<p>I am going through the book Pattern Recognition by Bishop.</p>

<p>At one point he says</p>

<blockquote>
  <p>For <span class="math-container">$M = 9$</span>, the training set error goes to zero, as we might expect because this polynomial contains 10 degrees of freedom corresponding to the <span class="math-container">$10$</span> coefficients <span class="math-container">$w_0, \dots, w_9$</span>, and so can be tuned exactly to the <span class="math-container">$10$</span> data points in the training set.</p>
</blockquote>

<p>where <span class="math-container">$M$</span> is the order of the hypothesis function, and <span class="math-container">$w$</span> are the weights of the hypothesis function.</p>

<p>I did not understand how having <span class="math-container">$10$</span> degrees of freedom will tune the model EXACTLY to the <span class="math-container">$10$</span> data points? Does it mean that whenever we have a number of data points in training set equal to the degrees of freedom, the error will be zero?</p>

<machine-learning><comparison><regression>
What is the relationship between degrees of freedom and the size of the training dataset?
sage76
# What is the relationship between degrees of freedom and the size of the training dataset?

(Asked by: username_0 on 2019-07-25)

I am going through the book Pattern Recognition by Bishop.

At one point he says

> For $M = 9$, the training set error goes to zero, as we might expect because this polynomial contains 10 degrees of freedom corresponding to the $10$ coefficients $w\_0, \dots, w\_9$, and so can be tuned exactly to the $10$ data points in the training set.

where $M$ is the order of the hypothesis function, and $w$ are the weights of the hypothesis function.

I did not understand how having $10$ degrees of freedom will tune the model EXACTLY to the $10$ data points? Does it mean that whenever we have a number of data points in training set equal to the degrees of freedom, the error will be zero?

**Tags:** machine-learning, comparison, regression


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