This data set contains example data for exploration of the theory of regression based regionalization. The 90th percentile of annual maximum streamflow is provided as an example response variable for 293 streamgages in the conterminous United States. Several explanatory variables are drawn from the GAGES-II data base in order to demonstrate how multiple linear regression is applied. Example scripts demonstrate how to collect the original streamflow data provided and how to recreate the figures from the associated Techniques and Methods chapter.

Site-specific multiple linear regression models were developed for eight sites in Ohio—six in the Western Lake Erie Basin and two in northeast Ohio on inland reservoirs--to quickly predict action-level exceedances for a cyanotoxin, microcystin, in recreational and drinking waters used by the public. Real-time models include easily- or continuously-measured factors that do not require that a sample be collected. Real-time models are presented in two categories: (1) six models with continuous monitor data, and (2) three models with on-site measurements. Real-time models commonly included variables such as phycocyanin, pH, specific conductance, and streamflow or gage height. Many of the real-time factors were averages over time periods antecedent to the time the microcystin sample was collected, including water-quality data compiled from continuous monitors. Comprehensive models use a combination of discrete sample-based measurements and real-time factors. Comprehensive models were useful at some sites with lagged variables (< 2 weeks) for cyanobacterial toxin genes, dissolved nutrients, and (or) N to P ratios. Comprehensive models are presented in three categories: (1) three models with continuous monitor data and lagged comprehensive variables, (2) five models with no continuous monitor data and lagged comprehensive variables, and (3) one model with continuous monitor data and same-day comprehensive variables. Funding for this work was provided by the Ohio Water Development Authority and the U.S. Geological Survey Cooperative Water Program.

Dataset

This dataset was created by FayeJavad

Contents

The Ice Cream Selling dataset is a simple and well-suited dataset for beginners in machine learning who are looking to practice polynomial regression. It consists of two columns: temperature and the corresponding number of units of ice cream sold.

The dataset captures the relationship between temperature and ice cream sales. It serves as a practical example for understanding and implementing polynomial regression, a powerful technique for modeling nonlinear relationships in data.

The dataset is designed to be straightforward and easy to work with, making it ideal for beginners. The simplicity of the data allows beginners to focus on the fundamental concepts and steps involved in polynomial regression without overwhelming complexity.

By using this dataset, beginners can gain hands-on experience in preprocessing the data, splitting it into training and testing sets, selecting an appropriate degree for the polynomial regression model, training the model, and evaluating its performance. They can also explore techniques to address potential challenges such as overfitting.

With this dataset, beginners can practice making predictions of ice cream sales based on temperature inputs and visualize the polynomial regression curve that represents the relationship between temperature and ice cream sales.

Overall, the Ice Cream Selling dataset provides an accessible and practical learning resource for beginners to grasp the concepts and techniques of polynomial regression in the context of analyzing ice cream sales data.

Summary : Fuel demand is shown to be influenced by fuel prices, people's income and motorization rates. We explore the effects of electric vehicle's rates in gasoline demand using this panel dataset.

Files : dataset.csv - Panel dimensions are the Brazilian state ( i ) and year ( t ). The other columns are: gasoline sales per capita (ln_Sg_pc), prices of gasoline (ln_Pg) and ethanol (ln_Pe) and their lags, motorization rates of combustion vehicles (ln_Mi_c) and electric vehicles (ln_Mi_e) and GDP per capita (ln_gdp_pc). All variables are all under the natural log function, since we use this to calculate demand elasticities in a regression model.

adjacency.csv - The adjacency matrix used in interaction with electric vehicles' motorization rates to calculate spatial effects. At first, it follows a binary adjacency formula: for each pair of states i and j, the cell (i, j) is 0 if the states are not adjacent and 1 if they are. Then, each row is normalized to have sum equal to one.

regression.do - Series of Stata commands used to estimate the regression models of our study. dataset.csv must be imported to work, see comment section.

dataset_predictions.xlsx - Based on the estimations from Stata, we use this excel file to make average predictions by year and by state. Also, by including years beyond the last panel sample, we also forecast the model into the future and evaluate the effects of different policies that influence gasoline prices (taxation) and EV motorization rates (electrification). This file is primarily used to create images, but can be used to further understand how the forecasting scenarios are set up.

