LOGEST

Given partial data about an exponential growth curve, calculates various parameters about the best fit ideal exponential growth curve.

Sample usage

LOGEST(B2:B10,A2:A10)

LOGEST(B2:B10, A2:A10, TRUE, TRUE)

Syntax

LOGEST(known_data_y, [known_data_x], [b], [verbose])

• known_data_y – The array or range containing dependent (y) values that are already known, used to curve fit an ideal exponential growth curve.

  • If known_data_y is a two-dimensional array or range, known_data_x must have the same dimensions or be omitted.

  • If known_data_y is a one-dimensional array or range, known_data_x may represent multiple independent variables in a two-dimensional array or range. I.e. if known_data_y is a single row, each row in known_data_x is interpreted as a separated independent value, and analogously if known_data_y is a single column.

• known_data_x – [ OPTIONAL – {1,2,3,…} with same length as known_data_y by default ] – The values of the independent variable(s) corresponding with known_data_y.

  • If known_data_y is a one-dimensional array or range, known_data_x may represent multiple independent variables in a two-dimensional array or range. I.e. if known_data_y is a single row, each row in known_data_x is interpreted as a separated independent value, and analogously if known_data_y is a single column.

• b – [ OPTIONAL – TRUE by default ] – Given a general exponential form of y = b*m^x for a curve fit, calculates b if TRUE or forces b to be 1 and only calculates the m values if FALSE.

• verbose – [ OPTIONAL – FALSE by default ] – A flag specifying whether to return additional regression statistics or only the calculated coefficient and exponents.

  • If verbose is TRUE, in addition to the set of exponents for each independent variable and the coefficient b, LOGEST returns

    • The standard error for each exponent and the coefficient,

    • The coefficient of determination (between 0 and 1, where 1 indicates perfect correlation),

    • Standard error for the dependent variable values,

    • The F statistic, or F-observed value indicating whether the observed relationship between dependent and independent variables is random rather than exponential,

    • The degrees of freedom, useful in looking up F statistic values in a reference table to estimate a confidence level,

    • The regression sum of squares, and

    • The residual sum of squares.

Notes

• The statistics calculated by LOGEST are similar to LINEST but use the linear model ln y = x1 ln m1 + … + xn ln mn + ln b for each independent variable x1 … xn. Therefore, additional statistics such as the standard error must be compared to the natural logarithms of the m and b values rather than the values themselves.

See also

TREND: Given partial data about a linear trend, fits an ideal linear trend using the least-squares method and/or predicts further values.

LINEST: Given partial data about a linear trend, calculates various parameters about the ideal linear trend using the least-squares method.

GROWTH: Given partial data about an exponential growth trend, fits an ideal exponential growth trend and/or predicts further values.

Examples