least.squares {animation} R Documentation

## Demonstrate the least squares method

### 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.

Yihui Xie

`lm`