Description Computes result values from the fitted curve of a multiple exponential regression for a group of specified observations relative to a group of specified independent variables.
This type of regression is often applied to exponential growth situations. Because of the type of formula and the often limited amount of data the formula is based on, using these formulas to estimate values outside of the range of data is dangerous, since they are likely to give exponentially wrong results.
Another problematic aspect of this function is that it assumes the range of data in question fits an exponential model. While this assumption is appropriate in some situations (for example, radioactive decay), in many other situations it is misleading, particularly in regards to economic data.
Note If you want GROWTH to return more than one result value, you must enter it as an array function. For information, see Array Functions.
Syntax GROWTH (known_y's [, known_x's] [, new_x's] [, constant])
| Argument | Description |
|---|---|
| known_y's | A list of observed values for the dependent variable. This must be a range reference or an array constant containing all numeric values and no empty cells. For a regression with a single independent variable, enter any type of range. For a regression with multiple independent variables, enter a single row or column of values. If you are using array constants, see Array Constants in Arguments for information on how to enter the array. |
| [known_x's] | Optional. A list of observed values for the independent variable(s). This must be a range reference or an array constant containing all numeric values and no empty cells. For a regression with a single independent variable, when known_y's is a single row or column, enter a range that exactly matches the size and shape of the known_y's range. When known_y's is more than one row and column, known_x's must be a range containing the same number of values as the known_y's range, although the two ranges may be different shapes. For a regression with multiple independent variables, when known_y's is a single row, enter a contiguous row of values for each independent variable, The number of columns must match the number of columns in known_y's. Similarly, when known_y's is a single column, enter a contiguous column of values for each independent variable, ensuring that the number of rows matches known_y's. If you are using array constants, see Array Constants in Arguments for information on how to enter the array. To fit the regression to a formula that uses polynomials, see "Polynomials," below. When you omit this argument, the function assumes a single independent variable of the sequence {1, 2, 3, ...}. |
| [new_x's] | Optional. A list of values for the independent variable(s) that will compute the results of this function. This must be a range reference or an array constant containing all numeric values and no empty cells. You may enter any number of values in new_x's. The shape of the range only matters if this is a regression with multiple independent variables, in which case it must have the same number of rows or colunms of independent variables as known_x's. If you omit this argument, the function uses the specified or default values in known_x's. |
| [constant] | Optional. A logical value that determines whether or not a constant is to be included. The constant allows the regression line to intercept the Y axis at a point other than (0,0). Use True (the default value if this argument is omitted) to include the constant. Use False to force the line to intercept the Y axis at 0. |
Remarks This function uses LOGEST internally to compute the regression's coefficients. The resulting formula is then used to compute the requested values.
Results range Before entering this function, select a results range according to the following criteria:
Equation The regression computed by GROWTH attempts to fit the following formula:
where C is the coefficient determined internally by the LOGEST function, n is the number of independent variables, and b is the constant.
This formula can be converted to a linear form if logarithms are taken of both sides. The formula then becomes:
y = lC1x1+lC2x2+ ... + lCnXn+lb
This is the same formula fitted by the LINEST function. LOGEST use LINEST internally to fit the linearized form of the equation. LOGEST then takes the LINEST coefficients (lC1, lC2 ,... lCn) and converts them to the LOGEST coefficients (C1, C2, ... Cn) by applying the EXP function: C1 = EXP(lC1). The same conversion is done with the constant, b.
Example This example of exponential regression uses the following data on the growth of the national debt of a small country.
| Year | National debt, in millions |
| 1971 | 0.5 |
| 1972 | 1.1 |
| 1973 | 1.4 |
| 1974 | 2.0 |
| 1975 | 4.4 |
| 1976 | 20.0 |
| 1977 | 445.0 |
In this case, the debt figures are the known_y's and we can use default values for the known_x's, since the years increment by one.
We want to use this data to find what the national debt would have been in June of 1973. If the national debt figures fill range A2:A8, this function returns 2.958273:
See Also INTERCEPT, LINEST, LOGEST, SLOPE, TREND