Sources: Fuel prices and sales: ANP (https://www.gov.br/anp/en/access-information/what-is-anp/what-is-anp) State population, GDP and vehicle fleet: IBGE (https://www.ibge.gov.br/en/home-eng.html?lang=en-GB) State EV fleet: Anfavea (https://anfavea.com.br/en/site/anuarios/)

It is a messy dataset, wherein, leaners can emphasis on learning how to clean and preprocess the data, along with how they can find meaning from this random messy data.

for, assignment I recommend: You are a data scientist at a real estate company tasked with building a model to predict house prices based on features like area, number of bedrooms, location, and age of the house.

Data set from PLOS ONE Article Published Entitled: Western Lowland Gorillas Signal Selectively Using Odor

Students typically find linear regression analysis of data sets in a biology classroom challenging. These activities could be used in a Biology, Chemistry, Mathematics, or Statistics course. The collection provides student activity files with Excel instructions and Instructor Activity files with Excel instructions and solutions to problems.

Students will be able to perform linear regression analysis, find correlation coefficient, create a scatter plot and find the r-square using MS Excel 365. Students will be able to interpret data sets, describe the relationship between biological variables, and predict the value of an output variable based on the input of an predictor variable.

Despite recent papers on problems associated with full-model and stepwise regression, their use is still common throughout ecological and environmental disciplines. Alternative approaches, including generating multiple models and comparing them post-hoc using techniques such as Akaike's Information Criterion (AIC), are becoming more popular. However, these are problematic when there are numerous independent variables and interpretation is often difficult when competing models contain many different variables and combinations of variables. Here, we detail a new approach, REVS (Regression with Empirical Variable Selection), which uses all-subsets regression to quantify empirical support for every independent variable. A series of models is created; the first containing the variable with most empirical support, the second containing the first variable and the next most-supported, and so on. The comparatively small number of resultant models (n = the number of predictor variables) means that post-hoc comparison is comparatively quick and easy. When tested on a real dataset – habitat and offspring quality in the great tit (Parus major) – the optimal REVS model explained more variance (higher R2), was more parsimonious (lower AIC), and had greater significance (lower P values), than full, stepwise or all-subsets models; it also had higher predictive accuracy based on split-sample validation. Testing REVS on ten further datasets suggested that this is typical, with R2 values being higher than full or stepwise models (mean improvement = 31% and 7%, respectively). Results are ecologically intuitive as even when there are several competing models, they share a set of “core” variables and differ only in presence/absence of one or two additional variables. We conclude that REVS is useful for analysing complex datasets, including those in ecology and environmental disciplines.

Description: This dataset is designed for predicting energy consumption based on various building features and environmental factors. It contains data for multiple building types, square footage, the number of occupants, appliances used, average temperature, and the day of the week. The goal is to build a predictive model to estimate energy consumption using these attributes.

The dataset can be used for training machine learning models such as linear regression to forecast energy needs based on the building's characteristics. This is useful for understanding energy demand patterns and optimizing energy consumption in different building types and environmental conditions.

These four labeled data sets are targeted at ordinal quantification. The goal of quantification is not to predict the label of each individual instance, but the distribution of labels in unlabeled sets of data.

With the scripts provided, you can extract CSV files from the UCI machine learning repository and from OpenML. The ordinal class labels stem from a binning of a continuous regression label.

We complement this data set with the indices of data items that appear in each sample of our evaluation. Hence, you can precisely replicate our samples by drawing the specified data items. The indices stem from two evaluation protocols that are well suited for ordinal quantification. To this end, each row in the files app_val_indices.csv, app_tst_indices.csv, app-oq_val_indices.csv, and app-oq_tst_indices.csv represents one sample.

