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All right.
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So now let's change track a little bit.
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We now have our template for our property that we want to get an estimate for.
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That template is currently populated with the average values in the dataset,
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so now let's get the estimated theta values for our model.
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And while we're doing that, we can also calculate the root mean squared error for our prediction interval.
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I'm going to be using scikit-learn to do this.
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Let's store our regression in a variable called "regr" and that's going to be equal to LinearRegression(),
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so this is scikit-learn's linear regression, and we can use that linear regression to already fit our values,
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so we can calculate all the theta parameters simply by calling the fit method on this and the fit method
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needs two inputs, namely the features and our target. If I hit Shift+Enter,
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this calculates all the theta values in the background. To get the predicted values or the fitted values,
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we can use "regr.predict(features)",
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so based on our features dataframe we are calculating all the predicted values using the thetas from
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our model.
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Let me store this in a variable called "fitted_vals". "fitted_vals"
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now has all our predictions.
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The next step is calculating our mean squared error and our root mean squared error.
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And this is where I'm going to throw it over to you. Can you calculate the mean squared error and the root
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mean squared error using our scikit-learn module?
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I'll give you a few seconds to pause the video and give this a go.
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Ready?
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Here's the solution.
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The MSE is going to be equal to the return value from our mean_squared_error
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function that we've imported at the top, "mean_squared_error" needs two inputs - the
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target and the fitted values.
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If we output the mean_squared_error for our regression it's currently equal to 0.035
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approximately.
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Now what about the root mean squared error,
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the RMSE? That's simply going to be equal to the square root of the mean squared error.
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Now I'm going to use numpy again,
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so "np.sqrt(MSE)"
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will give me the root mean squared error.
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The value of the RMSE is equal to 0.175, and the units for both,
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the mean squared error and the root mean squared error
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are still log dollar prices in thousands.
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Now we have everything in place to make our predictions.
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I'm going to delete this here, hit Shift+Enter and go down to the next cell.
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What I want to do here is I want to create a Python function which will estimate the log house prices
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for a specific property.
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We'll get the log prices first, the log estimate, using our data set and afterwards we'll do step 2 where
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we convert this output into today's dollar values.
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Now we've not written a Python function of our own for a little while.
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So this is a good chance to review this as well.
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The way you create a function is with the "def" keyword, "def" and then the function name,
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I'm going to call this function
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"get_log_estimate():".
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Let's have this function return a dummy value for now, so I'm going to say "log_estimate = 
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21" and then down here
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I'll specify a return value for this function, so I'll say "return log_estimate".
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Now that we've defined our function, we can use it.
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We can call it, so "get_log_estimate()"
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will output the value 21.
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Fair enough.
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So this is pretty much all the review.
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The thing I actually want to show you in this lesson is not just how to create your own Python function,
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but how to create a Python function with arguments some of which have a default value, because once you
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do that when calling the function the arguments that already have a default value are optional.
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Let me show you what I mean by that.
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If I come in here into my function definition and I specify an argument, say "nr_rooms",
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and hit Shift+Enter, when it comes to calling our Python function, I now need to supply this argument,
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so if I hit Shift+Enter now, I'll get a type error, because I'm missing one required positional argument,
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nr_rooms.
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Calling the function now requires that I have some value for the number of rooms.
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Only then will the code execute. Let's add four arguments to this function total, number of rooms being
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1, the next one being "students_per_classroom",
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so this will be our "PTRATIO", comma, and then we'll have "next_to_river",
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comma, and then we'll have a fourth argument, "high_
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confidence", and this last argument will be for whether or not we want to have a 95% prediction
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interval.
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All right.
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So now we have four arguments,
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meaning we need to specify values for all of these arguments here. To make one of these arguments optional,
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say next_to_river,
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I can give it a default value in our function signature, in our function definition.
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So next_to_river can be equal to say False and high_confidence can be equal to say True.
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What we've just done is made two of these arguments optional, meaning we only need to specify the number
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of rooms and the students per classroom.
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So coming down here where I'm calling this function, I can have 5 and say 19 and this cell will now
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execute just fine. All right,
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so we can't have this function returned the value 21 all the time.
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That's, that's just silly.
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What we actually want is we want this function to return the price estimate for a particular property,
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so we're going to use our regression object, regr, and  the predict method on that object
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and then, as an argument to the predict method, we need to supply a single row of features. That single
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row will be our property_stats, which currently hold on to the average values for all the features in
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our dataset.
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Check it out, if I press Shift+Enter to refresh the cell and then pull up the values stored inside property_
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stats,
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I can see an array with 11 features and all the average values.
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Okay, let's see what the log price estimate for this particular property is.
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"regr.predict(property_stats)", Shift+Enter and Shift+Enter again, we see that we get
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an array of two dimensions,
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mind you, it has two sets of square brackets, and then we get a price estimate in log dollars.
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Now if I wanted to get the raw number instead of an array we can access that value with 
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"[0][0]",
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so first row, first column, Shift+Enter and Shift+Enter again will give us the log price estimate of the
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array.
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Now of course this is fairly boring, right?
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Because even though we've inputed some values here as arguments the number of rooms and students per
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classroom, we're not really making use of them inside our function.
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So I'm going add a comment here that reads "Configure property"
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and then I'll add a second comment here that reads "Make prediction". When it comes to configuring our
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property, I'm thinking we can do it in a very, very similar way to the way we did it up here, so check
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it out.
