1. 2.5 Correlation and
Best-Fitting Lines

2. Scatter Plots and Correlation
• A __________________ is a graph used to
scatter plot
check for relationships between paired
data.
Positive Negative No
Correlation Correlation Correlation

3. Describe the correlation shown by each scatter plot:
• Describe the correlation shown by each
scatter plot:
Positive correlation, Negative correlation,
means as GPA increased, means as GPA increased,
Hours Studying tended to Hours of Video Games
increase. tended to decrease.

4. Approximating Best-Fitting Lines
• When data show a positive or negative
correlation, you can approximate the data
with a _________.
line

5. To fit a line to data:
scatter plot
1. Draw a _________________ of the data.
line
2. Sketch the _______ that follows the
pattern the closest. There should be as
above
many points _________ the line as there are
below
__________.
two
3. Choose ______ points on the line and
coordinates
estimate the ______________ of each point.
point-slope form
4. Use ____________________ to write an
equation of the line through the two points.

6. Example: Fitting a Line to Data
• The following data pairs give the average speed
of an airplane during the first ten minutes of an
airplane flight, with x in minutes and y in miles
per hour. Approximate the best-fitting line for
the data.
x (minutes) 1 2 3 4 5 6 7 8 9 10
y (miles per
180 250 290 310 400 420 410 490 520 510
hour)

7. x (minutes) 1 2 3 4 5 6 7 8 9 10
y (miles per hour) 180 250 290 310 400 420 410 490 520 510
Use the fitted line to estimate the speed of an
airplane at 5.5 minutes into the flight.

8. Your Turn!
• The U.S. production of beef from 1990 to 1997 is
shown in the table, where x is years since 1990 and y
is billions of pounds. Approximate the best-fitting
line for the data. Then, use the fitted line to
estimate the beef production in the year 2000.
x (years) 0 1 2 3 4 5 6 7
y (billions of
22.7 22.9 23.1 23.0 24.4 25.2 25.5 25.5
pounds)

9. x (years) 0 1 2 3 4 5 6 7
y (billions of pounds) 22.7 22.9 23.1 23.0 24.4 25.2 25.5 25.5