### Goals

This tutorial introduces the use of `quantileFit`

to estimate quantile regressions. After this tutorial, you should be able to estimate a basic model using either:

as your data inputs.

## Basic usage with a formula string

The `quantileFit`

procedure accepts dataset names and formula strings as direct inputs. This allows you to tell `quantileFit`

which data to load, saving the extra step of manually loading your data into matrices. For example, consider using data from the dataset `regsmpl.dta`

to fit the model:

$$ln(wage) = \alpha + \beta_1 * age + \beta_2 * age^2 + \beta_3 * tenure$$

```
// Create string with full path to dataset
dataset = getGAUSSHome() $+ "examples/regsmpl.dta";
// Estimate the model
call quantileFit(dataset, "ln_wage ~ age + age:age + tenure");
```

This code will produce the following output

Total observations: 28101

Number of variables: 3

VAR. / tau (in %) 5% 50% 95%

--------------------------------------------------- CONSTANT -0.7630 0.5112 0.0006 age 0.1103 0.0656 0.1271 age:age -0.0017 -0.0010 -0.0016 tenure 0.0356 0.0466 0.0196

In the results above, we get estimates for the default quantile levels, 5%, 50%, and 95%. In addition, note that because we use formula strings, GAUSS automatically includes variable names in the output table.

## Basic usage with matrix inputs

The `quantileFit`

procedure can also accept matrix inputs. We demonstrate using the same model as before. However, this time we:

- Create the data matrices
`y`

and`x`

from the`regsmpl.dta`

by loading the appropriate variables. - Use the matrices
`y`

and`x`

as the dependent and independent variable inputs, respectively, in the`quantileFit`

function call.

```
// Create string with full path to dataset
dataset = getGAUSSHome() $+ "examples/regsmpl.dta";
// Load dependent variable
y = loadd(dataset, "ln_wage");
// Load the independent variables
x = loadd(dataset, "age + age:age + tenure");
// Estimate the model with matrix inputs
call quantileFit(y, x);
```

This code will give us the same estimates as above but will use generic names for the variables since GAUSS matrices do not store variable names.

Total observations: 28101

Number of variables: 3

VAR. / tau (in %) 5% 50% 95%

--------------------------------------------------- CONSTANT -0.7630 0.5112 0.0006 X01 0.1103 0.0656 0.1271 X02 -0.0017 -0.0010 -0.0016 X03 0.0356 0.0466 0.0196

### Conclusion

This tutorial showed you how to estimate the parameters of a simple linear quantile regression using a dataset name and formula string or matrix inputs.

In the next tutorial we will learn how to specify quantile levels for the `quantileFit`

regression.