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Linear Regression Functions

Source: R/linear_regression.R
linear_regression.Rd

Functions to perform simple ordinary least squares (OLS) linear regression.

The OLS fit finds \(c_0\) and \(c_1\) that minimize

$$\mathcal{L}(c_0, c_1) := \sum_{i=0}^{n-1} (y_i - c_0 - c_1 x_i)^2$$

producing the model \(f(x)=c_0+c_1x\). The optional \(R^2\) output uses

$$R^2 = 1 - \frac{\sum_i (y_i - c_0 - c_1x_i)^2}{\sum_i (y_i - \bar{y})^2}$$

Usage

simple_ordinary_least_squares(x, y)

simple_ordinary_least_squares_with_R_squared(x, y)

Arguments

x

A numeric vector.

y

A numeric vector.

Value

A two-element numeric vector containing the intercept and slope of the regression line, or a three-element vector containing the intercept, slope, and R-squared value if applicable.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Simple Ordinary Least Squares
x <- c(1, 2, 3, 4, 5)
y <- c(2, 3, 5, 7, 11)
simple_ordinary_least_squares(x, y)
#> [1] -1.0  2.2
# Simple Ordinary Least Squares with R-squared
simple_ordinary_least_squares_with_R_squared(x, y)
#> [1] -1.0000000  2.2000000  0.9453125