Our first protocol is the artificial prevalence protocol (APP), where all possible distributions of labels are drawn with an equal probability. The second protocol, APP-OQ, is a variant thereof, where only the smoothest 20% of all APP samples are considered. This variant is targeted at ordinal quantification tasks, where classes are ordered and a similarity of neighboring classes can be assumed.

Usage

You can extract four CSV files through the provided script extract-oq.jl, which is conveniently wrapped in a Makefile. The Project.toml and Manifest.toml specify the Julia package dependencies, similar to a requirements file in Python.

Preliminaries: You have to have a working Julia installation. We have used Julia v1.6.5 in our experiments.

Data Extraction: In your terminal, you can call either

make

(recommended), or

julia --project="." --eval "using Pkg; Pkg.instantiate()"
julia --project="." extract-oq.jl

Outcome: The first row in each CSV file is the header. The first column, named "class_label", is the ordinal class.

Further Reading

Implementation of our experiments: https://github.com/mirkobunse/regularized-oq

This data release provides two example groundwater-level datasets used to benchmark the Automated Regional Correlation Analysis for Hydrologic Record Imputation (ARCHI) software package (Levy and others, 2024). The first dataset contains groundwater-level records and site metadata for wells located on Long Island, New York (NY) and some surrounding mainland sites in New York and Connecticut. The second dataset contains groundwater-level records and site metadata for wells located in the southeastern San Joaquin Valley of the Central Valley, California (CA). For ease of exposition these are referred to as NY and CA datasets, respectively. Both datasets are formatted with column headers that can be read by the ARCHI software package within the R computing environment. These datasets were used to benchmark the imputation accuracy of three ARCHI model settings (OLS, ridge, and MOVE.1) against the widely used imputation program missForest (Stekhoven and Bühlmann, 2012). The ARCHI program was used to process the NY and CA datasets on monthly and annual timesteps, respectively, filter out sites with insufficient data for imputation, and create 200 test datasets from each of the example datasets with 5 percent of observations removed at random (herein, referred to as "holdouts"). Imputation accuracy for test datasets was assessed using normalized root mean square error (NRMSE), which is the root mean square error divided by the standard deviation of the observed holdout values. ARCHI produces prediction intervals (PIs) using a non-parametric bootstrapping routine, which were assessed by computing a coverage rate (CR) defined as the proportion of holdout observations falling within the estimated PI. The multiple regression models included with the ARCHI package (OLS and ridge) were further tested on all test datasets at eleven different levels of the p_per_n input parameter, which limits the maximum ratio of regression model predictors (p) per observations (n) as a decimal fraction greater than zero and less than or equal to one. This data release contains ten tables formatted as tab-delimited text files. The “CA_data.txt” and “NY_data.txt” tables contain 243,094 and 89,997 depth-to-groundwater measurement values (value, in feet below land surface) indexed by site identifier (site_no) and measurement date (date) for CA and NY datasets, respectively. The “CA_sites.txt” and “NY_sites.txt” tables contain site metadata for the 4,380 and 476 unique sites included in the CA and NY datasets, respectively. The “CA_NRMSE.txt” and “NY_NRMSE.txt” tables contain NRMSE values computed by imputing 200 test datasets with 5 percent random holdouts to assess imputation accuracy for three different ARCHI model settings and missForest using CA and NY datasets, respectively. The “CA_CR.txt” and “NY_CR.txt” tables contain CR values used to evaluate non-parametric PIs generated by bootstrapping regressions with three different ARCHI model settings using the CA and NY test datasets, respectively. The “CA_p_per_n.txt” and “NY_p_per_n.txt” tables contain mean NRMSE values computed for 200 test datasets with 5 percent random holdouts at 11 different levels of p_per_n for OLS and ridge models compared to training error for the same models on the entire CA and NY datasets, respectively. References Cited Levy, Z.F., Stagnitta, T.J., and Glas, R.L., 2024, ARCHI: Automated Regional Correlation Analysis for Hydrologic Record Imputation, v1.0.0: U.S. Geological Survey software release, https://doi.org/10.5066/P1VVHWKE. Stekhoven, D.J., and Bühlmann, P., 2012, MissForest—non-parametric missing value imputation for mixed-type data: Bioinformatics 28(1), 112-118. https://doi.org/10.1093/bioinformatics/btr597.

