Explore the Coefficents and Intercepts

Quick reference

• 00:05 So in the last video when we fed our data to our linear regression model,
• 00:09 we generated some coefficients and some intercepts.
• 00:12 So in this video I want to look at those and talk about them a little bit.
• 00:16 So to find out what these are, first we could call
• 00:20 lin.intercept_ and we can see it's at 31.47.
• 00:25 We'll talk about what that means in a second.
• 00:27 To find the coefficients, we can call it lincoef_ and
• 00:32 then we get an array of coefficients.
• 00:35 And you'll notice there's 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 of these.
• 00:40 That's because there are 13 columns in our data, right?
• 00:44 So if we remember X_train, which was just up here,
• 00:49 x, our columns, if we look at that, we could see 1,
• 00:54 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
• 01:01 So it's those 13 things, that's what these coefficients are, one for each one.
• 01:06 So we can actually create a coefficient data frame just to make it easier to read.
• 01:11 Let's call it cdf, coefficient data frame.
• 01:14 And let's just set this equal to, it's going to be a pd.DataFrame.
• 01:19 And we want to go lin.coef_ and then it's going to
• 01:25 be X_train, or X because they're the same,
• 01:30 .columns.
• 01:34 And then let's just create a column header called, I don't know, Coeff.
• 01:39 Needs to be in quotation marks.
• 01:46 And you notice we're getting an error.
• 01:47 That's because this is an array inside of an array, so
• 01:51 we need to designate this to be the zeroth item.
• 01:54 When we do that, it works out fine.
• 01:56 Then we can go cdf and we can call this.
• 01:57 So we have a list of our coefficients for each of our items.
• 02:03 So that's very cool.
• 02:05 So what does these two things mean, the coefficients and the intercept?
• 02:08 Well, the intercept is just simply not that important but
• 02:14 it's the expected mean value of y when all x is 0.
• 02:17 So if we go to our linear regression model, we can see here,
• 02:21 this is just from Wikipedia we looked at earlier.
• 02:24 When x is 0, y, here, is 5.
• 02:28 So the y intercept here is 5, right?
• 02:31 Ours is 31.
• 02:33 So ours would be way up here, not even on this chart.
• 02:36 So it's just something to keep in mind but it's not all that important.
• 02:39 When we look at a scatterplot later on, we'll remark on this but
• 02:44 that's really all.
• 02:45 The thing that's more interesting are the coefficients, right?
• 02:49 Each of these coefficients, as I said, relates to one of these columns.
• 02:52 And basically it means, if we hold all other things fixed,
• 02:57 a one unit increase in x correlates to an increase of
• 03:02 whatever that coefficient is in, for instance, price.
• 03:05 So, it looks like, for instance here,
• 03:09 as taxes go down, price goes down this much.
• 03:15 So for instance age,
• 03:18 as the house gets older the price of the house will go up just a very little bit,
• 03:23 so apparently age doesn't have a whole lot to do with things.
• 03:25 So here as the crime rate goes up, the price goes down.
• 03:29 Think about that.
• 03:31 As there's more crime in the area, the houses get cheaper.
• 03:34 That kind of makes sense, right?
• 03:35 There's always cheaper houses where there's more crime.
• 03:39 Houses cost more in safer neighborhoods.
• 03:41 So it kind of makes sense.
• 03:42 So these are our coefficients and we'll talk about these more as we make
• 03:45 predictions and analyze our results, which we'll start to do in the next video.

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