To write an if-else statement in R that checks if a number is positive or negative, you can use the condition if (number > 0) { code for positive number } else { code for negative number }. If the number is greater than 0, the code inside the if block will be executed; otherwise, the code inside the else block will be executed.

First, you'd have to define a function that calculates the square of a number (e.g., square <- function(x) {return(x^2)}). Then you could use print(square(x)) to print the result of squaring a number. Note: 'x' should be replaced with the number you want to square.

The plotrix package in R provides enhanced functionalities for creating pie charts. It offers additional options and customizations beyond the basic pie() function, allowing for more advanced and specialized pie chart visualizations.

A nested function in R is a function that is defined within another function. It is created and exists within the scope of the outer function. The nested function can access variables from the outer function and can only be called from within the outer function.

When working with a large data set in R and facing memory limitations with a vector, you can handle the situation by processing the vector in smaller chunks or subsets to reduce memory usage. Alternatively, you can utilize external memory algorithms or databases specifically designed for efficient data processing. Additionally, optimizing the code for memory usage, minimizing unnecessary operations, and employing efficient algorithms can help overcome memory constraints and improve performance.

In R, the is.vector() function can be used to check if an object is a vector. It returns TRUE if the object is a vector and FALSE otherwise. This function is useful for checking the type of an object before performing operations specific to vectors.

R uses lexical scoping, also known as static scoping. In lexical scoping, variables are resolved based on their order of definition in the source code. When a variable is referenced within a function, R first looks for that variable within the function's local environment. If not found, it then looks in the environment of the function that called it, and so on, until it reaches the global environment. This scoping behavior ensures that global variables can be accessed within functions but can be overridden by variables with the same name defined within the local environment.

To customize the appearance of an R bar chart, you can use the col parameter to change the colors of the bars, the names.arg parameter to add labels to the bars, and the legend() function to add a legend. These options allow you to customize the colors, labels, and legend to suit your visualization needs.

To calculate the mode of a factor in R, you can apply the table() function to the factor. The table() function counts the frequencies of each level in the factor, allowing you to identify the most frequent level as the mode.

The apply() function in R can be used to apply a function to each element of a vector or columns of a data frame. The apply() function simplifies repetitive operations by iterating over the elements or columns and applying the specified function.

In R, there is no '===' operator. The '==' operator checks for equality of values, disregarding the types of the compared objects. It returns TRUE if the values are equal and FALSE otherwise.

If a matrix in R is created with elements of different data types, R will coerce the elements to the most flexible type. The most flexible type refers to the type that can accommodate all the values in the matrix. This ensures that all elements of the matrix are of the same data type for consistent operations.