Fitting a Line to Data Using Qpoints

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Fitting a Line to Data Using Q-points
(Q3,Q3)
(Q1,Q3)
(Q1,Q1)
(Q3,Q1)
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(No Transcript)
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A Line of Fit Using Q-Points

• Take notes when you see this animated pencil.

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Objectives

• Draw a trend line that fits or models a set of
  points to allow predictions

• Write an slope y-intercept equation that fits a
  set of real world data

• Use quartiles to find an equation to fit a set of
  data

• Write an point slope equation that fits a set of
  real world data

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What is a Line of Fit?
A line of fit is a line that shows a general
direction of the data set and has roughly the
same number of points above and below the line.
A line of fit is a trend line that models a data
set to allow for predictions interpolate and
extrapolate.
Interpolate is to obtain data within the observed
range.
Extrapolate is to obtain data outside the
observed range.
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Fitting a Line to Data Using the Q-Points
There are several ways to find the best-fitting
line for a given set of data points. In this
lesson, you will use the Q-points approach.
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Example Find the Best-Fitting Line
Nutrition Facts
The table on the right shows how many fat grams
there are in some hamburgers sold by national
chain restaurants.
Write an equation of your line.
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Example Using Q-points to Find the Best-Fitting
Line
SOLUTION
Find the 5-no. summary in both the x and y
directions.
x (7, 10, 12, 16, 18) y (20, 28, 32, 40, 46)
Since its a positive trend, use
(Q1x, Q1y) and (Q3x, Q3y) to find the slope of
the Q-line.
Thus, (Q1x, Q1y)
(Q3x, Q3y)
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Example Find the Slope of the Q-line
Find the slope of the Q-line passing through (10,
28) and (16, 40).
SOLUTION
b
40 - 28
Substitute values.
16 - 10
Simplify.
Slope is 2.
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Determining the Trends of x and y
In this scatter plot, x and y have
a positive trend, which means that the points can
be approximated by a line with
a positive slope.
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Determining the Trends of x and y
In this scatter plot, x and y have
a negative trend,
which means that the points can be approximated
by a line with a negative slope.
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Determining the Trends of x and y
In this scatter plot, x and y have
relatively no trend, which means that the points
cannot be approximated by a line.
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Closure
Use Q-points to find the best fit line

• Find the 5 number summary in both the x and y
  directions

• Determine the trend of the data set

• If its a positive trend, use (Q1,Q1) and (Q3,Q3)
  to find the slope of the Q-line

• If its a negative trend, use (Q1,Q3) and (Q3,Q1)
  to find the slope of the Q-line

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Closure
Positive trend positive slope
Negative trend negative slope
Writing the point slope form equation

• y y1 slope(x ? x1)

• y Q1y slope(x ? Q1x)

• y Q3y ? slope(x ? Q1x)

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Closure
Determining the Trends of x and y
Positive Trend
No Trend
Negative Trend