In order to calculate confidence intervals and hypothesis tests, it is assumed that the errors are independent and normally distributed with mean zero and variance 2 σ . Given a sample of N observations on X and Y, the method of least squares estimates β0 and β1 as well as various other quantities that describe the precision of the estimates and the goodness-of-fit of the straight line to the d...

We study the computation of the straight skeleton of a planar straight-line graph (PSLG) by means of the triangulation-based wavefront propagation proposed by Aichholzer and Aurenhammer in 1998, and provide both theoretical and practical insights. As our main theoretical contribution we explain the algorithmic extensions and modifications of their algorithm necessary for computing the straight ...

-In this paper, we present a fast and robust ellipse extraction method. The proposed method can extract ellipses with high accuracy and speed from images with complicated backgrounds. It consists of two parts. First, we extract arc segments from an ellipse approximated by short straight lines that are extracted by a fast line extraction algorithm. Second, the arc segments are used to calculate ...

Fast arm movements involving the shoulder and elbow joints have been analysed in normal controls and in patients with Parkinson's disease. The subjects were requested to draw on a graphic tablet triangles and squares of different size and shape. The patients produced a larger number of EMG burst compared with controls. The movements were accurate, and each segment of the geometric figures was p...

At the end of section 2.4: Finally, a statistical test was applied for each variable to determine if there was any significant trend with distance that would not allow the application of a straight multifractal analysis on the original data. The measure used was the coefficient of the slope of the regression line along the distance. This coefficient is derived using the least squares method and...

paper presents a new method that is capable of extracting circles from complicated and heavily corrupted images, which is not based on the Hough transform (HT). The proposed method consists of three parts. First, we approximately detect short straight lines from the image by using a fast line extraction algorithm. Second, it uses a least squares fitting algorithm for arc segments. The arc segme...

This paper is devoted to computations of eigenvalues and eigenvectors for the Schrödinger operator with constant magnetic field in a domain with corners, as the semi-classical parameter h tends to 0 . The eigenvectors corresponding to the smallest eigenvalues concentrate in the corners: They have a two-scale structure, consisting of a corner layer at scale √ h and an oscillatory term at scale h...

-1. When physiological condition is curvilinearly related to environmental conditions, the "optimum" environmental condition is frequently determined by intersecting two straight lines. 2. Errors in this method are discussed, and a more precise method is suggested. 3. The curvilinear function is described by polynomial regression. 4. Optimum values of the independent variable (i.e. those result...

Modelling Large Urban Environments using traditional modelling techniques would prove too time consuming a process. Consequently a method is required for generating large urban environments quickly without requiring a labour intensive process or expensive data. Some approaches to resolve this problem have been undertaken through the use of procedural modelling or statistics. However the test su...