cluster one is generated from the model:
$$y_{ik} = sin(2 * PI * x_k) + e_{ik}, x_k \sim N(0, 1), e_{ik} \sim N(0, 0.1), i = 1, \ldots, 100, k = 1, \ldots, 10.$$cluster two is generated from the model:
$$y_{ik} = cos(2 * PI * x_k) + e_{ik}, x_k \sim N(0, 1), e_{ik} \sim N(0, 0.1), i = 1, \ldots, 100, k = 1, \ldots, 10.$$
cluster three is generated from the model:
$$y_{ik} = e_{ik}, e_{ik} \sim N(0, 1), i = 1,\ldots, 100, k = 1, \ldots, 10.$$