Chemometrics is one of the most effective analytical methods among various laser-induced breakdown spectroscopy (LIBS) techniques, with principal component analysis (PCA) and partial least squares regression (PLSR) being the most typical. The above two methods perform linear feature transformation on the original spectra to reduce the issue of redundant spectral lines. It failed to determine which spectral lines are redundant although the achieved features can represent the effective information of the original spectra, finally resulting in poorer physical interpretability of the above two models. Elastic Net is a feature selection and regression modeling method that not only allows nonlinear feature dimensionality reduction of the original spectrum, but also eliminates the multicollinearity problem between spectral lines. Compared to PCA and PLSR, the Elastic Net model has a stronger capacity for model interpretation, and its regression coefficients directly reflect the influence of all original features on the response variable. To insight into the impact of effective spectral lines on quantitative results and to further comprehend the physical implications of LIBS quantitative analysis, this paper proposes three generalized linear models (GLM), Lasso, Ridge, and Elastic Net, to predict the copper content in raw copper ores/concentrates.To understand the physical significance of the original spectral lines in the dimensional reduction-quantitative models, Lasso, Ridge, and Elastic Net were utilized to determine the copper content in raw copper ores/concentrates. A spectrum acquisition device was designed using a nanosecond laser and an Echelle spectrometer (Fig.1). Five types of copper ores and four types of copper concentrates were selected as sample materials, finally obtained nine pieces of copper ore tablets (Fig.2). The gate delay of the spectrometer was set to 1 μs with a gate width of 2 μs. A total of 90 spectra were obtained from the nine types of copper ores/concentrates, of which 70 spectrums were used for training and the remaining 20 spectrums were used for testing (Tab.1). A brief analysis of the spectral characteristics of the nine types of copper ores/concentrates was conducted, identifying 11 atomic lines and 18 ionic lines for the subsequent procedure. The impact of parameter α in the Elastic Net model on the mean square error (MSE) of the validation/prediction set, and the number of valid analyzed spectral lines was analyzed in detail (Fig.4). Compare the proposed GLM methods (Lasso, Ridge, and Elastic Net) with five other methods: ordinary least squares (OLS), PLSR, support vector regression based on particle swarm optimization (PSO-SVR), Lasso-PSO-SVR, and Elastic Net-PSO-SVR. R², mean square error (MSE), and mean absolute percentage error (MAPE) were adopted to evaluate the performance of the eight models. Given the rare samples in this paper, leave-one-out cross-validation and paired T-tests were utilized to observe the statistical significance between the Elastic Net and PLSR models.Quantitative results indicate that the MSE of the testing sets for Lasso, Ridge, and Elastic Net were 1.706, 1.180, and 1.231, respectively (Tab.2). Compared to PLSR, the MSE of the above three methods was reduced by 7.4%, 33.2%, and 36.0%, respectively. In both the Ridge and Elastic Net models, all analyzed spectral lines were retained (Fig.5), while Lasso excluded 5 ionic spectral lines (217.941 nm, 218.963 nm, 221.027 nm, 221.811 nm, 229.437 nm) and 3 atomic spectral lines (249.215 nm, 327.396 nm, 510.554 nm). Significance analysis results (Tab.3, Tab.4) showed that overall performance of the Ridge and Elastic Net models is superior to traditional PLSR, while the performance of the Lasso model is comparable to PLSR.Compared to traditional and improved methods, the proposed three GLM methods (Lasso, Ridge, and Elastic Net) in this paper demonstrate a higher model fitting capability and generalization ability, while also maintaining a significant predictive advantage in small data sets. This provides a new approach for the detection of Cu element content in rare natural copper ores.