Linear Project Modeling Algebra Section 7

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Linear ProjectModeling Algebra Section 7
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Source National Household Survey on Drug
Abuse http//www.oas.samhsa.gov/2k8/youthDep
ress/youthDepress.htm
Percentages of Youths Aged 12 to 16 Who
Experienced a Past Year Major Depressive Episode
(MDE), by Age 2004-2006
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PERCENTAGE OF YOUTHS AGES 12 TO 16 WHO
EXPERIENCED MAJOR DEPRESSIVE EPISODE
PERCENTAGE
AGE OF YOUTHS
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FINDING EQUATION FOR DATA

• Pick two points from data (12, 4.1) (13, 6.2)
• Use Slope Formula m
• Plug in points (4.1-6.2) / (12-13) -2.1/-1 2.1
• Plug in slope and choose one set of points to
  plug into y-intercept formula ymxb and solve
  for b
• (4.1) 2.1(12) b
• Multiply 2.1 12 25.2
• Subtract 4.1 25.2 therefore b -21.1
• FORMULA Y 2.1x- 21.1

Y1-Y2 X1-X2
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INTERPRETING THE SLOPE FOR EVERY AGE INCREASE
AN ADDITIONAL 2.1 YOUTHS EXPERIENCE A MAJOR
DEPRESSIVE EPISODE
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Finding Vertical Intercept

• Y 2.1x-22.1
• PLUG IN ZERO FOR X
• Y2.1(0)-22.1
• Y -22.1
• Therefore when a child is born the percentage of
  a depressive episode is -22.1 According to our
  model this means when a child is born there is a
  negative percent of a child being born depressed.
• Yes, this equation models the situation near the
  intercepts

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Finding Horizontal Intercept

• Y 2.1x- 22.1
• Plug in zero for Y
• (0) 2.1x- 22.1
• 22.1 2.1x
• Divide 22.1 by 2.1
• X 10.5
• Therefore when a child is 10 and a half they will
  have a 0 chance of having a depressive episode
  according to the model.
• Yes, this equation models the situation near the
  intercepts

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Graph Containing Scatter Plot and Equation Y
2.1x- 22.1
PERCENTAGE
AGE OF YOUTHS
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How Model Can Be Used to Make Estimations About
Trend Observed

• The model can be used to see when teens and
  individuals in their early twenties are most
  likely to have a higher percentage of a major
  depressive episode
• Age 18 y 2.1(18) 22.1 15.7
• Age 21 y 2.1(21) 22.1 22