In the field of data-driven material development, an imbalance in data sets where data points are concentrated in certain regions often causes difficulties in building regression models when machine learning methods are applied. One example of inorganic functional materials facing such difficulties is photocatalysts. Therefore, advanced data-driven approaches are expected to help efficiently develop novel photocatalytic materials even if an imbalance exists in data sets. We propose a two-stage machine learning model aimed at handling imbalanced data sets without data thinning. In this study, we used two types of data sets that exhibit the imbalance: the Materials Project data set (openly shared due to its public domain data) and the in-house metal-sulfide photocatalyst data set (not openly shared due to the confidentiality of experimental data). This two-stage machine learning model consists of the following two parts: the first regression model, which predicts the target quantitatively, and the second classification model, which determines the reliability of the values predicted by the first regression model. We also propose a search scheme for variables related to the experimental conditions based on the proposed two-stage machine learning model. This scheme is designed for photocatalyst exploration, taking experimental conditions into account as the optimal set of variables for these conditions is unknown. The proposed two-stage machine learning model improves the prediction accuracy of the target compared with that of the one-stage model.

New algorithms are continuously proposed in computational biology. Performance evaluation of novel methods is important in practice. Nonetheless, the field experiences a lack of rigorous methodology aimed to systematically and objectively evaluate competing approaches. Simulation studies are frequently used to show that a particular method outperforms another. Often times, however, simulation studies are not well designed, and it is hard to characterize the particular conditions under which different methods perform better. In this paper we propose the adoption of well established techniques in the design of computer and physical experiments for developing effective simulation studies. By following best practices in planning of experiments we are better able to understand the strengths and weaknesses of competing algorithms leading to more informed decisions about which method to use for a particular task. We illustrate the application of our proposed simulation framework with a detailed comparison of the ridge-regression, lasso and elastic-net algorithms in a large scale study investigating the effects on predictive performance of sample size, number of features, true model sparsity, signal-to-noise ratio, and feature correlation, in situations where the number of covariates is usually much larger than sample size. Analysis of data sets containing tens of thousands of features but only a few hundred samples is nowadays routine in computational biology, where “omics” features such as gene expression, copy number variation and sequence data are frequently used in the predictive modeling of complex phenotypes such as anticancer drug response. The penalized regression approaches investigated in this study are popular choices in this setting and our simulations corroborate well established results concerning the conditions under which each one of these methods is expected to perform best while providing several novel insights.

File List supplement1.txt Description Raw sample sizes (n) and standard errors (SE), geographically effective degrees of freedom (v*), adjusted standard errors (SE*), and adjusted 95% CI of OLS and RMA slopes for all data sets. Also provided is the information from Tables 1 and 2 to facilitate evaluation of each case, and the sources of the richness data (see Appendix A for full references). Data with linear relationships between rescaled temperature and ln richness are listed first, followed by nonlinear data divided into values to the left of their breakpoints (Cool) and to the right of their breakpoints (Warm) (see Table 2). North American reptiles, listed last, could not be analyzed with either linear or split-line regression.

