Course talk:CPSC312-2017-Linear Regression
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I like your project idea. What is your objective function? Is it least square error?
You may first work on only doing prediction. That is, given w and X, return y. You need to implement matrix operations.
Then work on fitting a model: given X and Y, return the "best" w with respect to the objective function.
If you still have energy, try a different objective function. But it is optional.