Non-linear least squaresNon-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.
Pearson correlation coefficientIn statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.
TibiaThe tibia (ˈtɪbiə; : tibiae ˈtɪbii or tibias), also known as the shinbone or shankbone, is the larger, stronger, and anterior (frontal) of the two bones in the leg below the knee in vertebrates (the other being the fibula, behind and to the outside of the tibia); it connects the knee with the ankle. The tibia is found on the medial side of the leg next to the fibula and closer to the median plane. The tibia is connected to the fibula by the interosseous membrane of leg, forming a type of fibrous joint called a syndesmosis with very little movement.
Intraclass correlationIn statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.
Correlation coefficientA correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution. Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement.
Posterior cruciate ligamentThe posterior cruciate ligament (PCL) is a ligament in each knee of humans and various other animals. It works as a counterpart to the anterior cruciate ligament (ACL). It connects the posterior intercondylar area of the tibia to the medial condyle of the femur. This configuration allows the PCL to resist forces pushing the tibia posteriorly relative to the femur. The PCL and ACL are intracapsular ligaments because they lie deep within the knee joint. They are both isolated from the fluid-filled synovial cavity, with the synovial membrane wrapped around them.
Anterior cruciate ligamentThe anterior cruciate ligament (ACL) is one of a pair of cruciate ligaments (the other being the posterior cruciate ligament) in the human knee. The two ligaments are also called "cruciform" ligaments, as they are arranged in a crossed formation. In the quadruped stifle joint (analogous to the knee), based on its anatomical position, it is also referred to as the cranial cruciate ligament. The term cruciate translates to cross. This name is fitting because the ACL crosses the posterior cruciate ligament to form an “X”.
Coriolis forceIn physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect.
CorrelationIn statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.
Spearman's rank correlation coefficientIn statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables). It assesses how well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables; while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not).