This data release contains three different datasets that were used in the Scientific Investigations Report: Spatial and Temporal Distribution of Bacterial Indicators and Microbial Source Tracking within Tumacácori National Historical Park and the Upper Santa Cruz River, Arizona, 2015-16. These datasets contain regression model data, estimated discharge data, and calculated flux and yields data. Regression Model Data: This dataset contains data used in a regression model development in the SIR. The period of data ranged from May 25, 1994 to May 19, 2017. Data from 2015 to 2017 were collected by the U.S. Geological Survey. Data prior to 2015 were provided by various agencies. Listed below are the different data contained within this dataset: - Season represented as an indicator variable (Fall, Spring, Summer, and Winter) - Hydrologic Condition represented as an indicator variable (rising limb, recession limb, peak, or unable to classify) - Flood (binary variable indicating if the sample was collected during a flood event or not) - Decimal Date (DT) represented as a continuous variable - Sine of DT represented as a continuous variable for periodic function to describe seasonal variation - Cosine of DT represented as a continuous variable for periodic function to describe seasonal variation Estimated Discharge: This dataset contains estimated discharge at four different sites between 03/02/2015 and 12/14/2016. The discharge was estimated using nearby streamgage relations and methods are described in detail in the SIR . The sites where discharge was estimated are listed below. - NW8; 312551110573901; Nogales Wash at Ruby Road - SC3; 312654110573201; Santa Cruz River abv Nogales Wash - SC10; 313343110024701; Santa Cruz River at Santa Gertrudis Lane - SC14; 09481740; Santa Cruz River at Tubac, AZ Calculated Flux and Yields: This dataset contains calculated flux and yields for E. coli and suspended sediment concentrations. Mean daily flux was calculated when mean daily discharge was available at a corresponding streamgage. Instantaneous flux was calculated when instantaneous discharge (at 15-minute intervals) were available at a corresponding streamgage, or from a measured or estimated discharge value. The yields were calculated using the calculated flux values and the area of the different watersheds. Methods and equations are described in detail in the SIR. Listed below are the data contained within this dataset: - Mean daily E. coli flux, in most probable number per day - Mean daily suspended sediment, in flux, in tons per day - Instantaneous E. coli flux, in most probable number per second - Instantaneous suspended sediment flux, in tons per second - E. coli, in most probable number per square mile - Suspended sediment, in tons per square mile

This data release supports the following publication: Mast, M. A., 2018, Estimating metal concentrations with regression analysis and water-quality surrogates at nine sites on the Animas and San Juan Rivers, Colorado, New Mexico, and Utah: U.S. Geological Survey Scientific Investigations Report 2018-5116. The U.S. Geological Survey (USGS), in cooperation with the U. S. Environmental Protection Agency (EPA), developed site-specific regression models to estimate concentrations of selected metals at nine USGS streamflow-gaging stations along the Animas and San Juan Rivers. Multiple linear-regression models were developed by relating metal concentrations in discrete water-quality samples to continuously monitored streamflow and surrogate parameters including specific conductance, pH, turbidity, and water temperature. Models were developed for dissolved and total concentrations of aluminum, arsenic, cadmium, iron, lead, manganese, and zinc using water-quality samples collected during 2005–17 by several agencies, using different collection methods and analytical laboratories. Calibration datasets in comma-separated format (CSV) include the variables of sampling date and time, metal concentrations (in micrograms per liter), stream discharge (in cubic feet per second), specific conductance (in microsiemens per centimeter at 25 degrees Celsius), pH, water temperature (in degrees Celsius), turbidity (in nephelometric turbidity units), and calculated seasonal terms based on Julian day. Surrogate parameters and discrete water-quality samples were used from nine sites including Cement Creek at Silverton, Colo. (USGS station 09358550); Animas River below Silverton, Colo. (USGS station 09359020); Animas River at Durango, Colo. (USGS station 09361500); Animas River Near Cedar Hill, N. Mex. (USGS station 09363500); Animas River below Aztec, N. Mex. (USGS station 09364010); San Juan River at Farmington, N. Mex. (USGS station 09365000); San Juan River at Shiprock, N. Mex (USGS Station 09368000); San Juan River at Four Corners, Colo. (USGS station 09371010); and San Juan River near Bluff, Utah (USGS station 09379500). Model archive summaries in pdf format include model statistics, data, and plots and were generated using a R script developed by USGS Kansas Water Science Center available at https://patrickeslick.github.io/ModelArchiveSummary/. A description of each USGS streamflow gaging station along with information about the calibration datasets also are provided.

