## 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 , and .

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 where the line crosses the y-axis.

**1a.** If , the line slopes upward to the right.

**1b.** If , the line is horizontal.

**1c.** If , the line slopes downward to the right.

**Figure 1. **Three possible graphs of .

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

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

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