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## Example 7-1a

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**Example 7-1a**Determine whether thegraph shows a positivecorrelation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it. The graph shows average personal income forU.S. citizens. Answer: The graph shows a positive correlation. With each year, the average personal income rose.**Example 7-1b**Determine whether thegraph shows a positivecorrelation, 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 positivecorrelation, 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 positivecorrelation, 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 7-2a**The table shows the world population growing at a rapid rate.**Example 7-2b**Draw a scatter plotand determine whatrelationship exists, if any, in the data. Let the independentvariable x be the yearandlet the dependentvariable ybe thepopulation(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.**Slope formula**Letand Simplify. Example 7-2d Write the slope-intercept form of an equation for equation for the line of fit. Theline of fit shown passes through the data points (1850, 1000) and (1998, 5900). Step 1Find the slope.**Answer: The equation of the line is .**Example 7-2e Step 2 Use m= 33.1 and either the point-slope form or the slope-intercept form towrite the equation.You can use either data point.We chose (1850, 1000). Point-slope form Slope-intercept form**Check Check your result by substituting (1998, 5900) into**Line of fitequation Replace x with 1998 and y with 5900. Multiply. Subtract. Example 7-2f The solution checks.**Example 7-2g**The table shows the number of bachelor’s degrees received since 1988. 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.**Answer: Using (4, 1137) and (10, 1184),**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.**Use the prediction equationwhere x is the year and y is the**population (in millions), to predict the worldpopulation in 2010. Original equation Replace x with 2010. Simplify. Example 7-2a Answer: 6,296,000,000**Use the equation where x is the years since 1988 and y is**the number of bachelor’s degrees (in thousands), to predict the numberof bachelor’s degreesthat will be received in 2005. Example 7-3b Answer: 1,204,000