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In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many ways for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand ...
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
In the theory of differential equations, comparison theorems assert particular properties of solutions of a differential equation (or of a system thereof), provided that an auxiliary equation/inequality (or a system thereof) possesses a certain property. Differential (or integral) inequalities, derived from differential (respectively, integral ...
A percentage change is a way to express a change in a variable. It represents the relative change between the old value and the new one. [6]For example, if a house is worth $100,000 today and the year after its value goes up to $110,000, the percentage change of its value can be expressed as = = %.
The independent variable of a study often has many levels or different groups. In a true experiment, researchers can have an experimental group, which is where their intervention testing the hypothesis is implemented, and a control group, which has all the same element as the experimental group, without the interventional element.
A contrast is defined as the sum of each group mean multiplied by a coefficient for each group (i.e., a signed number, c j). [10] In equation form, = ¯ + ¯ + + ¯ ¯, where L is the weighted sum of group means, the c j coefficients represent the assigned weights of the means (these must sum to 0 for orthogonal contrasts), and ¯ j represents the group means. [8]
In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.
The objectives of experimental mathematics are "to generate understanding and insight; to generate and confirm or confront conjectures; and generally to make mathematics more tangible, lively and fun for both the professional researcher and the novice". [5] The uses of experimental mathematics have been defined as follows: [6]