This post covers Introduction to probability from Statistics for Engineers and Scientists by William Navidi.

Basic Ideas

• Multiple-Linear-Regression

  • In situations, there are several independent variables, $x_1, x_2,…, x_p$, that are related to a dependent variable $y$. If the relationship between the dependent and independent variables is linear, the technique of multiple regression can be used.

  • We describe the multiple regression model. Assume that we have a sample of $n$ items, and that on each item we have measured a dependent variable y and p independent variables $x_1,…, x_p$.

  • The $i^{th}$ sample item thus gives rise to the ordered set $(y_i, x_{1i}, \ldots, x_{pi})$.We can then fit the multiple regression model \(\begin{align*} y_i &= \beta_0 + \beta_1 x_{1i} +⋯+ \beta_p x_{pi} + \epsilon_{i} \end{align*}\)

  • One is the polynomial regression model, in which the independent variables are all powers of a single variable. The polynomial regression model of degree $p$ is \(y_i = \beta_0 + \beta_1 x_i + \beta_2 x^2_i + \ldots + \beta_p x^p_i + \epsilon_i\)

  • Models are considered to be linear models, even though they contain nonlinear terms in the independent variables. The reason they are still linear models is that they are linear in the coefficients $\beta_i$.