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.

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.

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 thenumber of mail-order prescriptions.

Answer: Positive correlation; with each year, the number of mail-order prescriptions has increased.

Determine whether each graph shows a positivecorrelation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.

Answer: no correlation

b. The graph shows thepercentage of voterparticipation in Presidential Elections.

The table shows the world population growing at a rapid rate.

Year Population (millions)1650 500

1850 1000

1930 2000

1975 4000

1998 5900

Draw a scatter plotand determine whatrelationship exists, if any, in the data.

Let the independentvariable x be the yearand let the dependentvariable y be 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.

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.

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

Letand

Simplify.

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 .

Check Check your result by substituting (1998, 5900) into

Line of fitequation

Subtract.

The solution checks.

Replace x with 1998 and y with 5900.

Multiply.

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

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.

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),

Use the prediction equationwhere 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

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