## Linear Regression

Read these sections on linear regression. Linear regression, the simplest form of regression, is used to obtain a linear relationship between two variables.

### Slope and Y-Intercept of a Linear Equation

For the linear equation $y=a+bx$$b = slope$ and $a = y-intercept$.

From algebra recall that the slope is a number that describes the steepness of a line and the y-intercept is the y coordinate of the point $(0,a)$ where the line crosses the y-axis.

1a. If $b > 0$ , the line slopes upward to the right.

1b. If $b=0$ , the line is horizontal.

1c. If $b < 0$ , the line slopes downward to the right.

Figure 1. Three possible graphs of $y=a+bx$.

Svetlana tutors to make extra money for college. For each tutoring session, she charges a one time fee of $25 plus$15 per hour of tutoring. A linear equation that expresses the total amount of money Svetlana earns for each session she tutors is $y=25+15x$

• What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.

#### Solution

The independent variable ($x$) is the number of hours Svetlana tutors each session. The dependent variable ($y$) is the amount, in dollars, Svetlana earns for each session.

The y-intercept is 25 ($a = 25$). At the start of the tutoring session, Svetlana charges a one-time fee of $25 (this is when $x = 0$). The slope is 15 ($b = 15$). For each session, Svetlana earns$15 for each hour she tutors.