intercept == TRUE) abline(coef(lmxdf), col='red')
if(intercept == FALSE) abline(0.0, coef(lmxdf), col='red')
dev.off()
library(car)
bitmap(file='residualsQQplot.png')
qqPlot(resid(lmxdf), main='QQplot of Residuals of Fit')
dev.off()
bitmap(file='residualsplot.png')
plot(xdf$X, resid(lmxdf), main='Scatterplot of Residuals of Model Fit')
dev.off()
bitmap(file='cooksDistanceLmplot.png')
plot(lmxdf, which=4)
dev.off()