1. A system for multivariate regression analysis of linear and nonlinear relationships comprising: a processor configured to receive input data comprising a set of independent variables and a dependent variable, and to perform multivariate regression analysis using a combination of linear and nonlinear regression techniques; a memory configured to store the input data and the results of the multivariate regression analysis; and a user interface configured to enable a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis.

2. The system of claim 1, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.

3. The system of claim 1, wherein the processor is further configured to perform variable selection and model selection to optimize the regression analysis.

4. A method for multivariate regression analysis of linear and nonlinear relationships comprising: receiving input data comprising a set of independent variables and a dependent variable; performing multivariate regression analysis using a combination of linear and nonlinear regression techniques; storing the input data and the results of the multivariate regression analysis; and displaying the results of the analysis.

5. The method of claim 4, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.

6. The method of claim 4, further comprising performing variable selection and model selection to optimize the regression analysis.

7. The method of claim 4, wherein the multivariate regression analysis comprises fitting a linear model to the input data and a nonlinear model to the input data, and combining the results of the linear and nonlinear models to produce a final prediction.

8. The method of claim 4, wherein the multivariate regression analysis comprises fitting a hierarchical model to the input data, wherein the hierarchical model comprises a linear model and one or more nonlinear models, and combining the results of the linear and nonlinear models to produce a final prediction. System and Method for Multivariate Regression Analysis of Linear and Nonlinear Relationships Abstract This invention describes a system for multivariate regression analysis of linear and nonlinear relationships, comprising a processor, memory, and user interface. The processor receives input data consisting of independent variables and a dependent variable, and performs multivariate regression analysis using a combination of linear and nonlinear regression techniques, including polynomial regression, logistic regression, and spline regression. The memory stores the input data and the results of the analysis. The user interface enables a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis. The processor is further configured to perform variable selection and model selection to optimize the regression analysis. This system can be used in various industries, including finance, healthcare, and social science, to analyze complex data and identify significant relationships between variables. , Claims:Claims :

1. A system for multivariate regression analysis of linear and nonlinear relationships comprising: a processor configured to receive input data comprising a set of independent variables and a dependent variable, and to perform multivariate regression analysis using a combination of linear and nonlinear regression techniques; a memory configured to store the input data and the results of the multivariate regression analysis; and a user interface configured to enable a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis.

2. The system of claim 1, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.

3. The system of claim 1, wherein the processor is further configured to perform variable selection and model selection to optimize the regression analysis.

4. A method for multivariate regression analysis of linear and nonlinear relationships comprising: receiving input data comprising a set of independent variables and a dependent variable; performing multivariate regression analysis using a combination of linear and nonlinear regression techniques; storing the input data and the results of the multivariate regression analysis; and displaying the results of the analysis.

5. The method of claim 4, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.

6. The method of claim 4, further comprising performing variable selection and model selection to optimize the regression analysis.

7. The method of claim 4, wherein the multivariate regression analysis comprises fitting a linear model to the input data and a nonlinear model to the input data, and combining the results of the linear and nonlinear models to produce a final prediction.

8. The method of claim 4, wherein the multivariate regression analysis comprises fitting a hierarchical model to the input data, wherein the hierarchical model comprises a linear model and one or more nonlinear models, and combining the results of the linear and nonlinear models to produce a final prediction.

