MATLAB and R Programming (ME-705) - Important Questions

Write an R script that performs the following steps: (a) Create a $m\times n$ matrix filled column-wise with integers from 1 to $mn$ where $m=4$ and $n=5$. (b) Print the matrix to the console. (c) Add a new column which contains the column-wise sums. (d) Extract and print the submatrix consisting of rows 2 to 4 and columns 1 and 3. Provide the exact R commands and the expected output.

Using R, create a data frame with the following columns: ID (integer), Name (character), Age (numeric), Gender (factor with levels 'M' and 'F'), Salary (numeric). Append one new row to this data frame. Then subset the data frame to obtain only rows where Age $>$ 30 and Gender == 'F'. Show the R code used and the resulting data frame.

Explain the basic R data types: numeric, integer, logical, character and complex. For each type give a one-line R example. Demonstrate arithmetic operators ($+$, $-$, $*$, $\,$$/$\,$, $^$) and logical operators ($>$, $\ge$, $<$, $\le$, $==$ , $!=$, $\&$, $|$, $!$) with at least two example expressions showing input and R output.

What are factors in R and why are they used? Convert the numeric vector c(1,2,2,3,1) into a factor with labels 'Low', 'Medium', 'High' and show the R command. Explain how to create an ordered factor for the same data and describe one situation where an ordered factor is required for modeling.

Describe the steps to install R and RStudio on a Windows machine. Explain how to install a CRAN package (for example, 'ggplot2') and how to load it in an R session. Also describe how to update all installed packages.

Write an R function that accepts an $n\times n$ matrix (which may contain complex entries), extracts its main diagonal, and returns the sum of the diagonal elements. Provide the function code and show its output for the example matrix matrix(c(1+2i,2,3,4,5+1i,6,7,8,9), nrow=3, byrow=TRUE).

Explain the differences between R matrices and R data frames. Provide one short R code example where a matrix is preferable and one short R code example where a data frame is preferable. Mention at least two reasons for each choice.