Regression Analysis Software . Below is a list of the regression procedures available in NCSS. You can jump to a description of a particular type of regression analysis in NCSS by clicking on one of the links below. To see how these tools can benefit you, we recommend you download and install the free trial of NCSS. Jump to: Introduction. Regression analysis refers to a group of techniques for studying the relationships among two or more variables based on a sample. NCSS makes it easy to run either a simple linear regression analysis or a complex multiple regression analysis, and for a variety of response types. NCSS has modern graphical and numeric tools for studying residuals, multicollinearity, goodness- of- fit, model estimation, regression diagnostics, subset selection, analysis of variance, and many other aspects that are specific to type of regression being performed. There aren’t many examples of how to perform linear regression using a programming language on the Internet. James McCaffrey explains how to do this using C#. Technical Details. This page is designed to give a general overview of the capabilities of the NCSS software for regression analysis. If you would like to examine the formulas and technical details relating to a specific NCSS procedure, click on the corresponding .
There you will find formulas, references, discussions, and examples or tutorials describing the procedure in detail. Simple Linear Regression. Simple linear regression fits a straight line to a set of data points. The simple linear regression model equation is of the form. Y = ? Linear Regression and Correlation. Box- Cox Transformation for Simple Linear Regression. Robust Linear Regression (Passing- Bablok Median- Slope)Linear Regression and Correlation. Because a large proportion of regression analyses involve only one independent (X, explanatory) variable, an individual procedure is dedicated to this specific scenario in NCSS. Statistical reports available in this procedure include data and model summaries, correlation and R- Squared analysis, summary matrices, analysis of variance reports, assumptions tests for residuals (do the residuals follow a normal distribution? Calculator with step by step explanations to find equation of the regression line and corelation coefficient.X plots, residual plots, RStudent vs. X plots, serial correlation plots, probability plots, and so forth. Sample Data. Sample Output. Box- Cox Transformation for Simple Linear Regression. The Box- Cox Transformation for Simple Linear Regression procedure in NCSS allows you to find an appropriate power- transformation exponent such that the residuals from simple linear regression are normally distributed, which is a key assumption in regression. The procedure finds the optimum maximum likelihood exponent and automatically calculates a confidence interval. The procedure also automatically tests the residuals for normality after fitting the linear regression model using the optimum exponent. The following is an example plot produced by this procedure demonstrating the properties of various possible transformation exponents. In the example, the optimum power transformation has an exponent of about - 0. Square Root(X)). Box- Cox Exponent (. The regression slope (? This method is often used for transference, where a reference interval is rescaled. Sample Output. Multiple Regression. Multiple Linear Regression refers to the case where there are multiple explanatory X variables and one continuous dependent Y variable in the regression model. The multiple linear regression model equation for k variables is of the form. Y = ? Multiple Regression – Basic. Multiple Regression for Appraisal. Multiple Regression with Serial Correlation. Principal Components Regression. Response Surface Regression. Robust Regression. Multiple Regression. The Multiple Regression analysis procedure in NCSS computes a complete set of statistical reports and graphs commonly used in multiple regression analysis. The Multiple Regression – Basic procedure eliminates many of the advanced multiple regression reports and inputs to focus on the most widely- used analysis reports and graphs. The Multiple Regression for Appraisal procedure presents the setup and reports in a manner that is relevant for appraisers. The Multiple Regression with Serial Correlation procedure contains methods (i. Data. NCSS is designed to work with both numeric and categorical independent variables. NCSS maintains groups of . Additional diagnostics include PRESS statistics, normality tests, the Durbin- Watson test, R- Squared, multicollinearity analysis, DFBETAS, eigenvalues, and eigenvectors. An extensive set of graphs for analysis of residuals are also available. Some Plots from a Typical Multiple Regression Analysis in NCSSPrincipal Components Regression. When multicollinearity occurs, least squares estimates are unbiased, but their variances are large so they may be far from the true value. By adding a degree of bias to the regression estimates, principal components regression reduces the standard errors. It is hoped that the net effect will be to give more reliable estimates. Some Plots from a Principal