Cost Function

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Model :

(x,y) => Data Set

m => number of data pairs in data set

(xi , yi) => element i in data set (x,y)

supervised learning algorithm:

training set

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learning algorithm

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size of house -> hypothesis h -> estimated price

linear regression : h (x) = theta0 + theta1*x

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h (x) = theta0 + theta1*x;

error = (theta0 + theta1*xi) - yi

sum of squared errors = sigma (1->m) error^2

mean sum of squared errors = 1/2m * (sum of squared errors)

...also referred to as cost function;

objective : find theta0 & theta1 so as to minimize cost function

exercise : h(x) = theta1 * x

given data sets (1,1) (2,2) (3,3)

find theta1, that minimizes cost function J(theta1)

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for 2 parameters theta0 and theta1:

plot as J(theta) as functions of theta0 and theta1