Section 2 5 Notes Scatter Plots and Lines

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. Experience (years) Hourly Rate of Pay 9 4 3 1 10 6 12 8 $17 $10 $7 $19 $12 $20 $15 a) Draw a scatter plot to show years of experience are related to hourly rate of pay.

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. Experience (years) Hourly Rate of Pay 9 4 3 1 10 6 12 8 $17 $10 $7 $19 $12 $20 $15 b) Write an equation to show years of experience (x) are related to hourly rate of pay (y).

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. Experience (years) Hourly Rate of Pay 9 4 3 1 10 6 12 8 $17 $10 $7 $19 $12 $20 $15 c) Use the function to predict the hourly rate of pay for 21 years of experience.

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 = – 5 x + 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 = 3 x – 2.