案例学习：预测房价

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From the course by University of Washington

机器学习：回归

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案例学习：预测房价

From the lesson

Simple Linear Regression

Our course starts from the most basic regression model: Just fitting a line to data. This simple model for forming predictions from a single, univariate feature of the data is appropriately called "simple linear regression".<p> In this module, we describe the high-level regression task and then specialize these concepts to the simple linear regression case. You will learn how to formulate a simple regression model and fit the model to data using both a closed-form solution as well as an iterative optimization algorithm called gradient descent. Based on this fitted function, you will interpret the estimated model parameters and form predictions. You will also analyze the sensitivity of your fit to outlying observations.<p> You will examine all of these concepts in the context of a case study of predicting house prices from the square feet of the house.

- Emily FoxAmazon Professor of Machine Learning

Statistics - Carlos GuestrinAmazon Professor of Machine Learning

Computer Science and Engineering

[MUSIC]

Okay, so that represented a kind of high level overview about this module,

as well as, other aspects that we're going to touch upon in this course.

But now let's delve into a specific case of simple linear regression and

talk about what this means.

So going back to our flowchart,

what we're gonna talk about now is specifically the machine learning model.

So that's that highlighted green box and everything else is grayed out so

you can forget about everything else for now.

We're just talking about our model and what form it takes.

So our simple linear regression model is just that.

It's very simple.

We're assuming we have just one input,

which in this case is, square feet of the house and

one output which is the house sales price and we're just gonna fit a line,.

A very simple function here not that quadratic function or

higher order polynomials we talked about before, just a very simple line.

And what's the equation of a line?

Well, it's just intercept plus slope times our variable of interest so

that we're gonna say that's wo + w1x.

And what this regression model then specifies is that each one of our

observations yi is simply that function evaluated at xi.

So that's w0 plus w1xI plus the error term which we called epsilon i.

So this is our regression model, and to be clear, this error, epsilon i,

is the distance from our specific observation back down to the line.

Okay, so the parameters of this model Are w0 and

w1 are intercept and slope and we call these the regression coefficients.

So that summarizes our simple linear regression model.

Very straight forward.

Very simple.

But we'll get to more complicated things later.

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