We often write the equation of a line in the form *y=mx+b*, where *m* is the slope of the line and *b* is the *y*-intercept. Since we will be adding at least two predictors to a multiple regression equation, it is helpful to modify our ordering and notation of this equation: * First, we may rewrite this equation by putting the intercept term first and the slope term second. ```tex y=b+mx ``` * Next, instead of using the names *b* and *m*, we use the names *b₀* and *b₁*, respectively. ```tex y=b_0+b_1x_1 ``` Notice that we've also changed our variable name *x* to *x₁* because it is our FIRST predictor. * We are now able to add as many predictors as we need in the form ```tex y = b_0 + b_1x_1 + b_2x_2 + ... + b_ix_i ``` where *y* is the response variable, *b₀* is the intercept, and *b_i* is the coefficient on the *i*th predictor variable. * The "slopes" (*b₁*, *b₂*, *b₃*, etc.) on the variables in multiple regression are called *partial regression coefficients*. While this is the proper mathematical way to write a multiple regression equation, it is often easier to write out the equation using actual variable names. For example, if we are modeling test scores (`score`) based on number of hours studied (`hours_studied`) and another variable that indicates whether a student ate breakfast (`breakfast`), our multiple regression equation might look like this: ```tex \text{score} = b_0 + b_1 * \text{hours\_studied} + b_2 * \text{breakfast} ``` Of course, after fitting our model, the intercept (*b₀*) and coefficients (*b₁* and *b₂*) could be filled in with actual numbers from the output of our regression. For instance, our final equation might have an intercept of 32.7, a coefficient of 8.5 on `hours_studied`, and a coefficient of 22.5 on `breakfast`: ```tex \text{score} = 32.7 + 8.5*\text{hours\_studied} + 22.5*\text{breakfast} ```