Simple Linear Regression Model

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note

• Linear regression
• Has the form $$\begin{gathered} (y={\beta }_0+{\beta }_1+ϵ \\ ) \end{gathered}$$
  • Simple linear regression equation: $$\begin{gathered} (E(y)={\beta }_0+{\beta }_{1}x \\ ) \end{gathered}$$
  • ϵ: random var referred to as error term
  • In practice, ${\beta }_0$​ and ${\beta }_1$​ are not known, but can be estimated with $b_0$​ and $b_1$​, where $b_0$ and $b_1$​ are computed by least squares method

Estimated simple linear regression model:

• $$\begin{gathered} (\hat{y}=b_0+b_{1}x \\ ) \end{gathered}$$
  • $$\begin{gathered} (\hat{y} \\ ) \end{gathered}$$​ is the point estimator of E(y)
• graph of Estimated simple linear regression model = estimated regression line = line of best fit