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Description of Statistical Computation

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 computationMon, 29 Nov 2021 17:52:57 +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/2021/Nov/29/t1638204779jg7d6ita577ozfi.htm/, Retrieved Sat, 11 May 2024 14:15:05 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 11 May 2024 14:15:05 +0200
QR Codes:

Original text written by user:555
IsPrivate?No (this computation is public)
User-defined keywords555
Estimated Impact0

Tree of Dependent Computations

Dataset

Dataseries X:
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Boxplots 
'1'	'Trt'	'NoCue'	'Neut'	433.5
'1'	'Trt'	'NoCue'	'Cong'	423.9
'1'	'Trt'	'NoCue'	'Inc'	490.9
'1'	'Trt'	'Cent'	'Neut'	385.2
'1'	'Trt'	'Cent'	'Cong'	368.6
'1'	'Trt'	'Cent'	'Inc'	473.4
'1'	'Trt'	'Double'	'Neut'	378.9
'1'	'Trt'	'Double'	'Cong'	378.9
'1'	'Trt'	'Double'	'Inc'	455.4
'1'	'Trt'	'Spatial'	'Neut'	328.1
'1'	'Trt'	'Spatial'	'Cong'	350.2
'1'	'Trt'	'Spatial'	'Inc'	407.2
'2'	'Trt'	'NoCue'	'Neut'	436.4
'2'	'Trt'	'NoCue'	'Cong'	441.9
'2'	'Trt'	'NoCue'	'Inc'	483.3
'2'	'Trt'	'Cent'	'Neut'	374.2
'2'	'Trt'	'Cent'	'Cong'	389.8
'2'	'Trt'	'Cent'	'Inc'	455.7
'2'	'Trt'	'Double'	'Neut'	357.0
'2'	'Trt'	'Double'	'Cong'	384.2
'2'	'Trt'	'Double'	'Inc'	433.0
'2'	'Trt'	'Spatial'	'Neut'	339.4
'2'	'Trt'	'Spatial'	'Cong'	337.6
'2'	'Trt'	'Spatial'	'Inc'	421.0
'3'	'Trt'	'NoCue'	'Neut'	428.7
'3'	'Trt'	'NoCue'	'Cong'	428.1
'3'	'Trt'	'NoCue'	'Inc'	503.3
'3'	'Trt'	'Cent'	'Neut'	371.2
'3'	'Trt'	'Cent'	'Cong'	368.0
'3'	'Trt'	'Cent'	'Inc'	436.5
'3'	'Trt'	'Double'	'Neut'	392.3
'3'	'Trt'	'Double'	'Cong'	356.3
'3'	'Trt'	'Double'	'Inc'	432.7
'3'	'Trt'	'Spatial'	'Neut'	331.3
'3'	'Trt'	'Spatial'	'Cong'	334.6
'3'	'Trt'	'Spatial'	'Inc'	431.4
'4'	'Trt'	'NoCue'	'Neut'	415.5
'4'	'Trt'	'NoCue'	'Cong'	433.3
'4'	'Trt'	'NoCue'	'Inc'	498.5
'4'	'Trt'	'Cent'	'Neut'	384.8
'4'	'Trt'	'Cent'	'Cong'	383.2
'4'	'Trt'	'Cent'	'Inc'	438.5
'4'	'Trt'	'Double'	'Neut'	370.3
'4'	'Trt'	'Double'	'Cong'	399.4
'4'	'Trt'	'Double'	'Inc'	445.9
'4'	'Trt'	'Spatial'	'Neut'	320.7
'4'	'Trt'	'Spatial'	'Cong'	342.8
