In henkar91/AdvRprogr_lab7: Linear regression analysis

library(linreg)
data("iris")

This vignette summarises the Least-squares estimation and related techniques of linear regression that are available in linreg package.The examples are provided based on Iris data set and linear regression formula:

example_formula <- Petal.Length~Sepal.Width+Sepal.Length

General information

The package contains linreg RC object, hence the syntax of calling it is:

linreg_example <- linreg$new(example_formula, data=iris)

The linreg includes calculations of these values:

• Estimate of regression coefficients: $$\mathbf{\hat{\mathrm{\beta}}=(X^TX)^{-1}X^Ty}$$
• The fitted values: $$\mathbf{\hat{y}=X\hat{\mathrm{\beta}}}$$
• The residuals: $$\mathbf{\hat{e}=y-\hat{{y}}}$$
• The degrees of freedom: $$df=n-p$$ where $n$ is the number of observations and $p$ is the number of parameters in the model.
• The residual variance: $$\hat{\sigma}^2\mathbf{=\frac{e^Te}{df}}$$
• The variance of the regression coefficients: $$\mathbf{\widehat{\mathrm{Var}}(\hat{\mathrm{\beta}})}=\hat{\sigma}^2\mathbf{(X^TX)^{-1}}$$

Methods

Below are listed available methods with examples:

• print(), returns the coefficients and coefficient names.

linreg_example$print()

• plot(), returns Residuals vs Fitted and Scale−Location plots

linreg_example$plot()

• resid(), returns return the vector of residuals $\mathbf{e}$.(in the example only first 5 values are displayed)

residuals <- linreg_example$resid()
residuals[1:5]

• pred(), returns the predicted values $\mathbf{\hat{y}}$ (in the example only first 5 values are displayed)

predicted <- linreg_example$pred()
predicted[1:5]

• coef(), returns the coefficients as a named vector

linreg_example$coef()

• summary(), returns the coefficients, their standard error, $t-value$, $p-value$, and the degrees of freedom in the model

linreg_example$summary()

sessionInfo()

henkar91/AdvRprogr_lab7 documentation built on May 17, 2019, 9:12 a.m.