least.squares: Demonstrate the least squares method

In animation: A Gallery of Animations in Statistics and Utilities to Create Animations

Description

This is a simple demonstration of the meaning of least squares in univariate linear regression.

Usage

least.squares(
  x,
  y,
  n = 15,
  ani.type = c("slope", "intercept"),
  a,
  b,
  a.range,
  b.range,
  ab.col = c("gray", "black"),
  est.pch = 19,
  v.col = "red",
  v.lty = 2,
  rss.pch = 19,
  rss.type = "o",
  mfrow = c(1, 2),
  ...
)

Arguments

x	a numeric vector: the independent variable
y	a numeric vector: the dependent variable
n	the sample size: when x and y are missing, we use simulated values of y (x = 1:n and y = a + b * x + rnorm(n))
ani.type	'slope': the slope is changing with the intercept fixed; 'intercept': intercept changing and slope fixed
a, b	the fixed intercept and slope; depending on ani.type, we only need to specify one of them; e.g. when ani.type == 'slope', we need to specify the value of a
a.range, b.range	a vector of length 2 to define the range of the intercept and the slope; only one of them need to be specified; see above
ab.col	the colors of two lines: the real regression line and the moving line with either intercept or slope changing
est.pch	the point character of the 'estimated' values given x
v.col, v.lty	the color and line type of the vetical lines which demonstrate the residuals
rss.pch, rss.type	the point character and plot type of the residual plot
mfrow	defines the layout of the graph; see par
...	other parameters passed to plot to define the appearance of the scatterplot

Details

With either the intercept or the slope changing, the lines will be moving in the graph and corresponding residuals will be plotted. We can finally see the best estimate of the intercept and the slope from the residual plot.

Value

The value returned depends on the animation type.

If it is a slope animation, the value will be a list containing

lmfit	the estimates of the intercept and slope with lm
anifit	the estimate of the slope in the animation

If it is an intercept animation, the second component of the above list will be the estimate of the intercept.

Note the estimate will not be precise generally.

Note

ani.options('nmax') specifies the maximum number of steps for the slope or intercept to move.

Author(s)

Yihui Xie

References

Examples at https://yihui.org/animation/example/least-squares/

See Also

lm

animation documentation built on Oct. 7, 2021, 9:18 a.m.