Components Regression Analysis in NCSSResponse Surface Regression. It calculates the minimum or maximum of the surface. The program also has a variable selection feature that helps you find the most parsimonious hierarchical model. NCSS automatically scans the data for duplicates so that a lack- of- fit test may be calculated using pure error. One of the main goals of response surface analysis is to find a polynomial approximation of the true nonlinear model, similar to the Taylor’s series expansion used in calculus. Hence, you are searching for an approximation that works well in a specified region. As the region is reduced, the number of terms may also be reduced. In a very small region, a linear (first- order) approximation may be adequate. A larger region may require a quadratic (second- order) approximation. A Contour Plot from a Response Surface Regression Analysis in NCSSRidge Regression. When multicollinearity occurs, least squares estimates are unbiased, but their variances are large so they may be far from the true value. By adding a degree of bias to the regression estimates, it is anticipated that the net effect will be to give more reliable estimates. The Ridge Regression procedure in NCSS provides results on the least squares multicollinearity, the eigenvalues and eigenvectors of the correlations, ridge trace and variance inflation factor plots, standardized ridge regression coefficients, K analysis, ridge versus least squares comparisons, analysis of variance, predicted values, and residual plots. Some Plots from a Ridge Regression Analysis in NCSSRobust Regression. Specifically, it provides much better regression coefficient estimates when outliers are present in the data. Outliers violate the assumption of normally distributed residuals in least squares regression. They tend to distort the least squares coefficients by having more influence than they deserve. Typically, you would expect that the weight attached to each observation would be about 1/N in a dataset with N observations. However, outlying observations may receive a weight of 1. This leads to serious distortions in the estimated coefficients. Because of this distortion, these outliers are difficult to identify since their residuals are much smaller than they should be. When only one or two independent variables are used, these outlying points may be visually detected in various scatter plots. However, the complexity added by additional independent variables often hides the outliers from view in scatter plots. Robust regression down- weights the influence of outliers. This makes residuals of outlying observations larger and easier to spot. Robust regression is an iterative procedure that seeks to identify outliers and minimize their impact on the coefficient estimates. The amount of weighting assigned to each observation in robust regression is controlled by a special curve called an influence function. There are two influence functions available in NCSS. Although robust regression can be very beneficial when used properly, careful consideration should be given to the results. Essentially, robust regression conducts its own residual analysis and down- weights or completely removes various observations. You should study the weights it assigns to each observation, determine which observations have been largely eliminated, and decide if these observations should be included in the analysis. The Robust Regression procedure in NCSS provides all the necessary output for a standard robust regression analysis. Logistic Regression. Logistic Regression is used to study the association between multiple explanatory X variables and one categorical dependent Y variable. NCSS includes two logistic regression procedures: 1. Conditional Logistic Regression. Logistic Regression. In most cases where logistic regression is used, the dependent variable is binary (yes/no, present/absent, positive/negative, etc.), but if the response has more than two categories, the Logistic Regression procedure in NCSS can still be used. This special case is sometimes called multinomial logistic regression or multiple group logistic regression. The Logistic Regression procedure in NCSS provides a full set of analysis reports, including response analysis, coefficient tests and confidence intervals, analysis of deviance, log- likelihood and R- Squared values, classification and validation matrices, residual diagnostics, influence diagnostics, and more. This procedure also gives Y vs. X plots, deviance and Pearson residual plots, ROC curves. It can conduct an independent variable subset selection using the latest stepwise search algorithms. Sample Output. Some Residual and ROC Plots from a Logistic Regression Analysis in NCSS Conditional Logistic Regression. In general, there may be 1 to m cases matched with 1 to n controls, however, the most common design utilizes 1: 1 matching. Nonlinear Regression. NCSS includes several procedures for nonlinear regression and curve fitting: 1. Nonlinear Regression. Curve Fitting – General. Michaelis- Menten Equation. Sum of Functions Models. Fractional Polynomial Regression.
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