'4'	'Trt'	'Spatial'	'Inc'	407.0
'5'	'Trt'	'NoCue'	'Neut'	429.1
'5'	'Trt'	'NoCue'	'Cong'	436.9
'5'	'Trt'	'NoCue'	'Inc'	499.0
'5'	'Trt'	'Cent'	'Neut'	378.1
'5'	'Trt'	'Cent'	'Cong'	394.6
'5'	'Trt'	'Cent'	'Inc'	471.4
'5'	'Trt'	'Double'	'Neut'	370.6
'5'	'Trt'	'Double'	'Cong'	370.7
'5'	'Trt'	'Double'	'Inc'	447.1
'5'	'Trt'	'Spatial'	'Neut'	332.5
'5'	'Trt'	'Spatial'	'Cong'	329.9
'5'	'Trt'	'Spatial'	'Inc'	418.3
'6'	'Trt'	'NoCue'	'Neut'	435.3
'6'	'Trt'	'NoCue'	'Cong'	422.7
'6'	'Trt'	'NoCue'	'Inc'	480.0
'6'	'Trt'	'Cent'	'Neut'	390.7
'6'	'Trt'	'Cent'	'Cong'	366.9
'6'	'Trt'	'Cent'	'Inc'	461.5
'6'	'Trt'	'Double'	'Neut'	354.1
'6'	'Trt'	'Double'	'Cong'	385.6
'6'	'Trt'	'Double'	'Inc'	435.4
'6'	'Trt'	'Spatial'	'Neut'	336.3
'6'	'Trt'	'Spatial'	'Cong'	335.0
'6'	'Trt'	'Spatial'	'Inc'	399.6
'7'	'Trt'	'NoCue'	'Neut'	435.4
'7'	'Trt'	'NoCue'	'Cong'	412.3
'7'	'Trt'	'NoCue'	'Inc'	484.9
'7'	'Trt'	'Cent'	'Neut'	387.8
'7'	'Trt'	'Cent'	'Cong'	380.5
'7'	'Trt'	'Cent'	'Inc'	443.4
'7'	'Trt'	'Double'	'Neut'	361.9
'7'	'Trt'	'Double'	'Cong'	346.4
'7'	'Trt'	'Double'	'Inc'	452.1
'7'	'Trt'	'Spatial'	'Neut'	351.1
'7'	'Trt'	'Spatial'	'Cong'	345.6
'7'	'Trt'	'Spatial'	'Inc'	424.7
'8'	'Trt'	'NoCue'	'Neut'	402.9
'8'	'Trt'	'NoCue'	'Cong'	412.7
'8'	'Trt'	'NoCue'	'Inc'	502.4
'8'	'Trt'	'Cent'	'Neut'	387.8
'8'	'Trt'	'Cent'	'Cong'	358.2
'8'	'Trt'	'Cent'	'Inc'	437.8
'8'	'Trt'	'Double'	'Neut'	357.4
'8'	'Trt'	'Double'	'Cong'	401.8
'8'	'Trt'	'Double'	'Inc'	459.5
'8'	'Trt'	'Spatial'	'Neut'	360.1
'8'	'Trt'	'Spatial'	'Cong'	335.6
'8'	'Trt'	'Spatial'	'Inc'	405.1
'9'	'Trt'	'NoCue'	'Neut'	419.2
'9'	'Trt'	'NoCue'	'Cong'	420.1
'9'	'Trt'	'NoCue'	'Inc'	500.0
'9'	'Trt'	'Cent'	'Neut'	386.1
'9'	'Trt'	'Cent'	'Cong'	381.4
'9'	'Trt'	'Cent'	'Inc'	460.0
'9'	'Trt'	'Double'	'Neut'	370.2
'9'	'Trt'	'Double'	'Cong'	369.4
'9'	'Trt'	'Double'	'Inc'	445.4
'9'	'Trt'	'Spatial'	'Neut'	351.2
'9'	'Trt'	'Spatial'	'Cong'	336.6
'9'	'Trt'	'Spatial'	'Inc'	422.3
'10'	'Trt'	'NoCue'	'Neut'	441.6
'10'	'Trt'	'NoCue'	'Cong'	432.2
'10'	'Trt'	'NoCue'	'Inc'	516.9
'10'	'Trt'	'Cent'	'Neut'	382.5
'10'	'Trt'	'Cent'	'Cong'	376.9
'10'	'Trt'	'Cent'	'Inc'	442.9
'10'	'Trt'	'Double'	'Neut'	385.6
