Please prepare your submission in a document (Word or PDF) and clearly label all answers and output with their corresponding question number and part.

install.packages("psych") install.packages("GPArotation") install.packages("car") library("car") library("psych") library("GPArotation") library("hornpa") # Question 1 #part a # Create vectors for covariance matrix bears. vector1 <- c(3266.46, 1343.97, 731.54, 1175.50, 162.68, 238.37) vector2 <- c(1343.97, 721.91, 324.25, 537.35, 80.17, 117.73) vector3 <- c(731.54, 324.25, 179.28, 281.17, 39.15, 56.80) vector4 <- c(1175.50, 537.35, 281.17, 474.98, 63.73, 94.85) vector5 <- c(162.68, 80.17, 39.15, 63.73, 9.95, 13.88) vector6 <- c(238.37, 117.73, 56.80, 94.85, 13.88, 21.26) # Assigning names of variables in covariance matrix. column.names <- c("weight", "body length", "neck circumference", "girth", "head length", "head width") row.names <- c("weight", "body length", "neck circumference", "girth", "head length", "head width") matrix.names print(bears) #, , Covariance Matrix # weight body length neck circumference girth head length head width # weight 3266.46 1343.97 731.54 1175.50 162.68 238.37 # body length 1343.97 721.91 324.25 537.35 80.17 117.73 # neck circumference 731.54 324.25 179.28 281.17 39.15 56.80 # girth 1175.50 537.35 281.17 474.98 63.73 94.85 # head length 162.68 80.17 39.15 63.73 9.95 13.88 # head width 238.37 117.73 56.80 94.85 13.88 21.26 # Part b # reading bears covariance matrix bears = matrix(c(3266.46, 1343.97, 731.54, 1175.50, 162.68, 238.37, 1343.97, 721.91, 324.25, 537.35, 80.17, 117.73, 731.54, 324.25, 179.28, 281.17, 39.15, 56.80, 1175.50, 537.35, 281.17, 474.98, 63.73, 94.85, 162.68, 80.17, 39.15, 63.73, 9.95, 13.88, 238.37, 117.73, 56.80, 94.85, 13.88, 21.26), 6, 6) #print(bears) # finding eigen values print(eigen(bears)) # output # > print(eigen(bears)) # eigen() decomposition # $values # [1] 4478.8738170 152.4661641 32.3238574 8.1167581 1.5168560 0.5425475 # bears.PC.cov = prcomp(bears, scale=TRUE) #bears.pca <- prcomp(bears, center = TRUE, scale. = TRUE) #print(bears.pca) #print(summary(bears.pca)) #cov_mat <- bears #eigen(cov_mat) # PCA on bears bears_pca <- principal(bears, nfactor = 6, covar=F, rotate="none") #bears_pca$values bears_pca$loadings # scree plot plot(bears_pca$values, type="l") hornpa(k=6, size=120, reps=500, seed=30005) # Question 2 # part a # reading wine.csv into R Dataframe csv_data <- read.csv(file = '/home/vivekg/Desktop/7Oct_11PM/Solution/wine 1.csv') # printing head and tail of the dataframe print(head(csv_data, 10)) print(tail(csv_data, 10)) # printing names of columns names(csv_data) # selecting relevant columns for analysis wine <- csv_data[c("chem3","chem5","chem6","chem7","chem8","chem9")] print(head(wine, 10)) # Check for missing value sum(is.na(wine)) # Part b summary(wine) sd(wine$chem3) sd(wine$chem5) sd(wine$chem6) sd(wine$chem7) sd(wine$chem8) sd(wine$chem9) # Part c boxplot(wine$chem9, ylab = "chem3" ) # boxplot visualization for detecting univariate outlier boxplot(wine) summary(wine) outlier(wine) # Part d # Calculating mahalanobis distance md cutoff) excluded_mh <- names_outliers_MH #data_clean_mh <- wine[-excluded_mh, ] # showing list of outlier points wine[excluded_mh, ] summary(data_clean_mh) # Part e # The function pairs.panels [in psych package] can be also used to create a scatter plot of matrices, # with bivariate scatter plots below the diagonal, histograms on the diagonal, and the Pearson correlation above the diagonal. pairs.panels(wine, method = "pearson", # correlation method hist.col = "#00AFBB", density = TRUE, # show density plots ) # Part f # bears.PC.cov = prcomp(bears, scale=TRUE) # wine_pca <- prcomp(wine, center = FALSE, scale. = TRUE) # print(wine_pca) # print(summary(wine_pca)) # cov_mat <-cov(wine) # eigen(cov_mat) wine_pca <- principal(wine, nfactor = 6, covar=F, rotate="none") wine_pca$values wine_pca$loadings # scree plot plot(wine_pca$values, type="l") # parallal analysis for finding components to retain hornpa(k=6, size=120, reps=500, seed=0) # Part g # Part h w <-cov(wine) eigen(w) # Part i # Question 3 # Reading household data house_data <- read.csv(file = '/home/vivekg/Desktop/7Oct_11PM/Solution/household2 1.csv') #print(head(house_data, 10)) names(house_data) summary(house_data) sum(is.na(house_data)) cor(house_data) # Part a house<-house_data[, 3:11] cor(house) KMO(house) bartlett.test(house) # Part b # Text Done # Part c summary(house) # Part d KMO(house) bartlett.test(house) fa <-fa(house, nfactors=9, fm="minres", rotate="none") print(fa) fa5 <-fa(house, nfactors=5, fm="minres", rotate="none") print(fa5) fa$loadings fa5$loadings fa.parallel(house, fa = "fa") # Part e fa2 <-fa(house, nfactors=2, fm="minres", rotate="none") print(fa2) fa2$loadings # Part f #Second Eigenvalue # Part g # rotation of factors fa2_vm <-fa(house, nfactors=2, fm="minres", rotate="varimax") fa2_vm$loadings # Part h fa2_ob <-fa(house, nfactors=2, fm="minres", rotate="oblimin") fa2_ob$loadings # Part i # Part j