R Programming: part#5

CODE

# Q. (a) Check whether the data follows multivariate normal or not. Use the result

# di = (xi − x) S −1 (xi − x) ∼ χ2 where xi ∼ Nd (μ, σ 2 ) and x and S is the mean and the standard

# deviation. Identify if there is any outlier in the data. Use package R.

mnormal = function()

{

####### --------- Lybraries ------------#####

library("MASS");

require(graphics);

data_set=read.table("m-ba4c9807.txt",header=TRUE);

BA=data_set[1];

ABT=data_set[2];

MOT=data_set[3];

GM=data_set[4];

BA=t(BA);

ABT=t(ABT);

MOT=t(MOT);

GM=t(GM);

# 4 figures arranged in 2 rows and 2 columns

#attach(mtcars)

#par(mfrow=c(2,2))

# Graphical Assessment of Multivariate Normality

x = as.matrix(data_set) # n x p numeric matrix

#print(x)

center = colMeans(x) # centroid

n = nrow(x);

p = ncol(x);

cov = cov(x);

d = mahalanobis(x,center,cov) # distances

print(t(center))

print(n)

print(p)

print(t(cov))

print(d)

qqplot(qchisq(ppoints(n), df=p), d, main="QQ Plot Assessing Multivariate Normality", ylab="Mahalanobis D2")

abline(a=0,b=1)

}

# Q no. (b) Find find out the correlation matrix. Make the graphical representation.

# Extra : Write a program of your own in SAS to calculate Spearman rank correlation and

# Kendal’s tau between BA and ABT data.

corr = function()

{

####### --------- Lybraries ------------#####

library("MASS");

require(graphics);

require(corrgram);

data_set=read.table("m-ba4c9807.txt",header=TRUE);

BA=data_set[1];

ABT=data_set[2];

MOT=data_set[3];

GM=data_set[4];

BA=t(BA);

ABT=t(ABT);

MOT=t(MOT);

GM=t(GM);

# 4 figures arranged in 2 rows and 2 columns

#attach(mtcars)

#par(mfrow=c(2,2), pty="s")

# Graphical Assessment of Multivariate Normality

x = as.matrix(data_set) # n x p numeric matrix

#print(x)

corrp = cor(x, y = NULL, use = "everything", method = "pearson" );

corrk = cor(x, y = NULL, use = "everything", method = "kendall" );

corrs = cor(x, y = NULL, use = "everything", method = "spearman" );

#print(corrp);

#print(corrk);

#print(corrs);

#cor(x, y = NULL, use = "everything", method = c("pearson", "kendall", "spearman"))

#par(new=TRUE)

corrgram(corrp, type='cor', order=TRUE, lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main=" Pearson: Car Milage Data in PC2/PC1 Order");

corrgram(x, type='data', order=TRUE, lower.panel=panel.ellipse, upper.panel=panel.pts, text.panel=panel.txt, diag.panel=panel.minmax, main="Pearson: Car Milage Data in PC2/PC1 Order");

corrgram(corrp, type='cor', order=NULL, lower.panel=panel.shade, upper.panel=NULL, text.panel=panel.txt, main="Pearson: Car Milage Data (unsorted)");

corrgram(corrp, type='cor', order="OLO", lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main="Pearson: Car Milage Data in OLO Order");

corrgram(corrk, type='cor', order=TRUE, lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main=" Kendall: Car Milage Data in PC2/PC1 Order");

corrgram(x, type='data', order=TRUE, lower.panel=panel.ellipse, upper.panel=panel.pts, text.panel=panel.txt, diag.panel=panel.minmax, main="Kendall: Car Milage Data in PC2/PC1 Order");

corrgram(corrk, type='cor', order=NULL, lower.panel=panel.shade, upper.panel=NULL, text.panel=panel.txt, main="Kendall: Car Milage Data (unsorted)");

corrgram(corrk, type='cor', order="OLO", lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main="Kendall: Car Milage Data in OLO Order");

corrgram(corrs, type='cor', order=TRUE, lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main=" Spearman: Car Milage Data in PC2/PC1 Order");

corrgram(x, type='data', order=TRUE, lower.panel=panel.ellipse, upper.panel=panel.pts, text.panel=panel.txt, diag.panel=panel.minmax, main="Spearman: Car Milage Data in PC2/PC1 Order");

corrgram(corrs, type='cor', order=NULL, lower.panel=panel.shade, upper.panel=NULL, text.panel=panel.txt, main="Spearman: Car Milage Data (unsorted)");

corrgram(corrs, type='cor', order="OLO", lower.panel=panel.shade, upper.panel=panel.pie, text.panel=panel.txt, main="Spearman: Car Milage Data in OLO Order");

#corrgram(corrp, type='cor', order = "OLO", panel=panel.shade, lower.panel=panel, upper.panel=panel, diag.panel=NULL, text.panel=textPanel, label.pos=0.5, label.srt=0, cex.labels=NULL, font.labels=1, row1attop=TRUE, dir="left", gap=0, abs=FALSE)

}

# Q no. (c) Make one sample t-tests separately to check whether there is enough evidence for the

# fact that mean of the marginals are zero. Use both R and SAS. Assume tests are of size 5%.

ttest = function()

{

####### --------- Lybraries ------------#####

library("MASS");

require(graphics);

data_set=read.table("m-ba4c9807.txt",header=TRUE);

BA=data_set[1];

ABT=data_set[2];

MOT=data_set[3];

GM=data_set[4];

BA=t(BA);

ABT=t(ABT);

MOT=t(MOT);

GM=t(GM);

# 4 figures arranged in 2 rows and 2 columns

#attach(mtcars)

#par(mfrow=c(2,2))

# Graphical Assessment of Multivariate Normality

x = as.matrix(data_set) # n x p numeric matrix

#print(x)

BAt=t.test(BA,mu=0);

print(BAt);

ABTt=t.test(ABT,mu=0);

print(ABTt);

MOTt=t.test(MOT,mu=0);

print(MOTt);

GMt=t.test(GM,mu=0);

print(GMt);

}

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