Let's try with the economic sector. We can legitimately infer that the economic sector should be with a given customer going into default or not.

Let us start by fitting the linear model. As I was saying, this can be easily done in R employing the lm() function:

linear_regression_economic_sector <- lm(as.numeric(default_flag) ~ economic_sector, clean_casted_stored_data_validated_complete) 

As you can see, we define as y the default_flag attribute, and as x the economic_sector. The lm() function takes care of estimating β₀ and β₁.

You can have a look at the estimates by printing out the linear_regression_economic_sector object:

linear_regression_economic_sector

Which will give you this as an output:

Call:
 lm(formula = as.numeric(default_flag) ~ economic_sector, data = clean_casted_stored_data_validated_complete)

Coefficients:
    (Intercept)  economic_sector  
      2.741e+00       -2.083e-09  

Thinking again about the linear model definition, we can say that our intercept is the β₀ we were discussing before, while the β₁  is represented here from the -2.083e-09 related to the economic_sector variable.