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Warning! Excel 97 (and almost all other statistical software and textbooks) define Residuals the same way as in this course: Residual = Observed value – Fitted Value But Excel 2000 uses Residual = Fitted Value – Observed Value Result: Residual Plots from Excel 2000 are upside down!.

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slide8

Warning!

Excel 97 (and almost all other statistical software and textbooks) define Residuals the same way as in this course:

Residual = Observed value – Fitted Value

But Excel 2000 uses

Residual = Fitted Value – Observed Value

Result:

Residual Plots from Excel 2000 are upside down!

slide9

Logarithms and Exponential Relationships

Basic Rules:

ln(a x b) = ln (a) + ln(b)

ln(ex) = x,

Equivalently,

e(ln y) = y

slide10

Some Special Cases:

  • ln(y) = ln(a) + bx equivalent to y = aebx
  • Examples:
  • ln(y) = 3 + 2 x => y = ??
  • y = 5e-1.7x => ln(y) = ??
slide11

Some Special Cases:

  • ln(y) = ln(a) + bx equivalent to y = aebx
  • Examples:
  • ln(y) = 3 + 2 x => y = ??
  • y = 20.08e2x
  • y = 5e-1.7x => ln(y) = ??
  • ln(y) = 1.609 – 1.7 x
slide12

Example 2: Power Law

y = axb equivalent to ln(y) = ln(a) + b ln(x)

Examples:

y = 7x3 => ln(y) = ??

ln(y) = -0.2 + 1.5 ln(x) => y = ??

slide13

Example 2: Power Law

y = axb equivalent to ln(y) = ln(a) + b ln(x)

Examples:

y = 7x3 => ln(y) = ??

ln(y) = 1.946 + 3 ln(x)

ln(y) = -0.2 + 1.5 ln(x) => y = ??

y = 0.819 x1.5