7-3 Line of Best Fit Objectives

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Presentation transcript:

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?

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

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

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

Use the equation to find how many tornadoes may be reported in the United States in 2015. y = 10x + 500 1945 @ y-int. 1200 1000 x = 2015 – 1945 800 x = 70 600 y = 10(70) +500 y = 700 +500 400 y = 1200 200 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

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

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

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

Classwork/Homework 7-3 Worksheet

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