Description:System and Method for Multivariate Regression Analysis of Linear and Nonlinear Relationships
Field of the Invention
[0001] The present invention relates to a system and method for performing multivariate regression analysis on linear and nonlinear relationships. More specifically, the invention provides a novel approach for generating accurate predictions and meaningful insights from data sets that exhibit complex and nonlinear relationships between variables.
Background
[0002] The background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
[0003] Multivariate regression analysis is a statistical technique used to model the relationship between multiple independent variables and a dependent variable. This technique is widely used in various fields, including finance, economics, social sciences, and engineering, to identify the relationship between multiple variables and to predict future outcomes.
[0004] The traditional method of multivariate regression analysis assumes a linear relationship between the dependent variable and independent variables. However, in many cases, the relationship between variables is not linear, and therefore, more advanced methods are needed.
[0005] Recently, a new system and method for multivariate regression analysis have been developed that can handle both linear and nonlinear relationships between variables. This approach involves using machine learning algorithms to model complex relationships between variables and to predict future outcomes.
[0006] The system and method involve several steps, including data preprocessing, feature selection, and model development. In the data preprocessing step, the data is cleaned and transformed to ensure that it is suitable for analysis. This step can include data normalization, missing data imputation, and outlier detection.
[0007] In the feature selection step, the most important features or variables are selected based on their relevance to the problem being analyzed. This step can help reduce the dimensionality of the data and improve the performance of the model.
[0008] Finally, a machine learning model is developed using techniques such as artificial neural networks, decision trees, and support vector machines. These models enable analysts to capture complex relationships between variables, including nonlinear relationships, and to make accurate predictions.
[0009] The system and method for multivariate regression analysis have numerous applications in fields such as finance, marketing, and healthcare. In finance, the approach can be used to predict stock prices and to identify trends in financial data. In marketing, the approach can be used to predict consumer behavior and to identify patterns in customer data. In healthcare, the approach can be used to predict patient outcomes and to identify risk factors for disease.
[00010] Thus, the system and method for multivariate regression analysis provide a powerful and flexible framework for analyzing complex data sets. The approach enables researchers and analysts to model complex relationships between variables and to make accurate predictions, providing insights into the underlying processes that drive outcomes.
[00011] All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.
Summary
[00012] Various objects, features, and advantages of the disclosed subject matter can be more fully appreciated with reference to the following detailed description of the disclosed subject matter when considered in connection with the following drawings, in which like reference numerals identify like elements.
[00013] The present invention relates to a system and method for performing multivariate regression analysis on linear and nonlinear relationships. More specifically, the invention provides a novel approach for generating accurate predictions and meaningful insights from data sets that exhibit complex and nonlinear relationships between variables.
[00014] A system for multivariate regression analysis of linear and nonlinear relationships is a powerful tool for analyzing data with multiple independent variables and a dependent variable. The system includes a processor that receives input data comprising a set of independent variables and a dependent variable, and performs multivariate regression analysis using a combination of linear and nonlinear regression techniques. The system also includes a memory that stores the input data and the results of the multivariate regression analysis, and a user interface that enables a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis.
[00015] The nonlinear regression techniques used by the system include polynomial regression, logistic regression, and spline regression. These techniques are useful for modeling complex relationships between variables that cannot be accurately represented by linear regression alone. To optimize the regression analysis, the system includes a variable selection and model selection module. The module identifies the most relevant independent variables for the dependent variable and selects the most appropriate regression model based on goodness-of-fit metrics such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC).
[00016] Overall, the system for multivariate regression analysis of linear and nonlinear relationships is a powerful tool for analyzing complex data and identifying significant relationships between variables. It has a wide range of applications in various industries, including finance, healthcare, and social science.
[00017] The system can provide valuable insights for decision-making and strategy development, helping companies make data-driven decisions and stay ahead of the competition.For example, a financial institution may use the system to analyze the relationship between various economic indicators and stock prices. The institution could input variables such as GDP, inflation rate, interest rate, and exchange rate as independent variables, and stock prices as the dependent variable. The system could then perform multivariate regression analysis using a combination of linear and nonlinear regression techniques to identify the significant relationships between the variables. The institution could use this information to develop investment strategies and make informed decisions about stock portfolios.
[00018] The method for multivariate regression analysis of linear and nonlinear relationships is a powerful tool for analyzing data with multiple independent variables and a dependent variable. The method includes receiving input data comprising a set of independent variables and a dependent variable, and performing multivariate regression analysis using a combination of linear and nonlinear regression techniques. The method also includes storing the input data and the results of the multivariate regression analysis, and displaying the results of the analysis.
[00019] The nonlinear regression techniques used by the method include polynomial regression, logistic regression, and spline regression. These techniques are useful for modeling complex relationships between variables that cannot be accurately represented by linear regression alone.
[00020] To optimize the regression analysis, the method includes a variable selection and model selection step. This step identifies the most relevant independent variables for the dependent variable and selects the most appropriate regression model based on goodness-of-fit metrics such as the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC).
[00021] The multivariate regression analysis can include fitting a linear model to the input data and a nonlinear model to the input data, and combining the results of the linear and nonlinear models to produce a final prediction. Alternatively, the method can include fitting a hierarchical model to the input data, wherein the hierarchical model comprises a linear model and one or more nonlinear models, and combining the results of the linear and nonlinear models to produce a final prediction.
[00022] Overall, the method for multivariate regression analysis of linear and nonlinear relationships is a powerful tool for analyzing complex data and identifying significant relationships between variables. It has a wide range of applications in various industries, including finance, healthcare, and social science. The method can provide valuable insights for decision-making and strategy development, helping companies make data-driven decisions and stay ahead of the competition. For example, a healthcare company may use the method to analyze the relationship between various patient characteristics and the likelihood of developing a certain disease. The company could input variables such as age, gender, lifestyle, and family history as independent variables, and the disease as the dependent variable. The method could then perform multivariate regression analysis using a combination of linear and nonlinear regression techniques to identify the significant relationships between the variables. The company could use this information to develop targeted prevention and treatment strategies for patients.
Brief Description of the Drawings
[00023] The features and advantages of the present disclosure would be more clearly understood from the following description taken in conjunction with the accompanying drawings in which:
[00024] FIG. 1 represents an overview of system for multivariate regression analysis of linear and nonlinear relationships, according to some embodiments of the present disclosure.
[00025] FIG. 2 shows an exemplary detailed schematic flow diagram of a method for multivariate regression analysis of linear and nonlinear relationships, according to some embodiments of the present disclosure.
Detailed Description
[00026] The following is a detailed description of exemplary embodiments to illustrate the principles of the invention. The embodiments are provided to illustrate aspects of the invention, but the invention is not limited to any embodiment. The scope of the invention encompasses numerous alternatives, modifications and equivalent; it is limited only by the claims.
[00027] In view of the many possible embodiments to which the principles of the present discussion may be applied, it should be recognized that the embodiments described herein with respect to the drawing figures are meant to be illustrative only and should not be taken as limiting the scope of the claims. Therefore, the techniques as described herein contemplate all such embodiments as may come within the scope of the following claims and equivalents thereof.
[00028] The detailed description is described with reference to the accompanying figures. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. The use of the same reference numbers in different instances in the description and the figures may indicate similar or identical items.
[00029] The present invention relates to a system and method for performing multivariate regression analysis on linear and nonlinear relationships. More specifically, the invention provides a novel approach for generating accurate predictions and meaningful insights from data sets that exhibit complex and nonlinear relationships between variables.
[00030] FIG 1. depicts the system 100 for multivariate regression analysis of linear and nonlinear relationships comprises a processor 102 that is configured to receive input data comprising a set of independent variables and a dependent variable, and to perform multivariate regression analysis using a combination of linear and nonlinear regression techniques. The processor may use various statistical methods such as ordinary least squares regression, logistic regression, and nonlinear regression models such as polynomial regression and exponential regression.
