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The dashed green line represents the ground truth from which the samples were generated. In non-parametric statistics, the Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane (simple linear regression) by choosing the median of the slopes of all lines through pairs of points.
The program can generate graphs of the relationships between power, sample size and the detectable alternative hypothesis. It can plot graphs of any two of these variables while holding the third constant. Linear or logarithmic axes may be used and multiple curves can be plotted on each graph.
The data sets in the Anscombe's quartet are designed to have approximately the same linear regression line (as well as nearly identical means, standard deviations, and correlations) but are graphically very different. This illustrates the pitfalls of relying solely on a fitted model to understand the relationship between variables.
The formulas given in the previous section allow one to calculate the point estimates of α and β — that is, the coefficients of the regression line for the given set of data. However, those formulas do not tell us how precise the estimates are, i.e., how much the estimators α ^ {\displaystyle {\widehat {\alpha }}} and β ^ {\displaystyle ...
In linear regression, the model specification is that the dependent variable, is a linear combination of the parameters (but need not be linear in the independent variables). For example, in simple linear regression for modeling n {\displaystyle n} data points there is one independent variable: x i {\displaystyle x_{i}} , and two parameters, β ...
The Passing-Bablok procedure fits the parameters and of the linear equation = + using non-parametric methods. The coefficient b {\displaystyle b} is calculated by taking the shifted median of all slopes of the straight lines between any two points, disregarding lines for which the points are identical or b = − 1 {\displaystyle b=-1} .
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals.
MedCalc includes basic parametric and non-parametric statistical procedures and graphs such as descriptive statistics, ANOVA, Mann–Whitney test, Wilcoxon test, χ 2 test, correlation, linear as well as non-linear regression, logistic regression, and multivariate statistics. [5]