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We can make use of this input, the number of rooms, by changing a particular index of our n-dimensional
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array, so "property_stats[0]",
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so row number 1 and then column number will be "RM_IDX", which is column number 4,
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and we're gonna set that equal to "nr_rooms".
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Now we have this number here
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when calling the function, filtering through into configuring the feature that we're then going to make
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the prediction on.
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So Shift+Enter and Shift+Enter, you'll see that number change.
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Now as that changes from 5 to say 8, to 9, to 3, we can now get price estimates for properties
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that have the average values for Crime and LSTAT and Pollution from the dataset for all the features
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except for one feature, namely the number of rooms.
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This now depends on the input to our function. Let's do the same thing for PTRATIO,
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the students per classroom. I'll let you pause the video to add that line of Python code. Ready?
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Here it goes.
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So "property_stats[0][
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PTRATIO_IDX] = students_per
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_classroom"
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Now we can adjust the valuation of our property, based on how many kids there are per teacher, Shift+Enter,
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and Shift+Enter again and changing this and hitting Shift+
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Enter again,
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se can see that for a PTRATIO of 10 to 1, the log price estimate is 3.05 and then for
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a PTRATIO of say 20,
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so a much bigger class, the log price estimate will go down.
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Right?
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So it'll be 2.68. Brilliant.
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Now you can see where this is going.
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Right?
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Next up is this "next_to_river" argument that I've given here.
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This is gonna be all about our CHAS variable. Now,
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CHAS was a dummy variable, right?
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It's either equal to 0 or it's equal to 1.
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The way we're gonna configure our features is using an if-else clause,
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so "if next_to_river:", new line, "property_stats[0]
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[CHAS_IDX] = 1",
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new line, "else:", "property_stats[0][CHAS_
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IDX]
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= 0"
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What code
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did I just write here? In English,
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this would read "if the property is next to the river,
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if next to the river is true, then we're going to change one feature, namely the column for Charles River,
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to 1, otherwise,
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if next to river is false which is the default in this case, property_stats for the Charles
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River column should be equal to 0".
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The value of this point in our array is conditional on the value of next_to_river, which should either
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be true or false.
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We're calling our function
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like so. This value here that we're getting for a three room dwelling with PTRATIO of 20, we're getting
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a value of 2.68.
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This property here is not next to the river.
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If I hit Shift+Enter on this cell to refresh and refresh this cell, then we see what this property would be priced
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that if it was not next to the river.
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If however, "next_to_river = True" and I refresh the cell, then we can see
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the premium of this property reflected in the price
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if it was next to the river.
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And that's because again living next to the river is a desirable thing.
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All right, so you can see where this is going.
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What we've just done is we've created a function and we're configuring the property that we're getting
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the estimate for using the arguments to that function.
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So number of rooms, students per classroom and whether the property is next to the river. For all the
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other features, like pollution and highway accessibility,
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we're just using the average values of the dataset.
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If we wanted to, we could add more lines of code here and increase the number of arguments that are being
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supplied to this function to set those as well.
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But for this exercise, let's keep it simple, let's keep it to 3 custom inputs.
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Now, what about this fourth one that I made you add earlier, "high_confidence"? What I had in
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mind for this one was to calculate the range.
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So let's add another comment here and I'm going to have that read "Calc Range".
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This is our prediction interval.
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I'm going to adopt the same pattern, so "if high_confidence:", "Do X", "else:", "Do Y".
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Now what am I trying to get at here?
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If high confidence is equal to True, then I want to calculate the two standard deviation prediction interval,
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I want to calculate the 95% prediction interval and otherwise, I want to calculate the one standard
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deviation prediction interval,
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68% prediction interval. The prediction intervals of course have an upper and a lower
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bound,
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so "upper_bound = log_estimate + 2*RMSE",
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yes that's our root mean squared error
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coming back in here, and the "lower_bound = log_estimate - 2*
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RMSE"
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Now what about if we don't want a high confidence prediction interval?
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What if we don't want a large range?
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Well, I can copy these two lines and I can paste them in here and instead of using two times the root
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mean squared error, we can simply use 1 times the root means squared error to calculate our range.
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So this is a wide range and this is a narrow range.
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The last thing I'm going to do is I want to make this very explicit, so I'll say "interval = 95" and here
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I'm going to say "interval = 68".
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I'm going to use this variable here in a print statement later on.
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For now what we're gonna do is return all of these calculations, so check it out, we're going to return our "log_
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estimate", we're going to return our "upper_bound",
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we're gonna return our "lower_bound" and we're going to return our interval. Hitting Shift+Enter, I
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refresh the cell and hitting Shift+Enter on this one,
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I can now see that I get a tuple.
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This is what the parentheses are telling us and that tuple consists of four things, the log price estimate,
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plus two standard deviations and minus two standard deviations for the range - an upper and a lower bound,
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plus an indication if this is a wide range or a narrow range.
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In this case, it is a wide range. Why? Because confidence is set to True by default. To get a narrow range,
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I can use "high_confidence = False" in which case we will enter the else block of
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the function and get the following output. We get the same log estimate, but the upper and the lower bound
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will be plus and minus one standard deviation, one times the root mean squared error, and our prediction
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interval
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in this case, will be 68%, so this is the 68% prediction interval
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and this is the 95% prediction interval.
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00:19:37,000 --> 00:19:44,290
Now that we have a price estimate and an upper and a lower bound and a prediction interval, the next
209

210
00:19:44,290 --> 00:19:49,560
thing to do is to convert all of these log prices into dollar values.