Section 2.5 Notes: Scatter Plots and Lines of Regression

Data with two variables, such as year and number of visitors, are called bivariate data. A set of bivariate data graphed as ordered pairs in a coordinate plane is called a scatter plot.

When you find a line that closely approximates a set of data, you are finding a line of fit for the data. An equation of such a line is often called prediction equation because it can be used to predict one of the variables given the other.  Example 1: The table shows the median income of U.S. families for the period 1970–2002. Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the median income in 2015.        

Example 2: The table shows the winning times for an annual dirt bike race for the period 2000–2008. Use a graphing calculator to make a scatter plot of the data. Find the line of regression. Then use the function to predict the winning time in 2015.

Example 3: The table below shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each technician earns.

a) Draw a scatter plot to show how years of experience are related to hourly rate of pay.

Experience (years)

9 4 3 1 10 6 12 8

Hourly Rate of Pay

$17 $10 $10 $7 $19 $12 $20 $15

Example 3: The table below shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each technician earns.

b) Write an equation to show how years of experience (x) are related to hourly rate of pay (y).      

Experience (years)

9 4 3 1 10 6 12 8

Hourly Rate of Pay

$17 $10 $10 $7 $19 $12 $20 $15

Example 3: The table below shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each technician earns.

c) Use the function to predict the hourly rate of pay for 21 years of experience.

Experience (years)

9 4 3 1 10 6 12 8

Hourly Rate of Pay

$17 $10 $10 $7 $19 $12 $20 $15

Example 7: Write an equation in slope-intercept form for the line that passes through (3, –2) and is perpendicular to the line whose equation is y = –5x + 1.

Example 8: Write an equation in slope-intercept form for the line that passes through (3, 5) and is perpendicular to the line whose equation is y = 3x – 2.