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