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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 average personal income for U.S. citizens. Answer:The graph shows a positive correlation. With each year, the average personal income rose.

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

Example 7-2a The table shows the world population growing at a rapid rate. YearPopulation (millions)

Example 7-2b 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 7-2c 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 7-2d 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 1Find the slope. Slope formula Let and Simplify.

Example 7-2e Step 2Use 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 formSlope-intercept form Answer:The equation of the line is.

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

Example 7-2g The table shows the number of bachelor’s degrees received since Years Since Bachelor’s Degrees Received (thousands) Source: National Center for Education Statistics

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

Example 7-3b Use the equationwhere 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 Answer: 1,204,000