So now, if we look at the values
again and see that these are the weights
for the values at that particular timestamp
and b is the bias or the slope,
we can do a standard linear regression
like this to predict the value of y
at any step by multiplying out
the x values by the weights and then adding the bias.
So for example, if I take
20 items in my series and print them out,
I can see the 20x values.
If I want to predict them,
I can pass that series into my model to get a prediction.
The NumPy new axis then just
reshapes it to the input dimension
that's used by the model.
The output will look like this.
The top array is the 20 values that provide the input to
our model and the bottom is
the predicted value back from the model.
So we've trained our model to say that
when it sees 20 values like this,
the predicted next value is 49.08478.
So if we want to plot our forecasts for every point on
the time-series relative to
the 20 points before it where our window size was 20,
we can write code like this.
We create an empty list of forecasts and
then iterate over the series
taking slices and window size,
predicting them, and adding
the results to the forecast list.
We had split our time series
into training and testing sense
taking everything before a certain time
is training and the rest is validation.
So we'll just take the forecasts after
the split time and load
them into a NuimPy array for charting.
That chart looks like this with
the actual values in
blue and the predicted ones in orange.
You can see that our predictions look pretty
good and getting them was
relatively simple in comparison with
all the statistical gymnastics
that we had to do in the last videos.
So let's measure the mean absolute error
as we've done before,
and we can see that we're in a similar ballpark to where
we were with a complex analysis that we did previously.
Now that's just using a single layer in
a neural network to calculate a linear regression.
Let's see if we could do better with
a fully-connected DNN next.
Before you get to that,
we'll go through the workbook for this lesson
to ensure that you understand
everything we've done up to now.
The next video will be a screencast of going through
that and then you'll work on the DNN after that.