'10'	'Trt'	'Double'	'Cong'	385.9
'10'	'Trt'	'Double'	'Inc'	457.8
'10'	'Trt'	'Spatial'	'Neut'	342.2
'10'	'Trt'	'Spatial'	'Cong'	331.5
'10'	'Trt'	'Spatial'	'Inc'	408.1
'11'	'Ctrl'	'NoCue'	'Neut'	446.7
'11'	'Ctrl'	'NoCue'	'Cong'	433.8
'11'	'Ctrl'	'NoCue'	'Inc'	517.3
'11'	'Ctrl'	'Cent'	'Neut'	380.3
'11'	'Ctrl'	'Cent'	'Cong'	371.6
'11'	'Ctrl'	'Cent'	'Inc'	493.7
'11'	'Ctrl'	'Double'	'Neut'	390.9
'11'	'Ctrl'	'Double'	'Cong'	394.2
'11'	'Ctrl'	'Double'	'Inc'	482.1
'11'	'Ctrl'	'Spatial'	'Neut'	345.2
'11'	'Ctrl'	'Spatial'	'Cong'	330.7
'11'	'Ctrl'	'Spatial'	'Inc'	391.5
'12'	'Ctrl'	'NoCue'	'Neut'	420.7
'12'	'Ctrl'	'NoCue'	'Cong'	442.7
'12'	'Ctrl'	'NoCue'	'Inc'	513.3
'12'	'Ctrl'	'Cent'	'Neut'	374.7
'12'	'Ctrl'	'Cent'	'Cong'	373.0
'12'	'Ctrl'	'Cent'	'Inc'	486.7
'12'	'Ctrl'	'Double'	'Neut'	380.0
'12'	'Ctrl'	'Double'	'Cong'	374.9
'12'	'Ctrl'	'Double'	'Inc'	495.7
'12'	'Ctrl'	'Spatial'	'Neut'	352.6
'12'	'Ctrl'	'Spatial'	'Cong'	347.6
'12'	'Ctrl'	'Spatial'	'Inc'	424.4
'13'	'Ctrl'	'NoCue'	'Neut'	422.1
'13'	'Ctrl'	'NoCue'	'Cong'	424.2
'13'	'Ctrl'	'NoCue'	'Inc'	503.6
'13'	'Ctrl'	'Cent'	'Neut'	364.8
'13'	'Ctrl'	'Cent'	'Cong'	364.3
'13'	'Ctrl'	'Cent'	'Inc'	474.6
'13'	'Ctrl'	'Double'	'Neut'	383.8
'13'	'Ctrl'	'Double'	'Cong'	363.6
'13'	'Ctrl'	'Double'	'Inc'	477.1
'13'	'Ctrl'	'Spatial'	'Neut'	338.0
'13'	'Ctrl'	'Spatial'	'Cong'	332.8
'13'	'Ctrl'	'Spatial'	'Inc'	420.3
'14'	'Ctrl'	'NoCue'	'Neut'	431.7
'14'	'Ctrl'	'NoCue'	'Cong'	436.4
'14'	'Ctrl'	'NoCue'	'Inc'	481.9
'14'	'Ctrl'	'Cent'	'Neut'	376.7
'14'	'Ctrl'	'Cent'	'Cong'	388.7
'14'	'Ctrl'	'Cent'	'Inc'	484.4
'14'	'Ctrl'	'Double'	'Neut'	383.4
'14'	'Ctrl'	'Double'	'Cong'	363.5
'14'	'Ctrl'	'Double'	'Inc'	467.4
'14'	'Ctrl'	'Spatial'	'Neut'	315.9
'14'	'Ctrl'	'Spatial'	'Cong'	354.7
'14'	'Ctrl'	'Spatial'	'Inc'	408.6
'15'	'Ctrl'	'NoCue'	'Neut'	430.9
'15'	'Ctrl'	'NoCue'	'Cong'	446.8
'15'	'Ctrl'	'NoCue'	'Inc'	505.1
'15'	'Ctrl'	'Cent'	'Neut'	372.7
'15'	'Ctrl'	'Cent'	'Cong'	382.8
'15'	'Ctrl'	'Cent'	'Inc'	483.5
'15'	'Ctrl'	'Double'	'Neut'	369.3
'15'	'Ctrl'	'Double'	'Cong'	378.1
'15'	'Ctrl'	'Double'	'Inc'	461.1
'15'	'Ctrl'	'Spatial'	'Neut'	342.6
'15'	'Ctrl'	'Spatial'	'Cong'	336.2
