For example, trajectories of objects under the influence of gravity follow a parabolic path, when air resistance is ignored.
Other types of curves, such as conic sections (circular, elliptical, parabolic, and hyperbolic arcs) or trigonometric functions (such as sine and cosine), may also be used, in certain cases. cannot be postulated, one can still try to fit a plane curve. If the order of the equation is increased to a second degree polynomial, the following results: A line will connect any two points, so a first degree polynomial equation is an exact fit through any two points with distinct x coordinates. The black dotted line is the "true" data, the red line is a first degree polynomial, the green line is second degree, the orange line is third degree and the blue line is fourth degree. Polynomial curves fitting points generated with a sine function. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. Fitted curves can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. A related topic is regression analysis, which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data.
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Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
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