1. 7-3 Line of Best Fit Objectives
Determine a line of best fit for a set of linear data

2. Line of Best Fit (Regression Line)
Used to predict missing X and Y values
Should have approximately the same number of points above it as it has below it
Usually estimated “by eye” or by using a calculator

3. Line of Best Fit
line that approximates a trend for the data in a scatter plot
shows pattern and direction

4. How to Find the Line of Best Fit
The line of best fit should:
pass through as many points as possible
allow remaining points to be grouped equally above and below the line

5. Why make a Line of Best Fit?
Provides type and strength of the correlation
Helps us to make predictions by
INTERPOLATING
EXTRAPOLATING
Interpolating: Estimating a value BETWEEN two measurements in a set of data
Extrapolating: Estimating a value BEYOND the range of a set of data

6. Interpolating – what would the wife’s age be of a husband who is 57?
Extrapolating - what would the wife’s age be of a husband who is 84?

7. Do you notice a trend? Year 1950 1955 1960 1965 1970 1975 1980 1985
1990
1995
# of Tornadoes
201
593
616
897
654
919
866
684
1133
1234
1200
1000
800
600
400
Do you notice a trend?
200
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995

8. If the trend continues, there will be 1200 tornadoes reported in 2015.
Use the line of best fit to predict how many tornadoes may be reported in the United States in 2015.
1200
1000
800
600
If the trend continues, there will be 1200 tornadoes reported in 2015.
400
200
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015

9. y = 10x + 500 What is the equation for this line? y = mx + b y-int:
1200
1000
y-int:
500
800
Right 10
Up 100 m: 10
600
400
200
y = 10x + 500
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015

10. Use the equation to find how many tornadoes may be reported in the United States in 2015.
y = 10x + 500
y-int.
1200
1000
x = 2015 – 1945
800
x = 70
600
y = 10(70) +500
y =
400
y = 1200
200
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015

11. X 2 5 1 4 3 Y 77 93 70 63 90 75 84
Using the data table, write the equation of the line of best fit
Find the y-intercept
Find the approximate slope
Use the largest and smallest x values as points 63
y = 6x + 63

12. Residuals
Residual: Difference between the actual data point and the line of best fit

13. 5. Find the residuals at the years 1955, 1965, 1975, and 1980.
1200
1000
Find the residuals:
1955:
1965:
1975:
1980:
-400
800
300
200
600
400
200
1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
2005
2010
2015

14. Classwork/Homework
7-3 Worksheet