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Polynomial regression models are usually fit using the method of least squares.The least-squares method minimizes the variance of the unbiased estimators of the coefficients, under the conditions of the Gauss–Markov theorem.
In the more general multiple regression model, there are independent variables: = + + + +, where is the -th observation on the -th independent variable.If the first independent variable takes the value 1 for all , =, then is called the regression intercept.
In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of independent Bernoulli trials, where each trial has probability of success . [1]
Consider a situation where a small ball is being tossed up in the air and then we measure its heights of ascent h i at various moments in time t i.Physics tells us that, ignoring the drag, the relationship can be modeled as
Another approach to robust estimation of regression models is to replace the normal distribution with a heavy-tailed distribution. A t-distribution with 4–6 degrees of freedom has been reported to be a good choice in various practical situations.