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 car company wants to enter a new market and needs an estimation of exactly which variables affect the car prices. The goal is: - Which variables are significant in predicting the price of a car - How well do those variables describe the price of a car

BackgroundThis study aimed to explore the adverse influences of mobile phone usage on pilots’ status, so as to improve flight safety.MethodsA questionnaire was designed, and a cluster random sampling method was adopted. Pilots of Shandong Airlines were investigated on the use of mobile phones. The data was analyzed by frequency statistics, linear regression and other statistical methods.ResultsA total of 340 questionnaires were distributed and 317 were returned, 315 of which were valid. The results showed that 239 pilots (75.87%) used mobile phones as the main means of entertainment in their leisure time. There was a significant negative correlation between age of pilots and playing mobile games (p

The file contain dataset with two variables (x & y). The dataset is for Linear regression ML Models. The dataset can be used for Testing purpose. The x variable is the independent variable, and y is the dependent variable. The dataset has a correlation of 0.9981 showing the dataset is best suited for linear models and can be used for the testing purpose.

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.

IntroductionThis study uses a non-linear model to explore the impact mechanism of change rates between internet search behavior and confirmed COVID-19 cases. The research background focuses on epidemic monitoring, leveraging internet search data as a real-time tool to capture public interest and predict epidemic development. The goal is to establish a widely applicable mathematical framework through the analysis of long-term disease data.MethodsData were sourced from the Baidu Index for COVID-19-related search behavior and confirmed COVID-19 case data from the National Health Commission of China. A logistic-based non-linear differential equation model was employed to analyze the mutual influence mechanism between confirmed case numbers and the rate of change in search behavior. Structural and operator relationships between variables were determined through segmented data fitting and regression analysis.ResultsThe results indicated a significant non-linear correlation between search behavior and confirmed COVID-19 cases. The non-linear differential equation model constructed in this study successfully passed both structural and correlation tests, with dynamic data fitting showing a high degree of consistency. The study further quantified the mutual influence between search behavior and confirmed cases, revealing a strong feedback loop between the two: changes in search behavior significantly drove the growth of confirmed cases, while the increase in confirmed cases also stimulated the public's search behavior. This finding suggests that search behavior not only reflects the development trend of the epidemic but can also serve as an effective indicator for predicting the evolution of the pandemic.DiscussionThis study enriches the understanding of epidemic transmission mechanisms by quantifying the dynamic interaction between public search behavior and epidemic spread. Compared to simple prediction models, this study focuses more on stable common mechanisms and structural analysis, laying a foundation for future research on public health events.

This dataset contains a collection of 100 randomly generated data points representing the relationship between the number of hours a student spends studying and their corresponding performance, measured as a score. The data has been generated to simulate a real-world scenario where study hours are assumed to influence academic outcomes, making it an excellent resource for linear regression analysis and other machine learning tasks.

Each row in the dataset consists of:

Hours: The number of hours a student dedicates to studying, ranging between 0 and 10 hours. Scores: The student's performance score, represented as a percentage, ranging from 0 to 100. Use Cases: This dataset is particularly useful for:

Linear Regression: Exploring how study hours influence student performance, fitting a regression line to predict scores based on study time. Data Science & Machine Learning: Practicing regression analysis, training models, and applying other predictive algorithms. Educational Research: Simulating data-driven insights into student behavior and performance metrics. Features: 100 rows of data. Continuous numerical variables suitable for regression tasks. Generated for educational purposes, making it ideal for students, teachers, and beginners in machine learning and data science. Potential Applications: Build a linear regression model to predict student scores. Investigate the correlation between study time and performance. Apply data visualization techniques to better understand the data. Use the dataset to experiment with model evaluation metrics like Mean Squared Error (MSE) and R-squared.

The aim of this data set is to be used along with my notebook Linear Regression Notes which provides a guideline for applying correlation analysis and linear regression models from a statistical approach.

A fictional call center is interested in knowing the relationship between the number of personnel and some variables that measure their performance such as average answer time, average calls per hour, and average time per call. Data were simulated to represent 200 shifts.

Baseline multiple linear regression model with end fitness as the response variable, showing the calculated variable inflation factors (VIFs).

Context

This dataset was given by our professor as a lab work of machine learning.

Content

In the exam.xls file, the results of a computer science exam are recorded. The following parameters are used:

id = final digit of the student matriculation number group = name of the learning group sex = gender (m = male, f = female) quanti = number of solved exercises points = total score achieved from the exercises exam = total score achieved from the final written exam (* "Students must have to participate in the final written exam. If not, he/she will be considered as fail") passed = self-explanatory

Please solve the following tasks as far as possible with the IBM SPSS Modeler in a single stream/with python programming language.

TASK 1: (statistics) Determine the average, median, mode, and standard deviation of the points from the exercises.

TASK 2: (regression)

Check whether the points in the exam (y value) is dependent from the total score from the exercises (x value) by preparing the data graphically! Perform a linear regression! What are the parameters of the trend line? Determine (by hand) the correlation coefficient between the points (x value) in the exercises and in the points in the exam (y value). Interpret the result!

Acknowledgements

Basically, We used IBM SPSS Modeler for performing the task, as most of the students were not from the computer science background. But due to my self-interest, I also tried to solve the task with the python data science library.

