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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 y-hat. y-hat. 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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