# Approximate overall magnitudes of kernel regression partials dx/dy and dy/dx.

### Description

Uses Vinod (2015) and runs kernel regression of x on y, and also of y on x by using the ‘np’ package. The function goes on to compute a summary magnitude of the overall approximate partial derivative dx/dy (and dy/dx), after adjusting for units by using an appropriate ratio of standard deviations. Of course, the real partial derivatives of nonlinear functions are generally distinct for each observation.

### Usage

1 | ```
mag(x, y)
``` |

### Arguments

`x` |
Vector of data on the dependent variable |

`y` |
Vector of data on the regressor |

### Value

vector of two magnitudes of kernel regression partials dx/dy and dy/dx.

### Note

This function is intended for use only after the direction of causal path
is already determined by various functions in this package (e.g. `somePairs`

).
For example, if the researcher knows that x causes y, then only
dy/dx denoted by dydx is relevant.
The other output of the function dxdy is to be ignored.
Similarly, only ‘dxdy’ is relevant if y is known to be the cause of x.

### Author(s)

Prof. H. D. Vinod, Economics Dept., Fordham University, NY

### References

Vinod, H. D.'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, http://dx.doi.org/10.1080/03610918.2015.1122048

Vinod, H. D. 'Matrix Algebra Topics in Statistics and Economics Using R', Chapter 4 in Handbook of Statistics: Computational Statistics with R, Vol.32, co-editors: M. B. Rao and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2014, pp. 143-176.

### See Also

See `mag_ctrl`

.

### Examples

1 2 |