Calculates the regression coefficients values for a given input variable.
Syntax
PCR_PARAM(X, Mask, Y, Intercept, Return_type, Parameter Index, Alpha)
- X
- is the independent variables data matrix, such that each column represents one variable.
- Mask
- is the boolean array to choose the explanatory variables in the model. If missing, all variables in X are included.
- Y
- is the response or the dependent variable data array (one dimensional array of cells (e.g. rows or columns)).
- Intercept
- is the constant or the intercept value to fix (e.g. zero). If missing, an intercept will not be fixed and is computed normally.
- Return_type
- is a switch to select the return output (1 = value (default), 2 = std. error, 3 = t-stat, 4 = P-value, 5 = upper limit (CI), 6 = lower limit (CI))
Method Description 1 Mean value 2 Standard error 3 T-stat 4 P-Value 5 Upper limit 6 Lower limit - Parameter Index
- is a switch to designate the target parameter (0 = intercept (default), 1 = first variable, 2 = 2nd variable, etc.).
- Alpha
- is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
Remarks
- The underlying model is described here.
- $$ \mathbf{y} = \mathbf{X}\boldsymbol\beta + \boldsymbol\varepsilon $$
$$\hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1} \mathbf{X}^{\rm T}\mathbf{y} = \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i \mathbf{x}^{\rm T}_i \,\big)^{-1} \big(\, \tfrac{1}{n}{\textstyle\sum} \mathbf{x}_i y_i \,\big).$$
Where:
- $\hat{\boldsymbol\beta}$ is the estimated regression coefficients.
- The sample data may include missing values.
- Each column in the input matrix corresponds to a separate variable.
- Each row in the input matrix corresponds to an observation.
- Observations (i.e. rows) with missing values in X or Y are removed.
- The number of rows of the response variable (Y) must be equal to the number of rows of the explanatory variable (X).
- The MLR_PARAM function is available starting with version 1.60 APACHE.
Files Examples
Related Links
References
- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Kenney, J. F. and Keeping, E. S. (1962) "Linear Regression and Correlation." Ch. 15 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 252-285
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