Publications by Jagdish Chhabria
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Problem Set 1 Calculate the product of a matrix and its transpose. Set up matrix A (A = matrix( c( 1, 2, 3, -1, 0, 4), nrow=2, byrow=TRUE)) ## [,1] [,2] [,3] ## [1,] 1 2 3 ## [2,] -1 0 4 Define X= \[AA^T\] (X = A %*% t(A)) ## [,1] [,2] ## [1,] 14 11 ## [2,] 11 17 Define Y= \[A^TA\] (Y = t(A) %*% A) ## ...
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Problem Set 1 What is the rank of the matrix A? \[A = \begin{bmatrix}1&2&3&4\\-1&0&1&3\\0&1&-2&1\\5&4&-2&-3\\\end{bmatrix}\] The rank of an invertible matrix is equal to its dimension. So let’s check whether this matrix is invertible by calculating it’s determinant. A<-matrix(c(1,2,3,4,-1,0,1,3,0,1,-2,1,5,4,-2,-3),nrow=4,byrow=TRUE) det.ma...
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DS605_Assignment_1_Jagdish_Chhabria
1. Problem Set 1 1) Calculate the dot product u:v where u = [0:5; 0:5] and v = [3;4] u<-c(0.5,0.5) v<-c(3,-4) dot.u.v=u%*%v cat("The dot product of u and v is:",dot.u.v,"\n") ## The dot product of u and v is: -0.5 2) What are the lengths of u and v? length.u<-sqrt(u%*%u) cat("The length of u is:",length.u,"\n") ## The length of u is: 0.7071...
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DATA 605 Assignment 2 Jagdish Chhabria
Problem set 1 (1) Show that \[A^TA \neq AA^T\] in general. (Proof and demonstration.) Let \[A = \begin{bmatrix}a & b\\ c & d\\ \end{bmatrix}\] and let \[A^T = \begin{bmatrix}e & f\\ g & h\\ \end{bmatrix}\] Then \[AA^T = \begin{bmatrix}ae+bg & af+bh\\ ce+dg & cf+dh\\ \end{bmatrix}\] and \[A^TA = \begin{bmatrix}ea+fc & eb+fd\\ ga+hc & gb+hd...
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Let X be a random variable normally distributed with parameters \(\mu\) = 70 and \(\sigma\) = 10 Estimate: (a) P(X > 50) We calculate the standard normal variable as follows: \(Z=\frac{Y-\mu}{\sigma}\) P(X>50)=P(Z>50-70/10)=P(Z>-2)=1-P(Z<-2) 1-pnorm(-2,0,1) ## [1] 0.9772499 P(X < 60) We calculate the standard normal variable as follows: \(Z=\f...
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1. Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, standard error,and p-values only. Discuss whether the assumptions of simple linear regression met. library(tidyverse) ## -- Attaching packages --------------------------------------------------...
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1.Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. (5.6, 8.8), (6.3, 12.4), (7, 14.8), (7.7, 18.2), (8.4, 20.8) y<-c(8.8,12.4,14.8,18.2,20.8) X<-c(5.6,6.3,7,7.7,8.4) model1<-lm(y~X) summary(model1) ## ## Call: ## lm(formula = y ~ X) ## ## Residuals: ## 1 ...
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Principles of Data Visualization and Introduction to ggplot2 I have provided you with data about the 5,000 fastest growing companies in the US, as compiled by Inc. magazine. lets read this in: inc <- read.csv("https://raw.githubusercontent.com/charleyferrari/CUNY_DATA_608/master/module1/Data/inc5000_data.csv", header= TRUE) And lets preview this...
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R Markdown This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com. When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within t...
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The Physical Bank Branch - Asset or Liability? A lot has been said about the utility of bank branches over the years - as a way to bank the unbanked, extend small business credit, aid in educating people about financial literacy. Several studies since the Great Financial Crisis have shown a clear increase in adoption of digital banking for the mo...
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