Regression analysis is a statistical process for estimating the relationships among variables. Regression analysis is widely used for prediction and forecasting. So why is regression analysis also used as statistical test?

bergvolk0k
2022-10-17
Answered

Regression analysis is a statistical process for estimating the relationships among variables. Regression analysis is widely used for prediction and forecasting. So why is regression analysis also used as statistical test?

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Audrey Russell

Answered 2022-10-18
Author has **16** answers

On my viewpoint, regression analysis is a mathematical tool which can be used in various circonstances and for various kind of problems. Of course, in many statistical problems a regression technic is currently used. But they are also problems involving regressions where nothing is randomly specified and where no statistics are needed. A mathematical tool on one hand and mathematical or physical problem on the other hand, are two different thinks.

cousinhaui

Answered 2022-10-19
Author has **5** answers

Regression analysis is surely an important tool for prediction and forecasting, but it is also commonly used as a statistical test for many purposes, e.g. to investigate whether a given variable is associated with another one independently of confounders, or whether a given multivariable model significantly predicts a given variable, and so on. In all these applications, regression provides a number of parameters, including measures of the strength of these associations and corresponding p values. In this view, it is one of the most important statistical tests used in many fields of sciences.

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${Y}_{i}={\alpha}_{0}+{\alpha}_{1}{x}_{i}+{\alpha}_{2}{x}_{i}^{2}$

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${Y}_{i}={\alpha}_{0}+{\alpha}_{1}{x}_{i}+{\alpha}_{2}{x}_{i}^{2}$

How is this a linear regression when it has quadratic terms in it?

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$\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$

$\left[\begin{array}{c}7\\ 8\end{array}\right]$

In such an arrangement how do I include B3? I would think I would want to add it in as always 1 in $X$. IE

$\left[\begin{array}{cc}1& 2\\ 2& 3\\ 1& 1\end{array}\right]$

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$\left[\begin{array}{c}7\\ 8\end{array}\right]$

In such an arrangement how do I include B3? I would think I would want to add it in as always 1 in $X$. IE

$\left[\begin{array}{cc}1& 2\\ 2& 3\\ 1& 1\end{array}\right]$

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