Inspiration

Your data will be in front of the world's largest data science community. What questions do you want to see answered?

R code and datasets for analyses presented in Hutschenreiter et al. 2024 "How to count bird calls? Vocal activity indices may provide different insights into bird abundance and behaviour depending on species traits" (Methods in Ecology and Evolution)

Correlation coefficients (R2) from simple linear regressions between the US News and World Report Score and its contributors.

Pearson’s correlation and multiple stepwise linear regression analysis of risk factors associated with CIMT.

Vitamin D insufficiency appears to be prevalent in SLE patients. Multiple factors potentially contribute to lower vitamin D levels, including limited sun exposure, the use of sunscreen, darker skin complexion, aging, obesity, specific medical conditions, and certain medications. The study aims to assess the risk factors associated with low vitamin D levels in SLE patients in the southern part of Bangladesh, a region noted for a high prevalence of SLE. The research additionally investigates the possible correlation between vitamin D and the SLEDAI score, seeking to understand the potential benefits of vitamin D in enhancing disease outcomes for SLE patients. The study incorporates a dataset consisting of 50 patients from the southern part of Bangladesh and evaluates their clinical and demographic data. An initial exploratory data analysis is conducted to gain insights into the data, which includes calculating means and standard deviations, performing correlation analysis, and generating heat maps. Relevant inferential statistical tests, such as the Student’s t-test, are also employed. In the machine learning part of the analysis, this study utilizes supervised learning algorithms, specifically Linear Regression (LR) and Random Forest (RF). To optimize the hyperparameters of the RF model and mitigate the risk of overfitting given the small dataset, a 3-Fold cross-validation strategy is implemented. The study also calculates bootstrapped confidence intervals to provide robust uncertainty estimates and further validate the approach. A comprehensive feature importance analysis is carried out using RF feature importance, permutation-based feature importance, and SHAP values. The LR model yields an RMSE of 4.83 (CI: 2.70, 6.76) and MAE of 3.86 (CI: 2.06, 5.86), whereas the RF model achieves better results, with an RMSE of 2.98 (CI: 2.16, 3.76) and MAE of 2.68 (CI: 1.83,3.52). Both models identify Hb, CRP, ESR, and age as significant contributors to vitamin D level predictions. Despite the lack of a significant association between SLEDAI and vitamin D in the statistical analysis, the machine learning models suggest a potential nonlinear dependency of vitamin D on SLEDAI. These findings highlight the importance of these factors in managing vitamin D levels in SLE patients. The study concludes that there is a high prevalence of vitamin D insufficiency in SLE patients. Although a direct linear correlation between the SLEDAI score and vitamin D levels is not observed, machine learning models suggest the possibility of a nonlinear relationship. Furthermore, factors such as Hb, CRP, ESR, and age are identified as more significant in predicting vitamin D levels. Thus, the study suggests that monitoring these factors may be advantageous in managing vitamin D levels in SLE patients. Given the immunological nature of SLE, the potential role of vitamin D in SLE disease activity could be substantial. Therefore, it underscores the need for further large-scale studies to corroborate this hypothesis.

This dataset contains detailed information about vehicles, including their engine characteristics, fuel consumption, and CO2 emissions. It is a valuable resource for analyzing the impact of various factors like engine size, transmission type, and fuel type on a vehicle's carbon emissions.

Features:

Engine Size (L): The engine size of the vehicle in liters. Cylinders: Number of cylinders in the engine. Fuel Consumption (City, Highway, Combined): Fuel consumption in liters per 100 kilometers for city, highway, and combined driving conditions. Fuel Consumption (Combined - MPG): Fuel consumption in miles per gallon for combined driving conditions. CO2 Emissions (g/km): Carbon dioxide emissions measured in grams per kilometer. Categorical Columns: Make: Manufacturer of the vehicle. Model: Specific model name. Vehicle Class: Vehicle category (e.g., sedan, SUV, etc.). Transmission: Type of transmission (automatic, manual, etc.). Fuel Type: Type of fuel used (e.g., gasoline, diesel, hybrid, etc.). This dataset is ideal for exploring:

The correlation between fuel efficiency and CO2 emissions. The role of vehicle specifications in determining environmental impact. Regression modeling and machine learning applications.

The correlation coefficient between the IMFs of and the original signal (see the description of Supplementary Table S2) was calculated to identify the IMFs with the real components of the original signal (see Supplementary Table S1). The correlation coefficients were calculated using the following equations as described by Wharton et al., 2013 and Jha et al., 2006.

Linear regression analysis of co-expression network quality scores.

Linear correlation (Pearson) coefficient between each pair of C-GFs.

This project relates to Bellabeat company, a high-tech manufacturer of health-focused products for women, and meet different characters and team members. Data sets include with Character Dataset and Product Dataset. with linear correlation review and explore the relationship between each values

Note: High-sensitivity cardiac troponin T levels were natural logarithm transformed. BMI, body-mass index; BP, blood pressure; HDL, high-density lipoprotein; LDL, low-density lipoprotein; hs-CRP, high-sensitivity C-reactive protein; NT-proBNP, N-terminal pro B-type natriuretic peptide; eGFR, estimated glomerular filtration rate.