Using the model for prediction

Let's say we have unseen data of TV ad spending and that we want to know their corresponding impact on the sales of the company. So, we need to use the learned model to do that for us. Let's suppose that we want to know how much sales will increase from $50000 of TV advertising.

Let's use our learned model coefficients to make such a calculation:

y = 7.032594 + 0.047537 x 50 

# manually calculating the increase in the sales based on $50k
7.032594 + 0.047537*50000

Output:

9,409.444

We can also use Statsmodels to make the prediction for us. First, we need to provide the TV ad value in a pandas DataFrame since the Statsmodels interface expects it:

# creating a Pandas DataFrame to match Statsmodels interface expectations
new_TVAdSpending = pd.DataFrame({'TV': [50000]})
new_TVAdSpending.head()

Output:

Now, we can go ahead and use the predict function to predict the sales value:

# use the model to make predictions on a new value
preds = lm.predict(new_TVAdSpending)

array([ 9.40942557])

Let's see how the learned least squares line looks. In order to draw the line, we need two points, with each point represented by this pair: (x, predict_value_of_x).

So, let's take the minimum and maximum values for the TV ad feature:

# create a DataFrame with the minimum and maximum values of TV
X_min_max = pd.DataFrame({'TV': [advertising_data.TV.min(), advertising_data.TV.max()]})
X_min_max.head()

Output:

Let's get the corresponding predictions for these two values:

# predictions for X min and max values
predictions = lm.predict(X_min_max)
predictions

Output:

array([  7.0658692,  21.12245377])

Now, let's plot the actual data and then fit it with the least squares line:

# plotting the acutal observed data
advertising_data.plot(kind='scatter', x='TV', y='sales')
#plotting the least squares line
plt.plot(new_TVAdSpending, preds, c='red', linewidth=2)

Output:

Extensions of this example and further explanations will be explained in the next chapter.