aschleg

library(readr)
library(caret)

# Enter csv file path. If the data is in xls or xlsx, you will need to use read.table or the read_table function
# in the readr package
data <- read_csv("") 
attach(data)
summary(data)

#Enter column name with categorical variables you want to model and predict between the empty quotations.

aschleg

# Quick function for performing linear regression with only one predictor variable.
# Takes two arguments, x and y. Variables must have same length.
# Output will be similar to output of lm() with one predictor.
# Gist created as part of post on linear regression:  http://www.aaronschlegel.com/notebook/simple-linear-regression-models-r/

simple.linear.coef <- function(x, y) {
  # Find length of x to get sample size. Assuming x and y have the same sample size.
  n <- length(x)
  
  if (n != length(y))

aschleg

# Simple function for fitting a regression line with two predictor variables.
# Function takes two arguments:
#   x must be a matrix or dataframe with only two columns (variables)
#   y must be a vector containing the response values of the same length
# Output is similar to the lm() function
# Function used as a demonstration in post on multiple regression here: http://wp.me/p4aZEo-5Lh

two.predictor.regression <- function(x, y) {
  y <- as.matrix(y)
  if (ncol(y) > 1) {

aschleg

# Sample function demonstrating how a 2x2 or 3x3 matrix inverse is computed. 
# Requires an object with no more than 3 columns and an equal number of rows that can be coerced into a matrix.
# Used in post on computing the inverse of a matrix if one exists: http://wp.me/p4aZEo-5Ln


matrix.inverse <- function(mat) {
  A <- as.matrix(mat)
  
  # If there are more than four columns in the supplied matrix, stop routine
  if ((ncol(A) >= 4) | (nrow(A) >= 4)) {

aschleg

# Example function for calculating Working-Hotelling and Bonferroni confidence intervals at a 95% level.
# Function takes two arguments:
#   x: predictor variable. Must be a vector.
#   y: response variable. Must be a vector.
# Plots are built using ggplot2
# gridExtra package, https://cran.r-project.org/web/packages/gridExtra/index.html, is used to plot multiple ggplots
# Function used to demonstrate how to construct simultaneous confidence intervals in post here: http://wp.me/p4aZEo-5Mg


working.hotelling.bonferroni.intervals <- function(x, y) {

aschleg

# Sample function demonstrating how the Newton-Raphson method for root-finding is performed.
# Requires the numDeriv package for finding the derivative. One could replace this with the limit using a 
# small enough h value.
# Requires three inputs:
#   f: univariate function
#   a: lower bound (also represents starting value for method)
#   b: upper bound
# Newton-Raphson method for finding roots was examined in post here: http://wp.me/p4aZEo-5My

newton.raphson <- function(f, a, b, tol = 1e-5, n = 1000) {

aschleg

# Simple function for performing the secant method of root finding.
# Function takes three arguments:
#   f: the function in question
#   x0: first starting value
#   x1: second starting value
# Function used in post on demonstrating the secant method here: http://wp.me/p4aZEo-5MH

secant.method <- function(f, x0, x1, tol = 1e-9, n = 500) {
  if (is.function(f) == FALSE) {
    stop('f is not a function')

aschleg

# Sample function for evaluating a function root using the bisection method
# Inputs required are a function and the starting points to calculate the midpoint
# Function used in post demonstrating the bisection method of root-finding here: http://wp.me/p4aZEo-5MU

bisection <- function(f, a, b, n = 1000, tol = 1e-7) {
  # If the signs of the function at the evaluated points, a and b, stop the function and return message.
  if (!(f(a) < 0) && (f(b) > 0)) {
    stop('signs of f(a) and f(b) differ')
  } else if ((f(a) > 0) && (f(b) < 0)) {
    stop('signs of f(a) and f(b) differ')

aschleg

# Simple function for computing the trace of a matrix. Should replicate the output of sum(diag(matrix)).
# Function requires a square n x n matrix as input.
# Used in post demonstrating the trace of a matrix here: http://wp.me/p4aZEo-5Nb


trace <- function(A) {
  n <- dim(A)[1] # get dimension of matrix
  
  # Check that the matrix is square
  if (n != dim(A)[2]) {

aschleg

# Performs Neville's Algorithm (https://en.wikipedia.org/wiki/Neville%27s_algorithm) for 
# interpolating a polynomial given a set of x and y values.
# Parameters:
#   x: x values of interpolating points
#   y: values corresponding to x values
#   x0: desired point to approximate interpolated polynomial
# Returns:
#   List containing approximated value of interpolated polynomial and matrix representing
#   the intermediate values of Q