'15'	'Ctrl'	'Spatial'	'Inc'	421.7
'16'	'Ctrl'	'NoCue'	'Neut'	425.6
'16'	'Ctrl'	'NoCue'	'Cong'	417.5
'16'	'Ctrl'	'NoCue'	'Inc'	495.2
'16'	'Ctrl'	'Cent'	'Neut'	373.9
'16'	'Ctrl'	'Cent'	'Cong'	378.6
'16'	'Ctrl'	'Cent'	'Inc'	490.9
'16'	'Ctrl'	'Double'	'Neut'	381.9
'16'	'Ctrl'	'Double'	'Cong'	358.5
'16'	'Ctrl'	'Double'	'Inc'	464.4
'16'	'Ctrl'	'Spatial'	'Neut'	340.3
'16'	'Ctrl'	'Spatial'	'Cong'	351.1
'16'	'Ctrl'	'Spatial'	'Inc'	408.4
'17'	'Ctrl'	'NoCue'	'Neut'	421.6
'17'	'Ctrl'	'NoCue'	'Cong'	432.6
'17'	'Ctrl'	'NoCue'	'Inc'	502.8
'17'	'Ctrl'	'Cent'	'Neut'	386.0
'17'	'Ctrl'	'Cent'	'Cong'	389.3
'17'	'Ctrl'	'Cent'	'Inc'	487.0
'17'	'Ctrl'	'Double'	'Neut'	369.5
'17'	'Ctrl'	'Double'	'Cong'	368.7
'17'	'Ctrl'	'Double'	'Inc'	482.0
'17'	'Ctrl'	'Spatial'	'Neut'	350.8
'17'	'Ctrl'	'Spatial'	'Cong'	333.9
'17'	'Ctrl'	'Spatial'	'Inc'	421.7
'18'	'Ctrl'	'NoCue'	'Neut'	432.5
'18'	'Ctrl'	'NoCue'	'Cong'	413.6
'18'	'Ctrl'	'NoCue'	'Inc'	484.4
'18'	'Ctrl'	'Cent'	'Neut'	388.4
'18'	'Ctrl'	'Cent'	'Cong'	374.6
'18'	'Ctrl'	'Cent'	'Inc'	475.4
'18'	'Ctrl'	'Double'	'Neut'	380.8
'18'	'Ctrl'	'Double'	'Cong'	372.6
'18'	'Ctrl'	'Double'	'Inc'	464.2
'18'	'Ctrl'	'Spatial'	'Neut'	337.4
'18'	'Ctrl'	'Spatial'	'Cong'	338.3
'18'	'Ctrl'	'Spatial'	'Inc'	407.7
'19'	'Ctrl'	'NoCue'	'Neut'	436.6
'19'	'Ctrl'	'NoCue'	'Cong'	421.7
'19'	'Ctrl'	'NoCue'	'Inc'	494.7
'19'	'Ctrl'	'Cent'	'Neut'	393.5
'19'	'Ctrl'	'Cent'	'Cong'	393.9
'19'	'Ctrl'	'Cent'	'Inc'	482.2
'19'	'Ctrl'	'Double'	'Neut'	368.6
'19'	'Ctrl'	'Double'	'Cong'	384.2
'19'	'Ctrl'	'Double'	'Inc'	477.8
'19'	'Ctrl'	'Spatial'	'Neut'	344.0
'19'	'Ctrl'	'Spatial'	'Cong'	339.6
'19'	'Ctrl'	'Spatial'	'Inc'	392.7
'20'	'Ctrl'	'NoCue'	'Neut'	412.5
'20'	'Ctrl'	'NoCue'	'Cong'	424.3
'20'	'Ctrl'	'NoCue'	'Inc'	488.2
'20'	'Ctrl'	'Cent'	'Neut'	372.9
'20'	'Ctrl'	'Cent'	'Cong'	393.0
'20'	'Ctrl'	'Cent'	'Inc'	475.3
'20'	'Ctrl'	'Double'	'Neut'	384.2
'20'	'Ctrl'	'Double'	'Cong'	366.5
'20'	'Ctrl'	'Double'	'Inc'	460.0
'20'	'Ctrl'	'Spatial'	'Neut'	338.1
'20'	'Ctrl'	'Spatial'	'Cong'	372.3
'20'	'Ctrl'	'Spatial'	'Inc'	418.3

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
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()