resline | Fit a resistant line to bivariate data | resline |

York University

The data points are divided into thirds, based on the sorted values of the X= variable. The median X and Y value within each third define "summary points" which are used to calculate robust estimates of slope and intercept.

Power transformations are found by calculating a "ratio of slopes" table, transforming the X and Y coordinates of summary points to all powers in the list [ -1.0, -0.5, log, sqrt, raw, 2.0], and forming the ratio of the slopes of the lines connecting the first pair of summary points and the second pair of summary points. The optimal transformation is the one whose slope ratio is closest to 1 (or whose log is closest to zero).

The `resline` macro requires that all values for the X and Y
variables are **positive**.
If any data values are negative, the recommended solution is to
add a constant to all values to make them positive.

- DATA=_LAST_
- Name of the input data set.
- X=
- The name of the independent variable.
- Y=
- The name of the response variable.
- ID=
- The name of a character variable to identify each observation, used to label points in the output.
- ENDS=.5
- The greatest range of either end-third.
- PLOT=FIT RESID,
- Keywords to request one or more printer plots to show.

**FIT**requests a plot of observed and fitted values vs. X for the raw data.**RESID**requests a plot of residuals vs X. - OUT=_FIT_
- The name of an output data set containing
fitted values (FIT) and residuals (RESIDUAL), in addition to the
X=, Y=, and ID= variables for all non-missing observations.
Note that the ID variable is named
**ID** - OUTSUM=_SUMVAL_
- The name of an output data set containing median summary values for the thirds (THIRD) of the data.

%include data(nations); *include macros(resline); *-- included in autocall library; %resline(data=nations, x=income, y=imr, id=nation);The printed output includes the following:

Warning: 4 row(s) with missing data have been removed. Summary Values X Y n Low 101.000 131.150 34 Mid 426.000 51.700 51 High 3574.500 14.850 16 R ('R' -> half-range rule; '=' -> equal X value rule) Parameters of fitted resistant line slope intercept -0.033482 111.67558plus tables of fitted values and residuals, and plots. In addition, the following table indicates that a log transformation of IMR comes closest to having a linear relationship to (raw) INCOME.

----- Ratio of Slopes table ------ Rows are powers of X, columns are powers of Y -1.0 -0.5 log sqrt raw 2.0 -1.0 2.163 1.921 1.708 1.521 1.356 1.081 -0.5 1.898 1.685 1.499 1.334 1.189 0.948 log 1.663 1.477 1.314 1.169 1.042 0.831 sqrt 1.457 1.294 1.151 1.024 0.913 0.728 raw 1.275 1.132 1.007 0.896 0.799 0.637 2.0 0.975 0.866 0.770 0.685 0.611 0.487 ------- 5 Best powers ------- Power of X Power of Y Slope Ratio log Ratio raw log 1.007 0.003 sqrt sqrt 1.024 0.010 2.0 -1.0 0.975 -0.011 log raw 1.042 0.018 -0.5 2.0 0.948 -0.023

lowess Locally weighted scatterplot smoother