# Definition

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

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### 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.

`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.  