Definition: Regression line
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Simple linear regression ▷
Regression line
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Metadata: ID: D164 | shortcut: regline | author: JoramSoch | date: 2021-10-27, 07:30.
Definition: Let there be a simple linear regression with independent observations using dependent variable $y$ and independent variable $x$:
\[\label{eq:slr} y_i = \beta_0 + \beta_1 x_i + \varepsilon_i, \; \varepsilon_i \sim \mathcal{N}(0, \sigma^2) \; .\]Then, given some parameters $\beta_0, \beta_1 \in \mathbb{R}$, the set
\[\label{eq:regline} L(\beta_0, \beta_1) = \left\lbrace (x,y) \in \mathbb{R}^2 \mid y = \beta_0 + \beta_1 x \right\rbrace\]is called a “regression line” and the set
\[\label{eq:regline-ols} L(\hat{\beta}_0, \hat{\beta}_1)\]is called the “fitted regression line”, with estimated regression coefficients $\hat{\beta}_0, \hat{\beta}_1$, e.g. obtained via ordinary least squares.
- Wikipedia (2021): "Simple linear regression"; in: Wikipedia, the free encyclopedia, retrieved on 2021-10-27; URL: https://en.wikipedia.org/wiki/Simple_linear_regression#Fitting_the_regression_line.
Metadata: ID: D164 | shortcut: regline | author: JoramSoch | date: 2021-10-27, 07:30.