This dataset contains simulated datasets, empirical data, and R scripts described in the paper: “Li, Q. and Kou, X. (2021) WiBB: An integrated method for quantifying the relative importance of predictive variables. Ecography (DOI: 10.1111/ecog.05651)”.

A fundamental goal of scientific research is to identify the underlying variables that govern crucial processes of a system. Here we proposed a new index, WiBB, which integrates the merits of several existing methods: a model-weighting method from information theory (Wi), a standardized regression coefficient method measured by ß* (B), and bootstrap resampling technique (B). We applied the WiBB in simulated datasets with known correlation structures, for both linear models (LM) and generalized linear models (GLM), to evaluate its performance. We also applied two other methods, relative sum of wight (SWi), and standardized beta (ß*), to evaluate their performance in comparison with the WiBB method on ranking predictor importances under various scenarios. We also applied it to an empirical dataset in a plant genus Mimulus to select bioclimatic predictors of species’ presence across the landscape. Results in the simulated datasets showed that the WiBB method outperformed the ß* and SWi methods in scenarios with small and large sample sizes, respectively, and that the bootstrap resampling technique significantly improved the discriminant ability. When testing WiBB in the empirical dataset with GLM, it sensibly identified four important predictors with high credibility out of six candidates in modeling geographical distributions of 71 Mimulus species. This integrated index has great advantages in evaluating predictor importance and hence reducing the dimensionality of data, without losing interpretive power. The simplicity of calculation of the new metric over more sophisticated statistical procedures, makes it a handy method in the statistical toolbox.

Methods To simulate independent datasets (size = 1000), we adopted Galipaud et al.’s approach (2014) with custom modifications of the data.simulation function, which used the multiple normal distribution function rmvnorm in R package mvtnorm(v1.0-5, Genz et al. 2016). Each dataset was simulated with a preset correlation structure between a response variable (y) and four predictors(x1, x2, x3, x4). The first three (genuine) predictors were set to be strongly, moderately, and weakly correlated with the response variable, respectively (denoted by large, medium, small Pearson correlation coefficients, r), while the correlation between the response and the last (spurious) predictor was set to be zero. We simulated datasets with three levels of differences of correlation coefficients of consecutive predictors, where ∆r = 0.1, 0.2, 0.3, respectively. These three levels of ∆r resulted in three correlation structures between the response and four predictors: (0.3, 0.2, 0.1, 0.0), (0.6, 0.4, 0.2, 0.0), and (0.8, 0.6, 0.3, 0.0), respectively. We repeated the simulation procedure 200 times for each of three preset correlation structures (600 datasets in total), for LM fitting later. For GLM fitting, we modified the simulation procedures with additional steps, in which we converted the continuous response into binary data O (e.g., occurrence data having 0 for absence and 1 for presence). We tested the WiBB method, along with two other methods, relative sum of wight (SWi), and standardized beta (ß*), to evaluate the ability to correctly rank predictor importances under various scenarios. The empirical dataset of 71 Mimulus species was collected by their occurrence coordinates and correponding values extracted from climatic layers from WorldClim dataset (www.worldclim.org), and we applied the WiBB method to infer important predictors for their geographical distributions.

