App Multiple Linear Regression

Multiple Linear Regression is a statistical method used to model the relationship between one dependent variable and two or more independent variables by fitting a linear equation to observed data. Multiple linear regression explains how several predictors simultaneously affect an outcome variable.

Main components of multiple linear regression:

- Dependent variable (Y): This is the variable we want to predict. It is often also called the "target variable" or "response."

- Independent variables (X1, X2, ..., Xn): These are the variables we use to predict the dependent variable. They are often also called "predictors" or "explanatory variables."

- Regression model: The equation of multiple linear regression has the following form:

Y = beta_0 + beta_01* X1 + beta_2*X2 + ... + beta_n* Xn

where:

Y is the dependent variable. X1, X2, ..., Xn are the independent variables.

beta_0 is the constant (intercept). beta_1,beta_2, ..., beta_n are the regression coefficients that indicate the influence of the corresponding independent variables on the dependent variable.

Applications: - Economics (income prediction);- Healthcare (risk factor analysis); -Engineering; - Social sciences; -Business forecasting.

Example:Predicting house price based on: -Size of house; -Number of bedrooms; - Age of the house

In the app each object Object_k( object_1, object_2 ... object_m)are describe by independent variables( Xki – features, i = 1...n ) and one dependent variable( Yk -target). A method such as ordinary least squares (OLS) is used to calculate the optimal values of the coefficients (beta_0, beta_1, beta_2, ..., beta_n). The target value is calculate by:

Y = beta_0 + beta_01* P1 + beta_2 *P2 + ... + beta_n* Pn

where: P1, P2...Pn are predictors of target.

The application save data for multiple regression models in database (DB) type SQLite named AppMultipleLinearRegression.db. The regression models are distinguish by name.

The startup screen of the application (App Multiple Linear Regression Solver) displays a list of samples of regression models( in spinner list) and buttons for enabling the functions to create (New sample), load (Load), save(Save), save as(Save as), calculate (Calculate), and delete (Delete) samples of regression models. From the main screen, via the menu elements, you can also access functions such as language selection, saving and copying the database, initializing the database with sample data, and auxiliary functions such as help for the application, settings, and a link to the website with a description of all applications by the authors.

The functions for creating (New sample) include the dialog for input the size of matrix where entering a data of new sample – number of rows( the number include row for predicted data P1, P2...Pn– last row) and number of columns( the number include column for dependent data Y1, Y2,...Yk– last column). Then are generate table for entering relevant data. The populated table must named before saved. The function Load clear the table.

The old saved table may be showing by selected from spinner list. The showing table may be calculated and solution are appears in dialog App results. The function Print may be executed from this dialog in file AppMultipleLinearRegressionSolver.txt. The Print include activity Save Db/Save file by it are selected folder where to save the file. After selecting folder appears button for save. From the same activity may shown content of the selected file, to rename file or folder, to create new folder and also to delete selected file.

Multiple linear regression is a powerful data analysis tool, but it must be used with caution and an understanding of its limitations.

Disadvantages: Sensitive to multicollinearity (strong correlation between independent variables). Does not always capture nonlinear relationships. Requires careful validation and checking of assumptions.