[00031] In an embodiment, the system also includes a memory 104 that is configured to store the input data and the results of the multivariate regression analysis. The memory may also store various statistical models used for the regression analysis and the parameters estimated by these models.
[00032] In an embodiment, the system further includes a user interface 106 that is configured to enable a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis. The user interface may include various interactive components such as sliders, dropdown menus, and checkboxes to enable the user to adjust the parameters of the regression models and visualize the results of the analysis.
[00033] In an embodiment, for instance, the system may be used to analyse the relationship between various factors such as age, income, and education level and the likelihood of a person developing a certain medical condition. The user may input the data for these variables into the system and select the regression techniques to be used. The system may then perform multivariate regression analysis using a combination of linear and nonlinear regression techniques to estimate the probability of the person developing the medical condition. The results of the analysis may be displayed in various formats such as a scatter plot of the independent variables, a heatmap of the coefficients estimated by the regression models, and a line graph of the predicted probabilities.
[00034] In an embodiment, the multivariate regression analysis using a combination of linear and nonlinear regression techniques. The processor may use various machine learning methods such as neural networks, decision trees, and support vector machines to perform the regression analysis. The system also includes a memory that is configured to store the input data and the results of the multivariate regression analysis. The memory may also store various machine learning models used for the regression analysis and the parameters estimated by these models.
[00035] In an embodiment, the user interface may include various interactive components such as sliders, dropdown menus, and checkboxes to enable the user to adjust the parameters of the machine learning models and visualize the results of the analysis. For example, the system may be used to analyse the relationship between various factors such as customer demographics, purchasing behaviour, and website interactions and the likelihood of a customer making a purchase. The user may input the data for these variables into the system and select the machine learning models to be used. The system may then perform multivariate regression analysis using a combination of linear and nonlinear regression techniques to estimate the probability of the customer making a purchase. The results of the analysis may be displayed in various formats such as a scatter plot of the independent variables, a decision tree showing the most important factors influencing the purchasing behaviour, and a confusion matrix showing the accuracy of the machine learning models.
[00036] In an embodiment, the processor in the system for multivariate regression analysis may be further configured to perform variable selection and model selection to optimize the regression analysis. Variable selection involves selecting the most relevant independent variables to be included in the regression model, while model selection involves selecting the best regression model that fits the data. For example, suppose a company wants to predict the sales of their products based on various factors such as advertising spend, product price, and customer demographics. The company has a large dataset with many variables, some of which may not be relevant for predicting sales. The processor in the system may perform variable selection using techniques such as forward selection or backward elimination to identify the most relevant variables for predicting sales. The processor may then use these selected variables to perform the regression analysis and predict future sales.
[00037] Referring to the preceding embodiment, suppose a research team wants to analyse the relationship between a person's diet and their risk of developing heart disease. The team has a dataset with various independent variables such as age, gender, smoking status, exercise habits, and various dietary factors. The processor in the system may use techniques such as cross-validation and information criteria (such as AIC or BIC) to compare the performance of different regression models, including linear regression, logistic regression, and nonlinear regression models such as spline regression or random forest regression. The processor may select the best model based on its accuracy and interpretability and use this model to predict a person's risk of developing heart disease based on their diet and other factors.
[00038] Referring to the preceding embodiment, in both of these examples, the processor in the system performs variable selection and model selection to optimize the regression analysis and improve the accuracy of the predictions. The results of the analysis may be displayed in various formats such as graphs, charts, or tables to facilitate interpretation and decision-making.
[00039] The system comprises a processor, a memory, and a user interface. The processor is configured to receive input data comprising a set of independent variables and a dependent variable, and perform multivariate regression analysis using a combination of linear and nonlinear regression techniques. The memory is configured to store the input data and the results of the multivariate regression analysis. The user interface is configured to enable a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis.
[00040] For example, a user in the finance industry may use the system to analyze the relationship between stock prices and various economic indicators. The user inputs the economic indicators, such as GDP, inflation rate, and interest rate, as independent variables and stock prices as the dependent variable. The user selects the regression techniques to be used, such as linear regression, polynomial regression, and logistic regression. The system performs the multivariate regression analysis and displays the results in a user-friendly format, allowing the user to make data-driven decisions and develop investment strategies.
[00041] FIG 2. portrays the method 200 comprises (at step 204) receiving input data comprising a set of independent variables and a dependent variable, (at step 206) performing multivariate regression analysis using a combination of linear and nonlinear regression techniques, (at step 208) storing the input data and the results of the multivariate regression analysis, and (at step 208) displaying the results of the analysis.
[00042] The method also includes performing variable selection and model selection to optimize the regression analysis. For example, a healthcare company may use the method to analyze the relationship between patient characteristics and the likelihood of developing a certain disease. The company inputs the patient characteristics, such as age, gender, and lifestyle, as independent variables and the disease as the dependent variable. The method performs multivariate regression analysis using a combination of linear and nonlinear regression techniques, such as polynomial regression and spline regression. The method also performs variable selection and model selection to identify the most relevant independent variables and select the most appropriate regression model for the data.
[00043] The method comprises receiving input data comprising a set of independent variables and a dependent variable, performing multivariate regression analysis using a combination of linear and nonlinear regression techniques, storing the input data and the results of the multivariate regression analysis, and displaying the results of the analysis.
[00044] The method also includes fitting a hierarchical model to the input data, wherein the hierarchical model comprises a linear model and one or more nonlinear models, and combining the results of the linear and nonlinear models to produce a final prediction. For example, a social media company may use the method to analyze the relationship between user engagement and various features of their platform. The company inputs the features as independent variables and user engagement as the dependent variable. The method performs multivariate regression analysis using a combination of linear regression and nonlinear regression techniques, such as logistic regression and spline regression. The method also fits a hierarchical model to the data, combining the results of the linear and nonlinear models to produce a final prediction of user engagement.
[00045] Further, while operations are depicted in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Likewise, while several specific implementation details are contained in the above discussions, these should not be construed as limitations on the scope of the subject matter described herein, but rather as descriptions of features that may be specific to particular embodiments. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.
[00046] The term “memory,” as used herein relates to a volatile or persistent medium, such as a magnetic disk, or optical disk, in which a computer can store data or software for any duration. Optionally, the memory is non-volatile mass storage such as physical storage media. Furthermore, a single memory may encompass and in a scenario wherein computing system is distributed, the processing, memory and/or storage capability may be distributed as well.
[00047] Throughout the present disclosure, the term ‘server’ relates to a structure and/or module that include programmable and/or non-programmable components configured to store, process and/or share information. Optionally, the server includes any arrangement of physical or virtual computational entities capable of enhancing information to perform various computational tasks.
[00048] Throughout the present disclosure, the term “network” relates to an arrangement of interconnected programmable and/or non-programmable components that are configured to facilitate data communication between one or more electronic devices and/or databases, whether available or known at the time of filing or as later developed. Furthermore, the network may include, but is not limited to, one or more peer-to-peer network, a hybrid peer-to-peer network, local area networks (LANs), radio access networks (RANs), metropolitan area networks (MANS), wide area networks (WANs), all or a portion of a public network such as the global computer network known as the Internet, a private network, a cellular network and any other communication system or systems at one or more locations.
[00049] Throughout the present disclosure, the term “process”* relates to any collection or set of instructions executable by a computer or other digital system so as to configure the computer or the digital system to perform a task that is the intent of the process.
[00050] Throughout the present disclosure, the term ‘Artificial intelligence (AI)’ as used herein relates to any mechanism or computationally intelligent system that combines knowledge, techniques, and methodologies for controlling a bot or other element within a computing environment. Furthermore, the artificial intelligence (AI) is configured to apply knowledge and that can adapt it-self and learn to do better in changing environments. Additionally, employing any computationally intelligent technique, the artificial intelligence (AI) is operable to adapt to unknown or changing environment for better performance. The artificial intelligence (AI) includes fuzzy logic engines, decision-making engines, preset targeting accuracy levels, and/or programmatically intelligent software.

