animation (version 2.0-0)

least.squares: Demonstrate the least squares method.

Description

Demonstrate the least squares method. 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

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.

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.

References

http://animation.yihui.name/lm:least_squares

See Also

lm

Examples

par(mar = c(5, 4, 0.5, 0.1))
oopt = ani.options(interval = 0.3, nmax = ifelse(interactive(), 
    50, 2))

## default animation: with slope changing
least.squares()

## intercept changing
least.squares(ani.type = "intercept")

## save the animation in HTML pages
saveHTML({
    ani.options(interval = 0.3, nmax = ifelse(interactive(), 
        50, 2))
    par(mar = c(4, 4, 0.5, 0.1), mgp = c(2, 0.5, 0), tcl = -0.3)
    least.squares()
}, img.name = "least.squares", htmlfile = "least.squares.html", 
    ani.height = 450, ani.width = 600, title = "Demonstration of Least Squares", 
    description = c("We want to find an estimate for the slope", 
        "in 50 candidate slopes, so we just compute the RSS one by one. "))

ani.options(oopt)