least.squares {animation}R Documentation

Demonstrate the least squares method


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


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), ...)



a numeric vector: the independent variable


a numeric vector: the dependent variable


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))


'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


the colors of two lines: the real regression line and the moving line with either intercept or slope changing


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


defines the layout of the graph; see par


other parameters passed to plot to define the appearance of the scatterplot


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.


The value returned depends on the animation type.

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


the estimates of the intercept and slope with lm


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.


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


Yihui Xie


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

See Also


[Package animation version 2.5 Index]