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Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
The simple formula for the factorial, x! = 1 × 2 × ⋯ × x is only valid when x is a positive integer, and no elementary function has this property, but a good solution is the gamma function . [1] The gamma function is not only smooth but analytic (except at the non-positive integers), and it can be defined in several explicit ways.
Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform . Properties.
Definition. Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations.
In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn .
The sum of squares of residuals, also called the residual sum of squares: The total sum of squares (proportional to the variance of the data): The most general definition of the coefficient of determination is. In the best case, the modeled values exactly match the observed values, which results in and R2 = 1.
