Excel trendline equations

24 Jul 2007

When you add a trendline to a chart, Excel provides an option to display the trendline equation in the chart. This tip describes how to create formulas that generate the trendline coefficients. You can then use these formulas to calculate predicted y values for give values of x.

These equations assume that your sheet has two named ranges: x and y.

Linear Trendline

Equation: y = m \* x + b
m: =SLOPE(y,x)
b: =INTERCEPT(y,x)

Logarithmic Trendline

Equation: y = (c \* LN(x)) - b
c: =INDEX(LINEST(y,LN(x)),1)
b: =INDEX(LINEST(y,LN(x)),1,2)

Power Trendline

Equation: y=c\*x^b
c: =EXP(INDEX(LINEST(LN(y),LN(x),,),1,2))
b: =INDEX(LINEST(LN(y),LN(x),,),1)

Exponential Trendline

Equation: y = c \*e ^(b \* x)
c: =EXP(INDEX(LINEST(LN(y),x),1,2))
b: =INDEX(LINEST(LN(y),x),1)

2nd Order Polynomial Trendline

Equation: y = (c2 \* x^2) + (c1 \* x ^1) + b
c2: =INDEX(LINEST(y,x^\{1,2}),1)
C1: =INDEX(LINEST(y,x^\{1,2}),1,2)
b = =INDEX(LINEST(y,x^\{1,2}),1,3)

3rd Order Polynomial Trendline

Equation: y = (c3 \* x^3) + (c2 \* x^2) + (c1 \* x^1) + b
c3: =INDEX(LINEST(y,x^\{1,2,3}),1)
c2: =INDEX(LINEST(y,x^\{1,2,3}),1,2)
C1: =INDEX(LINEST(y,x^\{1,2,3}),1,3)
b: =INDEX(LINEST(y,x^\{1,2,3}),1,4)

Higher Order Polynomial Trendline

Notice the pattern in the two preceding sets of formulas.