<｜begin▁of▁sentence｜>### Instruction:
Imagine you're a veterinarian tasked with examining a group of 100 animals, each assessed based on 50 different health indicators. You're pondering whether these indicators might actually be projecting a simpler underlying health pattern that could be understood with fewer dimensions. In essence, you're pondering if there's a way to consolidate this complex health data into a more manageable form, without losing the essence of your insight into the animals' wellness. This is akin to translating a vast array of symptoms into a concise set of diagnoses.

In this scenario, you're considering using the `select_dimension` function from the `graspologic.embed` library. This method, inspired by the work of Zhu and Godsie, can help you sift through the data to find the most concise yet informative set of health indicators. How would you apply this technique to determine the most effective number of health indicators that still capture the core health trends within your animal population?
### Response:
import numpy as np
from graspologic.embed import select_dimension
from scipy.stats import ortho_group

# Generate a random orthogonal matrix and simulate data
n_samples = 100
n_features = 50
matrix = ortho_group.rvs(dim=n_features)
data = np.dot(np.random.randn(n_samples, n_features), matrix.T)

# Select the dimension
elbows, sing_vals = select_dimension(data, n_components=None, n_elbows=2, threshold=None, return_likelihoods=False)

# Print the selected embedding dimensions and associated singular values
print('Selected embedding dimensions (elbows):', elbows)
print('Singular values:', sing_vals)
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