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Unformatted text preview: Years since 1610 y = 0.0414x  0.1523
R2 = 0.9345 2.5
Population in Thousands 2
1.5
1
0.5
0
0.5 0 20 40 1
Years since 1610 Exponential Transformation
Exponential Now to solve the
Now
equation for y, so we
don’t have to deal
with the logarithm.
with
Start by
Start
exponentiating, then
using properties of
logarithms to solve for
yhat.
yhat. ˆ
y = a(b) x log y = 1.54 + .0305x
10 = 10 (10 )
ˆ
y = 10 (10 )
log y 1.54 1.54 a = 10 1.54 b = 10 .0305 .0305 x 0.0305 x Exponential Transformation
Exponential This could also be
This
done using ln or
natural logarithms.
natural
The only difference
The
would be base e
instead of base 10.
instead y = 0.7042e0.0952x
R2 = 0.9345 250
Popula tion in Thousands 200
150
100
50
0
0 20 40
Years since 1610 60 80 Homework
Homework HW: read pgs 238 – 239
HW: Exercises 1, 3 – 5
Exercises...
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 Winter '13
 Jessell

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