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Linear trend estimation. Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered "tends" to increase or decrease over time. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading.
Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
In the case of a set of (x,y) data, the least absolute deviations line will always pass through at least two of the data points, unless there are multiple solutions. If multiple solutions exist, then the region of valid least absolute deviations solutions will be bounded by at least two lines, each of which passes through at least two data points.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Linear least squares ( LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals .
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
Linear predictor function. In statistics and in machine learning, a linear predictor function is a linear function ( linear combination) of a set of coefficients and explanatory variables ( independent variables ), whose value is used to predict the outcome of a dependent variable. [1] This sort of function usually comes in linear regression ...
e. Weighted least squares ( WLS ), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations ( heteroscedasticity) is incorporated into the regression. WLS is also a specialization of generalized least squares, when all the off ...
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