exams.forge (version 1.0.10)

lmr_data: 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, ...)

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

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

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)