Learning model coefficients

In order to estimate the coefficients of our model, we need to fit the data with a regression line that gives a similar answer to the actual sales. To get a regression line that best fits the data, we will use a criterion called least squares. So, we need to find a line that minimizes the difference between the predicted value and the observed (actual) one. In other words, we need to find a regression line that minimizes the sum of squared residuals (SSresiduals). Figure 2 illustrates this:

The following are the elements that exist in Figure 2:

• Black dots represent the actual or observed values of x (TV ad) and y (sales)
• The blue line represents the least squares line (regression line)
• The red line represents the residuals, which are the differences between the predicted and the observed (actual) values

So, this is how our coefficients relate to the least squares line (regression line):

• beta₀ is the intercept, which is the value of y when x =0
• beta₁ is the slope, which represents the change in y divided by the change in x

Figure 3 presents a graphical explanation of this:

Now, let's go ahead and start to learn these coefficients using Statsmodels:

# To use the formula notation below, we need to import the module like the following
import statsmodels.formula.api as smf
# create a fitted model in one line of code(which will represent the least squares line)
lm = smf.ols(formula='sales ~ TV', data=advertising_data).fit()
# show the trained model coefficients
lm.params

Output:

Intercept    7.032594
TV           0.047537
dtype: float64

As we mentioned, one of the advantages of linear regression models is that they are easy to interpret, so let's go ahead and interpret the model.