Linear regression for two variables is based on a linear equation with one independent variable. It has the form:

where a and b are constant numbers.

*x***is the independent variable, and** *y***is the dependent
variable.** Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable.

Example 6.1

The following examples are linear equations.

The graph of a linear equation of the form y = a + bx is a **straight line**. Any line that is not vertical can be described by this equation.

**Example 6.2**

Linear equations of this form occur in applications of life sciences, social sciences, psychology, business, economics, physical sciences, mathematics, and other areas.

**Example 6.3**

Aaron's Word Processing Service (AWPS) does word processing. Its rate is $32 per hour plus a $31.50 one-time charge. The total cost to a customer depends on the number of hours it takes to do
the word processing job.

See the following Problem.

**Problem**

Find the equation that expresses the **total cost** in terms of the **number of hours** required to finish the word processing job.

**Solution**

Let *x =* the number of hours it takes to get the job done.

Let *y* = the total cost to the customer.

The $31.50 is a fixed cost. If it takes x hours to complete the job, then (32) (*x*) is the cost of the word processing only. The total cost is:

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