7-3 Line of Best Fit
Objectives
• Determine a line of best fit for a set of linear data
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
Line of Best Fit
• line that approximates a trend for the data in a scatter plot• shows pattern and direction
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
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
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?
Year 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995
# of Tornadoes
201 593 616 897 654 919 866 684 1133 1234
1950
1955
1960
1965
1970
1975
1980
1990
1985
1995
200
400
600
800
1000
1200
Do you notice a trend?
1. Use the line of best fit to predict how many tornadoes may be reported in the United States in 2015.
1950
1955
1960
1965
1970
1975
1980
1990
1985
1995
200
400
600
800
1000
1200
2000
2005
2010
2015
If the trend continues, there will be 1200 tornadoes
reported in 2015.
1950
1955
1960
1965
1970
1975
1980
1990
1985
1995
200
400
600
800
1000
1200
2000
2005
2010
2015
2. What is the equation for this line?
500
y = mx + b
Up 100
Right 10y-int:
m: 10
y = 10x + 500
1950
1955
1960
1965
1970
1975
1980
1990
1985
1995
200
400
600
800
1000
1200
2000
2005
2010
2015
1945 @ y-int.
3. Use the equation to find how many tornadoes may be reported in the United States in 2015.
x = 2015 – 1945
x = 70
y = 10(70) +500
y = 700 +500
y = 10x + 500
y = 1200
X 2 5 1 0 4 2 3
Y 77 93 70 63 90 75 84
4. 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
2 1
2 1
y ym
x x
93 63
5 0m
30
65
m
y = 6x + 63
Residuals
Residual: Difference between the actual data point and the line of best fit
1950
1955
1960
1965
1970
1975
1980
1990
1985
1995
200
400
600
800
1000
1200
2000
2005
2010
2015
Find the residuals:
1955:
1965:
1975:
1980:
-400
300
200
5. Find the residuals at the years 1955, 1965, 1975, and 1980.
0
Classwork/Homework
7-3 Worksheet