# lm2: Fitting Bidimensional Regression Models In alexander-pastukhov/bidim-regression: Calculates the Bidimensional Regression Between Two 2D Configurations

## Description

lm2 is used to fit bidimensional linear regression models using Euclidean and Affine transformations following the approach by Tobler (1965).

## Usage

 1 lm2(formula, data, transformation)

## Arguments

 formula a symbolic description of the model to be fitted in the format A + B ~ C + D, where A and B are dependent and C and D are independent variables data a data frame containing variables for the model. transformation the transformation to be used, either 'euclidean', 'affine', or 'projective'.

## Value

lm2 returns an object of class "lm2". An object of class "lm" is a list containing at least the following components:

 transformation string with the transformation type (euclidean, affine, or projective) npredictors number of predictors used in the model: 4 for euclidean, 6 for affine, 8 for projective. df_model, df_residual degrees of freedom for the model and for the residuals transformation_matrix 3x3 transformation matrix coeff transformation coefficients, with a denoting the intercept terms. transformed_coeff scale, angle, and sheer coefficients, depends on transformation. fitted_values data frame containing fitted values for the original data set residuals data frame containing residuals for the original fit r.squared, adj.r.squared R-squared and adjusted R-squared. F, p.value F-statistics and the corresponding p-value, given the df_model and df_residual degrees of freedom. dAIC Akaike Information Criterion (AIC) difference between the regression model and the null model. A negative values indicates that the regression model is better. See Nakaya (1997). distortion_index Distortion index following Waterman and Gordon (1984), as adjusted by Friedman and Kohler (2003) lm an underlying linear model for Euclidean and affine transformations. formula formula, describing input and output columns data data used to fit the model Call function call information, incorporates the formula, transformation, and data.