showEqn: Show Matrices (A, b) as Linear Equations

Description

Shows what matrices \(A, b\) look like as the system of linear equations, \(A x = b\), but written out as a set of equations.

Usage

showEqn(A, b, vars, simplify = FALSE, reduce = FALSE,
  fractions = FALSE, latex = FALSE)

Arguments

either the matrix of coefficients of a system of linear equations, or the matrix cbind(A,b). Alternatively, can be of class 'lm' to print the equations for the design matrix in a linear regression model

if supplied, the vector of constants on the right hand side of the equations. When omitted the values b1, b2, ..., bn will be used as placeholders

vars

a numeric or character vector of names of the variables. If supplied, the length must be equal to the number of unknowns in the equations. The default is paste0("x", 1:ncol(A).

simplify

logical; try to simplify the equations?

reduce

logical; only show the unique linear equations

fractions

logical; express numbers as rational fractions?

latex

logical; print equations in a form suitable for LaTeX output?

Value

a one-column character matrix, one row for each equation

References

Fox, J. and Friendly, M. (2016). "Visualizing Simultaneous Linear Equations, Geometric Vectors, and Least-Squares Regression with the matlib Package for R". useR Conference, Stanford, CA, June 27 - June 30, 2016.

Examples

Run this code

# NOT RUN {
  A <- matrix(c(2, 1, -1,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  b <- c(8, -11, -3)
  showEqn(A, b)
  # show numerically
  x <- solve(A, b)
  showEqn(A, b, vars=x)

  showEqn(A, b, simplify=TRUE)
  showEqn(A, b, latex=TRUE)

  # lower triangle of equation with zeros omitted (for back solving)
  A <- matrix(c(2, 1, 2,
               -3, -1, 2,
               -2,  1, 2), 3, 3, byrow=TRUE)
  U <- LU(A)$U
  showEqn(U, simplify=TRUE, fractions=TRUE)
  showEqn(U, b, simplify=TRUE, fractions=TRUE)

  ####################
  # Linear models Design Matricies
  data(mtcars)
  ancova <- lm(mpg ~ wt + vs, mtcars)
  summary(ancova)
  showEqn(ancova)
  showEqn(ancova, simplify=TRUE)
  showEqn(ancova, vars=round(coef(ancova),2))
  showEqn(ancova, vars=round(coef(ancova),2), simplify=TRUE)

  twoway_int <- lm(mpg ~ vs * am, mtcars)
  summary(twoway_int)
  car::Anova(twoway_int)
  showEqn(twoway_int)
  showEqn(twoway_int, reduce=TRUE)
  showEqn(twoway_int, reduce=TRUE, simplify=TRUE)

  # Piece-wise linear regression
  x <- c(1:10, 13:22)
  y <- numeric(20)
  y[1:10] <- 20:11 + rnorm(10, 0, 1.5)
  y[11:20] <- seq(11, 15, len=10) + rnorm(10, 0, 1.5)
  plot(x, y, pch = 16)

  x2 <- as.numeric(x > 10)
  mod <- lm(y ~ x + I((x - 10) * x2))
  summary(mod)
  lines(x, fitted(mod))
  showEqn(mod)
  showEqn(mod, vars=round(coef(mod),2))
  showEqn(mod, simplify=TRUE)

# }