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In this lesson it's finally time to train our model.
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We're going to model our house prices using a technique called multivariable regression which is also
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known as multiple linear regression.
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But what does that mean?
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In a previous module we've been estimating movie revenue based on movie budgets.
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We were using a simple linear regression model that looked like this.
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We had one explanatory variable which were the movie budgets and we were busy estimating the values
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of these theta parameters, theta zero and theta one. When fitting more than one explanatory variable, more
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than one feature,
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the equation for the regression will look like this instead. This is the format of our model for our
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multivariable regression.
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Now, we don't have n different terms.
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We've got 13 features in our data set and these are the ones we're going to use.
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So in fact when we adapt this generic model to our specific circumstances, our equation will actually
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look something like this.
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The estimate of the price is equal to "theta0 + theta1 * RM", plus theta2 times our second 
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feature, plus theta3 times our third feature and so on until we get to our last one.
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What this equation is telling us is that our estimate of the property price will be a linear combination
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of these 13 features.
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So it's still a linear model.
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Okay.
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So this is the model for our regression that we will be fitting our data to.
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And when we run our Python code, we'll get a value for each of these theta parameters that we see here.
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These are going to be our coefficients that we're interested in.
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But before we write our code and run the numbers, did you ever wonder why this technique was called regression
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in the first place?
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Where does this name regression actually come from? I mean regression is such a strange word to be using
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for fitting a line to our data.
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Right?
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So this technique and the name actually go back a long long time to an English gentleman called Francis
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Galton,
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Sir Francis Galton in fact. Sir Galton lived in Victorian England and had quite a few talents.
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One of the many things he's remembered for today is his invention of the Galton board.
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Yep.
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He named this invention after himself.
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Anyhow, a Galton board is basically what you end up with if you were to take his Japanese pachinko machine
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and then extract all the fun out of it.
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The Galton Board is a contraption that has a bunch of balls and pins in it.
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When you turn this board upside down the balls go through a single opening at the top and then they
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start bouncing off the pins.
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And here's the fascinating part, what you end up with at the bottom of the board will look something
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like a histogram from matplotlib.
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In fact you get a very particular type of arrangement in the slots at the bottom.
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And if you squint a little bit you'll actually recognise our old friend, the normal distribution.
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Most of the balls end up in the middle but a very, very few balls bounce around like crazy on these pins
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and they end up on the sides of the board.
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They end up as outliers on the very, very left or on the very, very right hand edge.
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Needless to say a lot of statisticians at the time were very excited about this invention.
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But the thing is Sir Francis Galton was not a one trick pony.
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No sir.
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Being quite interested in both distributions and outliers,
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he looked very, very, very carefully at the sizes of things, from the sizes of the seeds of his sweet peas
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to the sizes of people.
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In particular, he was very, very interested in how size changes from one generation to the next, especially
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with regards to outliers.
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Now one thing that Sir Galton noticed was that when you had a very, very tall father and that father
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had a son and that son grew up to be an adult, the adult son was usually shorter than his father.
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Sir Galton called this phenomenon Regression to the Mean.
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That's where we get that word from, regression. Now you can even observe this phenomenon of the regression
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to the mean in say like the NBA. Professional basketball players tend to be very very tall.
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Right?
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For example Shaquille O'Neal was 7 foot 1 or 216 centimeters.
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At least that's what he's listed at on Wikipedia.
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But what about the sons of an NBA player? Shaquille O'Neal son Sharif O'Neal is slightly shorter than
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his father at two meters and eight centimeters or 6 foot 10.
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Another example is actually Michael Jordan who was listed at 6 foot 6 and Michael Jordan's son Jeffrey
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Jordan is listed at 6 foot 1.
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Now I realize that those are just two examples and there aren't that many sons of basketball players in the
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NBA whose height you can pull up on Wikipedia, but you'll find that this pattern holds on average the
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NBA players sons will end up shorter than their dads on average.
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This is regression to the mean in action.