## 15.1 The Linear Model

The linear model is easily the most famous and widely used model in all of statistics. Why? Because it can apply to so many interesting research questions where you are trying to predict a continuous variable of interest (the response or dependent variable) on the basis of one or more other variables (the predictor or independent variables).

The linear model takes the following form, where the x values represent the predictors, while the beta values represent weights.

$$y=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}+...\beta_{n}x_{n}$$

For example, we could use a regression model to understand how the value of a diamond relates to two independent variables: its weight and clarity. In the model, we could define the value of a diamond as $$\beta_{weight} \times weight + \beta_{clarity} \times clarity$$. Where $$\beta_{weight}$$ indicates how much a diamond’s value changes as a function of its weight, and $$\beta_{clarity}$$ defines how much a diamond’s value change as a function of its clarity.