What is the use of coefficient in in Regression

Question

What is the meaning of coefficient values in Machine Learning. After I print

model.print_summary()

It shows, coefficient values of for each column. But I really don't know what is the meaning of coef in this?

                      coef  exp(coef)  se(coef)        z      p  lower 0.95  upper 0.95     
EXPERIENCE IN DAYS -0.0013     0.9987    0.0001 -22.8579 0.0000     -0.0015     -0.0012  ***
GENDER              0.4598     1.5838    0.0786   5.8536 0.0000      0.3059      0.6138  ***
GRADE              -0.7267     0.4835    0.0444 -16.3717 0.0000     -0.8136     -0.6397  ***
STAFFING_TYPE      -0.4950     0.6096    0.0413 -11.9870 0.0000     -0.5759     -0.4140  ***

Is Large coef value represents strong feature or weaker feature ?

What is the use What is the use of coefficient in in Regression?

Note: Here model represents linear regression.

Answer 1

When you have a linear regression model with $n$ exogenic variables, the model is

$$ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_n x_n + \xi $$

So you are looking for coefficients $\beta_1$, $\beta_2$, $\ldots$, $\beta_n$, so that the difference between the output ($y$) of your model for a given input vector $(x_1, \dots, x_n)$ compared to your data is minimized.

In other words the coefficients determine how much a change of each input variable contributes to the output variable. For example, a coefficient of 0.4598 for your variable $x_2$ (Gender) means that the output variable $y$ increases for 0.4598 if the variable Gender increases for 1.