The National Health and Nutrition Examination Survey (NHANES) provides data and have considerable potential to study the health and environmental exposure of the non-institutionalized US population. However, as NHANES data are plagued with multiple inconsistencies, processing these data is required before deriving new insights through large-scale analyses. Thus, we developed a set of curated and unified datasets by merging 614 separate files and harmonizing unrestricted data across NHANES III (1988-1994) and Continuous (1999-2018), totaling 135,310 participants and 5,078 variables. The variables conveydemographics (281 variables),dietary consumption (324 variables),physiological functions (1,040 variables),occupation (61 variables),questionnaires (1444 variables, e.g., physical activity, medical conditions, diabetes, reproductive health, blood pressure and cholesterol, early childhood),medications (29 variables),mortality information linked from the National Death Index (15 variables),survey weights (857 variables),environmental exposure biomarker measurements (598 variables), andchemical comments indicating which measurements are below or above the lower limit of detection (505 variables).csv Data Record: The curated NHANES datasets and the data dictionaries includes 23 .csv files and 1 excel file.The curated NHANES datasets involves 20 .csv formatted files, two for each module with one as the uncleaned version and the other as the cleaned version. The modules are labeled as the following: 1) mortality, 2) dietary, 3) demographics, 4) response, 5) medications, 6) questionnaire, 7) chemicals, 8) occupation, 9) weights, and 10) comments."dictionary_nhanes.csv" is a dictionary that lists the variable name, description, module, category, units, CAS Number, comment use, chemical family, chemical family shortened, number of measurements, and cycles available for all 5,078 variables in NHANES."dictionary_harmonized_categories.csv" contains the harmonized categories for the categorical variables.“dictionary_drug_codes.csv” contains the dictionary for descriptors on the drugs codes.“nhanes_inconsistencies_documentation.xlsx” is an excel file that contains the cleaning documentation, which records all the inconsistencies for all affected variables to help curate each of the NHANES modules.R Data Record: For researchers who want to conduct their analysis in the R programming language, only cleaned NHANES modules and the data dictionaries can be downloaded as a .zip file which include an .RData file and an .R file.“w - nhanes_1988_2018.RData” contains all the aforementioned datasets as R data objects. We make available all R scripts on customized functions that were written to curate the data.“m - nhanes_1988_2018.R” shows how we used the customized functions (i.e. our pipeline) to curate the original NHANES data.Example starter codes: The set of starter code to help users conduct exposome analysis consists of four R markdown files (.Rmd). We recommend going through the tutorials in order.“example_0 - merge_datasets_together.Rmd” demonstrates how to merge the curated NHANES datasets together.“example_1 - account_for_nhanes_design.Rmd” demonstrates how to conduct a linear regression model, a survey-weighted regression model, a Cox proportional hazard model, and a survey-weighted Cox proportional hazard model.“example_2 - calculate_summary_statistics.Rmd” demonstrates how to calculate summary statistics for one variable and multiple variables with and without accounting for the NHANES sampling design.“example_3 - run_multiple_regressions.Rmd” demonstrates how run multiple regression models with and without adjusting for the sampling design.

Imbalanced data is a problem in that the number of samples in different categories or target value ranges varies greatly. Data imbalance imposes excellent challenges to machine learning and pattern recognition. The performance of machine learning models leans to be partially towards the majority of samples in the imbalanced dataset, which will further affect the effect of the model. The imbalanced data problem includes an imbalanced categorical problem and an imbalanced regression problem. Many studies have been developed to address the issue of imbalanced classification data. Nevertheless, the imbalanced regression problem has not been well-researched. In order to solve the problem of unbalanced regression data, we define an RNGRU model that can simultaneously learn the regression characteristics and neighbor characteristics of regression samples. To obtain the most comprehensive sample information of regression samples, the model uses the idea of confrontation to determine the proportion between the regression characteristics and neighbor characteristics of the original samples. According to the regression characteristics of the regression samples, an index ccr (correlation change rate) is proposed to evaluate the similarity between the generated samples and the original samples. And on this basis, an RNGAN model is proposed to reduce the similarity between the generated samples and the original samples by using the idea of confrontation.