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In scientific research, the null hypothesis (often denoted H 0) [1] is the claim that the effect being studied does not exist. [note 1] The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed.
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In statistical hypothesis testing, the alternative hypothesis is one of the proposed propositions in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). [1]
The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these.
The above image shows a table with some of the most common test statistics and their corresponding tests or models.. A statistical hypothesis test is a method of statistical inference used to decide whether the data sufficiently supports a particular hypothesis.
In statistics, Mallows's, [1] [2] named for Colin Lingwood Mallows, is used to assess the fit of a regression model that has been estimated using ordinary least squares.It is applied in the context of model selection, where a number of predictor variables are available for predicting some outcome, and the goal is to find the best model involving a subset of these predictors.
Ono & Soundararajan (1997) showed that the generalized Riemann hypothesis implies that Ramanujan's integral quadratic form x 2 + y 2 + 10z 2 represents all integers that it represents locally, with exactly 18 exceptions. In 2021, Alexander (Alex) Dunn and Maksym Radziwill proved Patterson's conjecture on cubic Gauss sums, under the assumption ...