lmr_data: 'lm' Simple Linear Regression

In exams.forge: Support for Compiling Examination Tasks using the 'exams' Package

lm Simple Linear Regression

Description

Computes an lm object for a simple linear regression from a range of x and y values, including intermediate values. If r is not given then zero correlation is used (with cor_data). digits determines the rounding for the x and y values. If only one value is given, then it will be used for x and y. If no value is given then it will be determined from the x and y values by 3+ceiling(-log10(diff(range(.)))).

Usage

lmr_data(xr, yr, n, r = 0, digits = NULL, ...)

lm_regression_data(xr, yr, n, r = 0, digits = NULL, ...)

Arguments

xr	numeric: range of x values
yr	numeric: range of y values
n	numeric: number of observations to generate
r	numeric: desired correlation, uses cor_data
digits	numeric(2): digits for rounding, for x digits[1] is used, for y digits[2] is used (default: NULL)
...	further parameters used in cor_data

Value

An object of the class lm with the additional components:

• x the generated x values

• y the generated y values

• sumx \sum_{i=1}^n x_i

• sumy \sum_{i=1}^n y_i

• sumx2 \sum_{i=1}^n x_i^2

• sumy2 \sum_{i=1}^n y_i^2

• sumxy \sum_{i=1}^n x_i y_i

• meanx the mean of x: 1/n \sum_{i=1}^n x_i

• meany the mean of y: 1/n \sum_{i=1}^n y_i

• varx the variation of x: \sum_{i=1}^n (x_i-\bar{x})^2

• vary the variation of y: \sum_{i=1}^n (y_i-\bar{y})^2

• varxy the common variation of x and y:\sum_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})

• sxy the covariance of x and y

• rxy the correlation of x and y

• b0 the intercept of the linear regression

• b1 the slope of the linear regression

• r2 the coefficient of determination of the linear regression

Examples

# Engine displacement typically ranges from 500 to 2000 cm^3
# Fuel economy typically ranges from 2 to 8 liter/100 km
lmr <- lmr_data(c(500, 2000), c(2, 8), n=8)
str(lmr)

exams.forge documentation built on Aug. 21, 2025, 5:41 p.m.