Claims
I/We Claim:
1. A system for multivariate regression analysis of linear and nonlinear relationships comprising:
a processor configured to receive input data comprising a set of independent variables and a dependent variable, and to perform multivariate regression analysis using a combination of linear and nonlinear regression techniques;
a memory configured to store the input data and the results of the multivariate regression analysis; and
a user interface configured to enable a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis.
2. The system of claim 1, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.
3. The system of claim 1, wherein the processor is further configured to perform variable selection and model selection to optimize the regression analysis.
4. A method for multivariate regression analysis of linear and nonlinear relationships comprising:
receiving input data comprising a set of independent variables and a dependent variable;
performing multivariate regression analysis using a combination of linear and nonlinear regression techniques;
storing the input data and the results of the multivariate regression analysis; and
displaying the results of the analysis.
5. The method of claim 4, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.
6. The method of claim 4, further comprising performing variable selection and model selection to optimize the regression analysis.
7. The method of claim 4, wherein the multivariate regression analysis comprises fitting a linear model to the input data and a nonlinear model to the input data, and combining the results of the linear and nonlinear models to produce a final prediction.
8. The method of claim 4, wherein the multivariate regression analysis comprises fitting a hierarchical model to the input data, wherein the hierarchical model comprises a linear model and one or more nonlinear models, and combining the results of the linear and nonlinear models to produce a final prediction.

