# Linear Regression and Some Alternatives

*Simple example*

regress DEPVAR INDVAR1 INDVAR2 INDVAR3, beta

Keyword beta is required if you want to obtain standardized regression coefficients.

*Example with estimation of robust (Huber-White) standard errors*

regress DEPVAR INDVAR1 INDVAR2 INDVAR3, beta robust

## More

Regression diagnostics and much else can be obtained *after* estimation of a regression model. Note that some statistics and plots will not work with survey data, i.e. if the `svy`

option (see complex samples) was used. Here are some useful post-estimation commands:

`estat hettest` | Breusch-Pagan/Cook-Weisberg test for heteroskedasticity. |

`estat vif` |
1/VIF for the independent variables. |

`rvfplot` | will display a plot of residuals vs. fitted values (helpful for assessing heteroskedasticity). |

`avplots` | will produce a tableau of added variable plots for all independen variables. |

`avplot experience` | will display an added variable plot for variable "experience". |

`avplot 3.group` | will display an added variable plot for the dummy variable that represents the category coded "3" of variable "group" (not the third value of this variable). |

`cprplot experience` | will produce a component plus residual plot for variable "experience". Options for this plot are available, such as "lowess" or "mspline". Note that an "augmented component plus residual plot" is available with command `acprplot` . It is said to do better in detecting non-linearity. |

`predict cd1, cooksd` | saves the values of Cook's d in variable "cd1". |

`dfbeta` | computes dfbeta for all independent variables and stores the values in variables whose names are given in the output. |

`predict dfbe1, dfbeta(educ)` | saves the values of dfbeta for variable "educ" in variable "dfbe1". |

`estat ic` | displays the values of AIC and BIC in the output. |

`collin x1 x2 x3` | produces additional statistics about collinearity, e.g., eigenvalues, condition number and the determinant of the correlation matrix. Note that `collin` is an ado file which has to be downloaded (start with `findit collin` ). |

## Alternatives to the regress command

### Two or more dependent variables

You may estimate models where two or more dependent variables are regressed on the same set of predictors. The advantage over a series of regressions with a single dependent variable is that you may test effects across regression equations. I cannot go into details here and will leave you just with the basic command:

mvreg depvar1 depvar2 = ivar1 ivar2 ivar3

You will not always want to use the same set of predictors, and in this case, a procedure called "seemingly unrelated regression" is the method of choice.

sureg (depvar1 ivar1 ivar2) (depvar2 ivar2 ivar3)

### Ridge regression

Some people recommend "ridge regression", particularly if collinearity is high (many others do not recommend it!). If you want to give it a try, there is an ado file `ridgereg`

which may be obtained via `findit ridgereg`

.

© W. Ludwig-Mayerhofer, Stata Guide | Last update: 26 Feb 2018