::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes a series of graphical tools for the purpose of Explorative Data Analysis. If we consider the model

response = constant + beta * explanatory variable + random component

then the following assumptions can be tested by the use of this software module:

are the data autocorrelated? (The model assumes no autocorrelation) is the random component generated by a fixed distribution? (The model assumes a fixed distribution) is the deterministic component constant? (The model assumes that the distribution has a fixed location) does the random component have a fixed variation? (The model assumes a distribution with fixed variation)

Enter (or paste) your data delimited by hard returns.

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Source code of R module

par1 <- as.numeric(par1) par2 <- as.numeric(par2) x <- as.ts(x) y <- as.ts(y) mylm <- lm(y~x) cbind(mylm$resid) library(lattice) bitmap(file="pic1.png") plot(y,type="l",main="Run Sequence Plot of Y[t]",xlab="time or index",ylab="value") grid() dev.off() bitmap(file="pic1a.png") plot(x,type="l",main="Run Sequence Plot of X[t]",xlab="time or index",ylab="value") grid() dev.off() bitmap(file="pic1b.png") plot(x,y,main="Scatter Plot",xlab="X[t]",ylab="Y[t]") grid() dev.off() bitmap(file="pic1c.png") plot(mylm$resid,type="l",main="Run Sequence Plot of e[t]",xlab="time or index",ylab="value") grid() dev.off() bitmap(file="pic2.png") hist(mylm$resid,main="Histogram of e[t]") dev.off() bitmap(file="pic3.png") if (par1 > 0) { densityplot(~mylm$resid,col="black",main=paste("Density Plot of e[t] bw = ",par1),bw=par1) } else { densityplot(~mylm$resid,col="black",main="Density Plot of e[t]") } dev.off() bitmap(file="pic4.png") qqnorm(mylm$resid,main="QQ plot of e[t]") qqline(mylm$resid) grid() dev.off() if (par2 > 0) { bitmap(file="pic5.png") acf(mylm$resid,lag.max=par2,main="Residual Autocorrelation Function") grid() dev.off() } summary(x) load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Model: Y[t] = c + b X[t] + e[t]",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"c",1,TRUE) a<-table.element(a,mylm$coeff[[1]]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"b",1,TRUE) a<-table.element(a,mylm$coeff[[2]]) 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,"Descriptive Statistics about e[t]",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"# observations",header=TRUE) a<-table.element(a,length(mylm$resid)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"minimum",header=TRUE) a<-table.element(a,min(mylm$resid)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Q1",header=TRUE) a<-table.element(a,quantile(mylm$resid,0.25)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"median",header=TRUE) a<-table.element(a,median(mylm$resid)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"mean",header=TRUE) a<-table.element(a,mean(mylm$resid)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Q3",header=TRUE) a<-table.element(a,quantile(mylm$resid,0.75)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"maximum",header=TRUE) a<-table.element(a,max(mylm$resid)) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")

Cite this software as:

Wessa P., (2017), Bivariate Explorative Data Analysis (v1.0.3) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL https://www.wessa.net/rwasp_edabi.wasp/

The R code is based on :

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03.

Diethelm Wuertz, et. al.(2006)., fExtremes: Rmetrics - Extreme Financial Market Data. R package, version 221.10065., http://www.rmetrics.org

Deepayan Sarkar (2006). lattice: Lattice Graphics. R package version 0.13-8.

Bell Lab Trellis Page: URL: http://cm.bell-labs.com/cm/ms/departments/sia/project/trellis/

Cleveland, W.S. (1993), Visualizing Data

Becker, R.A., Cleveland, W.S. and Shyu, M., The Visual Design and Control of Trellis Display, Journal of Computational and Graphical Statistics

To cite Wessa.net in publications use:
Wessa, P. (2024), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
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