r - 在 R 中创建多个偏差方差权衡图

Question

我对 R 比较陌生。我想知道如何创建以下图形。我被困了两个多小时。

假设红线——真正的关系——是 y = x^2。假设我想将 100 个线性模型拟合到 100 个随机样本(蓝线)。

我该怎么做？到目前为止，这就是我所拥有的:

# create the true relationship
f <- function(x) x^2  # true model
x <- seq(0, 1, by = 0.01)
y <- f(x)

# plot the true function
plot(x, y, type = "l", col = "red", ylim = c(-0.2, 1.2), lwd = 4)

# fit 100 models
set.seed(1)
for (i in 1:100)
{
    errors <- rnorm(n, 0, sigma)       # random errors, have standard deviation sigma
    obs_y <- f(obs_x) + errors         # observed y = true_model + error
    model <- lm(obs_y ~ obs_x)         # fit a linear model to the observed values
    points(obs_x[i], mean(obs_y[i]), col = "green")       # mean values
    abline(model, col = "purple")    # plot the fitted model
}

创建这个:

其中的绿点肯定是关闭的......而且我没有黑点...

谢谢!

Answer 1

这是经过多次调整后的代码:

f <- function(x) x^2
x <- seq(0, 1, by = 0.05)
n <- length(x)
sigma <- 0.05
y <- f(x)

plot(x, y, type = "l", col = "red", ylim = c(-0.2, 1.2), lwd = 2)

fitted <- ys <- matrix(0, ncol = n, nrow = 100)

set.seed(1)
for (i in 1:100)
{
  errors <- rnorm(n, 0, sigma)
  ys[i, ] <- obs_y <- f(x) + errors
  model <- lm(obs_y ~ x)
  fitted[i, ] <- fitted(model)
  abline(model, col = "purple", lwd = 0.1)
}

points(x = rep(x, each = 100), y = ys, cex = 0.1)
points(x = x, y = colMeans(fitted), col = 'green', cex = 0.3)