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Now that we've shuffled and split our data into training and test datasets, we can finally run our regression
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using scikit learn. To do that,
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I'm going to scroll back up and import this capability, so I'm going to say "from sklearn.linear_
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model import LinearRegression", I'm going to hit Shift+Enter on this cell,
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scroll back down where I left off, and then I'm going to create a regression object called "regr", set that
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equal to "LinearRegression()" and then I'm going to use this regression object and call
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the "fit" method on it, so "regr.fit()" and now what do I add between these parentheses?
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What do I give has an argument to our fit method?
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The data that we should supply is our training datasets, right?
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So, X_train being the training features and y_train being the training target
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values. And hitting Shift+Enter on this will train our model. Great! But we don't see any output on the
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thetas that we've just estimated and also we don't even know how well this model fits our data. Now,
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before printing out these values, before printing out the values of our theta parameters, let's make some
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predictions on what we expect to see. Making these predictions is a very important step because it provides
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a sense check on what the computer is going to spit out to us. We should never blindly trust the numbers
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that we get back. That's how silly, silly mistakes are made.
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Besides, we've done all this data exploration work up until now and we can use the knowledge that we
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gained to make some predictions.
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For example, we've used seaborn's pairplot to run individual regressions against our target prices.
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Also, we've created this wonderful correlation matrix to show the correlations of the individual features
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with our target. We know which correlations were positive and which correlations were negative.
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So given that this is how our model looks like, let's make some predictions on the signs of the coefficients.
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Let's predict what kind of signs we're going to see on these theta parameters.
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So, get out a piece of paper and write down if you expect the theta parameter for RM to be positive
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or negative, and then do the same thing for NOX, PTRATIO, CRIM, DIS and LSTAT. Did you pause
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the video and write this down?
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There is actually one more prediction that we said would make.
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Remember how a few lessons ago, I asked you if you thought that being next to the Charles River was a good
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thing for property prices or a bad thing?
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Well now it's time to also add your prediction to the sign of the CHAS dummy variable as well.
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Okay.
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So here's the solution to this challenge.
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I'm going to print out the value of our intercept and it's gonna be "regr.intercept_"
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and then I'm going to print out the values of all the coefficients. And to format these values nicely I'm going to
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actually put them in a data frame.
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So I'm going to see "pd.DataFrame()" and then our first argument
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is our data that we're gonna supply
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and these are the coefficients which we can find under 
"regr.coef_".
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The second argument that we're going to supply is called index,
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so "index = ".
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and then what
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we're going to supply as an index are the column names, so "X_train.columns".
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Yeah.
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So these are the column names.
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That way we can have the names of the coefficients next to the values.
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Let me show you what this looks like.
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Voila! We get something like this.
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We can our intercept printed here and we get the name and the value of the different coefficients.
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Now I'm going to come back up here in to the code where I'm creating our data frame and I'm going to
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specify third argument called columns.
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Yeah.
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And I set that equal to "['COEF']". When I hit Shift+Enter now, you'll
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see this little 0 here,
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this the lack of a column name changed to the value "coef".
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So "columns = " and then a list of 1 value, namely the string "coef" will add a column name to our data
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frame here.
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All right.
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So we've got our results.
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How do they stack up to your predictions?
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Remember, we're just looking at the sign of the coefficients here for now. Are the actual coefficients
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positive or negative according to our model? Did you predict the right sign for the coefficients?
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Because what we see here is that more crime is bad for house prices and also more pollution is bad
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for house prices.
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More rooms on the other hand is good for house prices.
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It's a positive coefficient. And more students in class is also a negative factor for the house prices
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as is higher values for LSTAT. Now looking at this,
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I think this is some really, really good news because the signs of our coefficients passed our first sense
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check. All these signs that we've just talked about
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makes sense logically.
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So the things that we would have expected to be bad for property prices from a logic point of view indeed
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have a negative coefficient associated with them.
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Oh and,
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do you remember how I asked you to make a prediction if living next to the Charles River was a good
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thing or not?
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Well, now we've got our answer.
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Looking at the sign on the CHAS variable, we can see that living next to the Charles River is indeed
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desirable and the properties that are on the river are more expensive than those that are are away from
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it, all else equal. In fact we can put a number to it,
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Bostonians are willing to pay a premium for a property that is next to the river and that premium is
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equal to about 2000 dollars.
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Remember, CHAS only has the values 0 or 1. When CHAS is equal to 1 then it's next to the river and
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1 times approximately 2 is equal to 2, right?
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And since our target values, our property prices, are in thousands,
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this translates into 2000 dollars.
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So what we've just done in Jupyter notebook is calculate all these theta parameters.
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Our model now looks like this. Using our training data,
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we've estimated all the values of these theta parameters and the beautiful thing about this linear model
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is that all our coefficients have a very clear meaning - an increase in the number of rooms by one will
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increase the price of the property by 3100 hundred dollars.
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Our model is easy to understand and to interpret, it's the very opposite of a black box that just spits
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out an answer
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and we don't know where it came from.