NxRegress - Simple Linear Regression Function

Calculates the value of the regression function for an intermediate x-value.

Syntax

NxRegress(X, Y, Regression_type, POrder, Const, target, Return_type, Alpha)

X

is the x-component of the input data table (a one-dimensional array of cells (e.g., rows or columns)).

Y

is the y-component (i.e. function) of the input data table (a one-dimensional array of cells (e.g., rows or columns)).

Regression_type

is the model description flag for the trend function (1 = Linear (default), 2 = Polynomial, 3 = Exponential, 4 = Logarithmic, 5 = Power).

Order	Description
1	Linear (default).
2	Polynomial.
3	Exponential.
4	Logarithmic.
5	Power.

POrder

is the polynomial order. This is only relevant for a polynomial type of trend and is ignored for all others. If missing, POrder = 1.

Const

is the constant or the intercept value to fix (e.g. zero). If missing, an intercept will not be fixed and is computed normally.

target

is the desired x-value to calculate the regression value for (a single value).

Return_type

is a switch to select the return output (1 = Forecast value (default), 2 = Upper limit, 3 = Lower Limit, 4 = R-Squared).

Method	Description
1	Forecast value (default).
2	C.I. upper limit.
3	C.I. lower limit.
4	R-Squared.

Alpha

is the statistical significance or confidence level (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.

Remarks

1. NxRegress supports the following trend functions:
   $$ \begin{cases} \mathrm{Linear} & Y=\alpha + \beta \times X \\ \mathrm{Polynomial} & Y=\alpha + \beta_1 \times X + \beta_2 \times X^2 + \cdots + \beta_N \times X^N \\ \mathrm{Exponential:} & Y= \alpha \times e^{\beta \times X} \\ \mathrm{Logarithm:} & Y= \alpha + \beta \times \ln(X) \\ \mathrm{Power:} & Y= \alpha \times X^{\beta} \\ \end{cases} $$
2. For exponential and logarithmic trends, the intercept value is not permitted to be fixed and thus is ignored.
3. The polynomial order argument must be a positive integer.
4. The trend function's coefficients that best fit your data are estimated using the "least squares" method.
5. The time series may include missing values (e.g. #N/A) at either end.

Examples

Example 1:

Files Examples

Related Links

• Wikipedia - Least squares regression

References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.