Example 1 Analyze Scatter Plots Example 2 Find a Line of Fit Example 3 Linear Interpolation Lesson 7 Contents

Scatter Plots A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane. Scatter plots are used to investigate a relationship between two quantities.

Types of relationships

Lines of fit If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. The line of fit describes a trend line. There is a statistical method to find the line of best fit, that’s the line that most closely approximates the data.

Making Predictions You can use the line of best fit to make predictions about the data. Linear extrapolation is predicting values that are outside the range of the data. Linear interpolation is predicting values that are inside the range of data.

Tongue Twister Activity

Witch Wished Which Wish? Tongue Twister Three Witches Wished Three Wishes, But Which Witch Wished Which Wish?

Tongue Twister Data # of People 2nd Block Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Discuss tongue twister activity and finish handout.

The graph shows average personal income for U.S. citizens. Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows average personal income for U.S. citizens. Answer: The graph shows a positive correlation. With each year, the average personal income rose. Example 7-1a

Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows the average students per computer in U.S. public schools. Answer: The graph shows a negative correlation. With each year, more computers are in the schools, making the students per computer rate smaller. Example 7-1b

a. The graph shows the number of mail-order prescriptions. Determine whether each graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. a. The graph shows the number of mail-order prescriptions. Answer: Positive correlation; with each year, the number of mail-order prescriptions has increased. Example 7-1c

Answer: no correlation Determine whether each graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. b. The graph shows the percentage of voter participation in Presidential Elections. Answer: no correlation Example 7-1d

Population (millions) The table shows the world population growing at a rapid rate. Year Population (millions) 1650 500 1850 1000 1930 2000 1975 4000 1998 5900 Example 7-2a

Draw a scatter plot and determine what relationship exists, if any, in the data. Let the independent variable x be the year and let the dependent variable y be the population (in millions). The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables. Example 7-2b

Draw a line of fit for the scatter plot. No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot. Example 7-2c

Write the slope-intercept form of an equation for equation for the line of fit. The line of fit shown passes through the data points (1850, 1000) and (1998, 5900). Step 1 Find the slope. Slope formula Let and Simplify. Example 7-2d

Answer: The equation of the line is . Step 2 Use m = 33.1 and either the point-slope form or the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000). Point-slope form Slope-intercept form Answer: The equation of the line is . Example 7-2e

Check Check your result by substituting (1998, 5900) into Line of fit equation Replace x with 1998 and y with 5900. Multiply. Subtract. The solution checks. Example 7-2f

The table shows the number of bachelor’s degrees received since 1988. Years Since 1988 2 4 6 8 10 Bachelor’s Degrees Received (thousands) 1051 1136 1169 1165 1184 Source: National Center for Education Statistics Example 7-2g

a. Draw a scatter plot and determine what relationship exists, if any, in the data. Answer: The scatter plot seems to indicate that as the number of years increase, the number of bachelor’s degrees received increases. There is a positive correlation between the two variables. Example 7-2h

b. Draw a line of best fit for the scatter plot. c. Write the slope-intercept form of an equation for the line of fit. Answer: Using (4, 1137) and (10, 1184), Example 7-2i

Use the prediction equation where x is the year and y is the population (in millions), to predict the world population in 2010. Original equation Replace x with 2010. Simplify. Answer: 6,296,000,000 Example 7-2a

Use the equation where x is the years since 1988 and y is the number of bachelor’s degrees (in thousands), to predict the number of bachelor’s degrees that will be received in 2005. Answer: 1,204,000 Example 7-3b

Summary What is a scatter plot? What is the line of best fit or trend line? Why is it useful? How can you come up with an equation for the line of best fit? Assignment: