Regression Modeling Using Stata

Regression is a useful tool for examining how variables fit together to any degree of complication desired. In Stata, the basic linear regression command is simply regress [y variable], [x variables], [options]. The regress command output contains an ANOVA table, but depending on the options you specify, this may or may not be relevant and may be suppressed. The default is non standardized coefficients, but standardised weights can be obtained after running the regression by typing regress, beta. The regress command looks for variables that have collinearity (that is, their individual line points are the same) and drops them (as indicated by the word “dropped” next to them).

KEY FEATURE

The computational complexity of a model can be decreased by narrowing down the number of features using feature selection.

It refers to a set of statistical procedures used in statistical modelling to estimate the associations between a dependent variable and one or more independent variables.

One such method is ordinary least squares, which finds “the one line (or hyperplane) that minimises the sum of squared differences between the true data and that line” (or hyperplane).

This allows to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values, for very specific mathematical reasons.

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    Hoskedasticity, or the assumption that all variables have similar variability, is one of the assumptions for linear regression. Stata provides the vce([correction type]) option if you suspect your data is heterosekdastic or if your observations include some within-subject data. The vce option modifies the type of standard error reported and is used by many Stata commands; for more information, see the vce tutorial. To learn more about these two options, the regress, vce () option can also take hc2 and hc3 type help regress.

    Multiple Regression Analysis Using Stata

    Multiple regression (a variation on simple linear regression) predicts the value of a dependent variable (also known as an outcome variable) based on the values of two or more independent variables (also known as predictor variables). For example, you could use multiple regression to see if coursework grade, revision time, lecture attendance, and IQ score can predict exam anxiety (i.e., the dependent variable would be “exam anxiety”, and the four independent variables would be “coursework mark”, “revision time”, “lecture attendance” and “IQ score”). You could also use multiple regression to see if income can be predicted based on age, gender, and educational level (i.e., the dependent variable would be “income”, and the three independent variables would be “age”, “gender” and “educational level”). A binomial logistic regression can be used when the dependent variable is dichotomous.
    Multiple regression can also be used to determine the model’s overall fit (variance explained) and the relative contribution of each independent variable to the total variance explained. For example, you might want to know how much variation in exam anxiety can be explained by coursework grade, revision time, lecture attendance, and IQ score “as a whole,” as well as the “relative contribution” of each independent variable to explaining the variance.
    This “quick start” guide will show you how to run multiple regression tests in Stata, as well as how to interpret and report the results. However, before we begin, you should be aware of the various assumptions that your data must meet in order for multiple regression to produce a valid result. Following that, we will go over these assumptions.

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