[求助]如何用R实现这个模拟

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下面的这个问题是Tibshirani在他的论文<Regression shrinkage and selection via the lasso>里面用到的一个例子，我现在想实现这个模拟，但

不知道改怎么做，在这请教各位前辈了。

论文原文如下：

In this example we simulated 50 data sets consisting of 20 observations from the model

      y=beta^{T}*x+sigma*epsilon

where beta=(3,1.5,0,0,2,0,0,0)^{T} and epsilon is standard normal.The correlation between x_i and x_j was rho^{|i-j|} with rho=0.5. We set sigma=3,and this gave a signal-to-noise ratio of approximately 5.7.

这个例子的目的是为了比较几种求解算法的误差，比如lasso,ridge regression,best subset等等。

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关键词：R实现 如何用 observations observation Approximate 模拟

from your equation, looks like x is a vector

but you also pointed out that correlation between x_i and x_j is ...

so is x a vector or ?

这里的x总共包含8个变量，从x_1到x_8，所以方程应该是

y=3x_1+1.5x_2+2x_5+sigma*epsilon

这里提到的相关关系，由于模拟一次采用多组数据，而这些数据之间是要保持相关关系的，这是我的理解。不知道正不正确。

For each observation, do you assume x1,x2 and x5 are correlated as you pointed out? And is signal to noise ratio the only restriction to x1,x2 and x5 besides correlation?

What do you assume between observations? Independent?