Linear Regression in ML §

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Review of Linear Model: §

1. are matrices or vectors.
2. A row or column of a matrix will use a subscript:
   • is a scalar, the ith row and jth column of
   • . is a vector, the ith row of
   • is a vector, the jth column of
3. Parameters will typically be Greek symbols:
4. Estimates will be Greek symbols wearing a hat:
5. is the probability that given , where:
   • X, Y are random variables
6. represents either a loss function, or the likelihood function
   • represent the log-likelihood function

X(n by p+1), features with columns of list Y(n by 1), target variable B(p+1 by 1) coefficient, parameters Y = XB + E

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Training linear model means finding optimal coefficients : §

Finding optimal amounts to find vector that minimizes the loss function , which is the sum of squared error:

which is equivalent to:

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Finding §

by taking the derivative of our loss function and setting it equal to zero

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TAGS §