LOGESTGiven 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