System and Method for Multivariate Regression Analysis of Linear and Nonlinear Relationships
Abstract
This invention describes a system for multivariate regression analysis of linear and nonlinear relationships, comprising a processor, memory, and user interface. The processor receives input data consisting of independent variables and a dependent variable, and performs multivariate regression analysis using a combination of linear and nonlinear regression techniques, including polynomial regression, logistic regression, and spline regression. The memory stores the input data and the results of the analysis. The user interface enables a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis. The processor is further configured to perform variable selection and model selection to optimize the regression analysis. This system can be used in various industries, including finance, healthcare, and social science, to analyze complex data and identify significant relationships between variables. , Claims:Claims
I/We Claim:
1. A system for multivariate regression analysis of linear and nonlinear relationships comprising:
a processor configured to receive input data comprising a set of independent variables and a dependent variable, and to perform multivariate regression analysis using a combination of linear and nonlinear regression techniques;
a memory configured to store the input data and the results of the multivariate regression analysis; and
a user interface configured to enable a user to input the independent and dependent variables, select the regression techniques to be used, and display the results of the analysis.
2. The system of claim 1, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.
3. The system of claim 1, wherein the processor is further configured to perform variable selection and model selection to optimize the regression analysis.
4. A method for multivariate regression analysis of linear and nonlinear relationships comprising:
receiving input data comprising a set of independent variables and a dependent variable;
performing multivariate regression analysis using a combination of linear and nonlinear regression techniques;
storing the input data and the results of the multivariate regression analysis; and
displaying the results of the analysis.
5. The method of claim 4, wherein the nonlinear regression techniques include polynomial regression, logistic regression, and spline regression.
6. The method of claim 4, further comprising performing variable selection and model selection to optimize the regression analysis.
7. The method of claim 4, wherein the multivariate regression analysis comprises fitting a linear model to the input data and a nonlinear model to the input data, and combining the results of the linear and nonlinear models to produce a final prediction.
8. The method of claim 4, wherein the multivariate regression analysis comprises fitting a hierarchical model to the input data, wherein the hierarchical model comprises a linear model and one or more nonlinear models, and combining the results of the linear and nonlinear models to produce a final prediction.