ols: Ordinary Least Squares Regression

In desk: Didactic Econometrics Starter Kit

Ordinary Least Squares Regression

Description

Estimates linear models using ordinary least squares estimation. Generated objects should be compatible with commands expecting objects generated by lm(). The object returned by this command can be plotted using the plot() function.

Usage

ols(
  formula,
  data = list(),
  na.action = NULL,
  contrasts = NULL,
  details = FALSE,
  ...
)

Arguments

formula	model formula.
data	name of data frame of variables in formula.
na.action	function which indicates what should happen when the data contain NAs.
contrasts	an optional list. See the contrasts.arg of model.matrix.default.
details	logical value indicating whether details should be printed out by default.
...	other arguments that lm.fit() supports.

Details

Let X be a model object generated by ols() then plot(X, ...) accepts the following arguments:

pred.int = FALSE	should prediction intervals be added to plot?
conf.int = FALSE	should confidence intervals be added to plot?
residuals = FALSE	should residuals be added to plot?
center = FALSE	should mean values of both variables be added to plot?

Value

A list object including:

coefficients/coef	estimated parameters of the model.
residuals/resid	residuals of the estimation.
effects	n vector of orthogonal single-df effects. The first rank of them correspond to non-aliased coefficients, and are named accordingly.
fitted.values	fitted values of the regression line.
df.residual/df	degrees of freedom in the model (number of observations minus rank).
se	vector of standard errors of the parameter estimators.
t.value	vector of t-values of single parameter significance tests.
p.value	vector of p-values of single parameter significance tests.
data/model	matrix of the variables' data used.
response	the endogenous (response) variable.
model.matrix	the model (design) matrix.
ssr	sum of squared residuals.
sig.squ	estimated error variance (sigma squared).
vcov	the variance-covariance matrix of the model's estimators.
r.squ	coefficient of determination (R squared).
adj.r.squ	adjusted coefficient of determination (adj. R squared).
nobs	number of observations.
ncoef/rank	integer, giving the rank of the model (number of coefficients estimated).
has.const	logical value indicating whether model has constant parameter.
f.val	F-value for simultaneous significance of all slope parameters.
f.pval	p-value for simultaneous significance of all slope parameters.
modform	the model's regression R-formula.
call	the function call by which the regression was calculated (including modform).

Examples

## Minimal simple regression model
check <- c(10,30,50)
tip <- c(2,3,7)
tip.est <- ols(tip ~ check)

## Equivalent estimation using data argument
tip.est <- ols(y ~ x, data = data.tip)

## Show estimation results
tip.est

## Show details
print(tip.est, details = TRUE)

## Plot scatter and regression line
plot(tip.est)

## Plot confidence (dark) and prediction bands (light), residuals and two center lines
plot(tip.est, pred.int = TRUE, conf.int = TRUE, residuals = TRUE, center = TRUE)

## Multiple regression model
fert.est <- ols(barley ~ phos + nit, data = log(data.fertilizer), details = TRUE)
fert.est

desk documentation built on April 4, 2025, 1:10 a.m.