Line of Best Fit

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Line of Best Fit
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Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
Holt McDougal Algebra 1
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Warm Up Identify the slope and the
y-intercept. 1. y 2x 1 2.
y x - 4
m 2, b 1
Identify the correlation (positive, negative, or
none) that you would expect to see between each
pair of data sets.
3. a persons height and shoe size
pos
4. the age of a car and its value
neg
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Objectives
Determine a line of best fit for a set of linear
data. Determine and interpret the correlation
coefficient.
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Vocabulary
residual least-squares line line of best
fit linear regression correlation coefficient
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A residual is the signed vertical distance
between a data point and a line of fit.
The least-squares line for a data set is the line
of fit for which the sum of the squares of the
residuals is as small as possible.
A line of best fit is the line that comes closest
to all of the points in the data set, using a
given process.
Linear regression is a process of finding the
least-squares line.
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The correlation coefficient is a number r, where
-1 r 1, that describes how closely the points
in a scatter plot cluster around a line of best
fit.
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Example1 Calculating Residuals
Two lines of fit for this data are y 2x 2 and
y x 4. For each line, find the sum of the
squares of the residuals. Which line is a better
fit?
X 1 2 3 4
Y 7 5 6 9
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Example1 Continued
Find the residuals
y x 4
Sum of squared residuals
(2)2 (1)2 (1)2 (1)2 4 1 1 1 7
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Example1 Continued
Find the residuals
y 2x 2
Sum of squared residuals
(3)2 (1)2 (2)2 (-1)2 9 1 4 1 15
The line y x 4 is a better fit.
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Check It Out! Example 1
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Check It Out! Example 1 Continued
Find the residuals.
Sum of squared residuals (2)2 (2)2 (2)2
(2)2 4 4 4 4 16
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Check It Out! Example 1 Continued
Find the residuals.
y x 8
Sum of squared residuals (3)2 (2)2 (1)2
(4)2 9 4 1 16 30
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Lesson Quiz
The table shows time spent on homework and number
of incorrect quiz answers for several students.

1. Two lines of fit are y -x 11 and
   y -0.5x 8. Find the sum of the squares
   of the residuals for each line. Which line is a
   better fit?

18 20 y -x 11