The goal of lasso regression is to obtain the subset of predictors that minimizes prediction error for a quantitative response variable. The lasso does this by imposing a constraint on the model parameters that causes regression coefficients for some variables to shrink toward zero. Variables with a regression coefficient equal to zero after the shrinkage process are excluded from the model. Variables with non-zero regression coefficients variables are most strongly associated with the response variable. Explanatory variables can be either quantitative, categorical or both.

Conclusion: From a pool of 23 categorical and quantitative predictor variables that best predicted the quantitative response variable measuring school connectedness in adolescents were selected. Categorical predictors included gender and a series of 5 binary categorical variables for race and ethnicity (Hispanic, White, Black, Native American and Asian) to improve interpretability of the selected model with fewer predictors. Binary substance use variables were measured with individual questions about whether the adolescent had ever used alcohol, marijuana, cocaine or inhalants. Additional categorical variables included the availability of cigarettes in the home, whether or not either parent was on public assistance and any experience with being expelled from school. Quantitative predictor variables include age, alcohol problems, and a measure of deviance that included such behaviors as vandalism, other property damage, lying, stealing, running away, driving without permission, selling drugs, and skipping school. Another scale for violence, one for depression, and others measuring self-esteem, parental presence, parental activities, family connectedness and grade point average were also included. All predictor variables were standardized to have a mean of zero and a standard deviation of one. Data were randomly split into a training set that included 70% of the observations (N=3201) and a test set that included 30% of the observations (N=1701). The least angle regression algorithm with k=10 fold cross validation was used to estimate the lasso regression model in the training set, and the model was validated using the test set. The change in the cross validation average (mean) squared error at each step was used to identify the best subset of predictor variables. 18 out of 23 variables were selected and These 18 variables accounted for 33.4% of the variance in the school connectedness response variable.

For detailed explanation : https://mlhackerblog.wordpress.com/2017/11/18/lasso-regression-to-predict-the-school-connectedness-of-a-student/