In SelinaSong0412/linr: Function to Fit Linear Regression

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(linr)

This is the introduction to my awesome package. You can look at the following introductions and practice with the whole usage of linr.

Usage

Using linr with defined vector Y (observations) and vector/matrix X (predictions). (Without dataset)

1. Conducting simple linear regression with linr

You can fit your model like this:

y = rnorm(300)
x = rnorm(300)
model.linr <- linr(y ~ x)

Then you could check many items generated by linr as follows:

model.linr$Call                      # This is how your model looks like
data.frame(model.linr$coefficients,  # Coefficient estimators
           model.linr$std.error,     # Standard error of estimators
           model.linr$T_statistic,   # T statistics of estimators
           model.linr$p_value.T)     # p value for T test 

# Other items also can be checked by 
data.frame(model.linr$MSE,           # Mean square error 
           model.linr$R.square,      # R^2 
           model.linr$Adj.R.square,  # Adjusted R^2 
           model.linr$F_statistic,   # F statistics of estimators
           model.linr$p_value.F)     # p value for F test 

# You could also look at the fitted values and residuals like this:
# head(model.linr$fitted.values)       # Look at the first 6 fitted values
# head(model.linr$residuals)           # Look at the first 6 residuals

1. Conducting multiple linear regression with linr

You can fit your multiple regression model with 3 options of matrix decompositiom methods:

(1). QR decompositiom methods

(2). SVD decompositiom methods

(3). Cholesky decompositiom methods (Default)

Here we first look at the default method:

Y = rnorm(300)
X = matrix(rnorm(6000), nrow = 300, ncol = 20)
model.linr.mul <- linr(Y ~ X, method = "cholesky")
# model.linr.mul <- linr(Y ~ X)                  # This do the same thing

# You can feel free to try the following alternative methods by yourself:
# model.linr.mul <- linr(Y ~ X, method = "qr")   # Using QR decomposition
# model.linr.mul <- linr(Y ~ X, method = "svd")  # Using SVD decomposition

Then you could check many items generated by linr as follows:

model.linr.mul$Call                      # This is how your model looks like
data.frame(model.linr.mul$coefficients,  # Coefficient estimators
           model.linr.mul$std.error,     # Standard error of estimators
           model.linr.mul$T_statistic,   # T statistics of estimators
           model.linr.mul$p_value.T)     # p value for T test 

# Other items also can be checked by 
data.frame(model.linr.mul$MSE,           # Mean square error 
           model.linr.mul$R.square,      # R^2 
           model.linr.mul$Adj.R.square,  # Adjusted R^2 
           model.linr.mul$F_statistic,   # F statistics of estimators
           model.linr.mul$p_value.F)     # p value for F test 

# You could also look at the fitted values and residuals like this:
# head(model.linr.mul$fitted.values)       # Look at the first 6 fitted values
# head(model.linr.mul$residuals)           # Look at the first 6 residuals

Using linr with regression formula and your own dataset

1. Conducting simple linear regression with linr on your data

# Here we use the R build-in dataset cars as an example:
# fit a linear model with dist as outcome and speed as predictor
model.linr.cars <- linr(dist ~ speed, data = cars) 

Then you could check items generated by linr as follows:

model.linr.cars$Call                      # This is how your model looks like
data.frame(model.linr.cars$coefficients,  # Coefficient estimators
           model.linr.cars$std.error,     # Standard error of estimators
           model.linr.cars$T_statistic,   # T statistics of estimators
           model.linr.cars$p_value.T)     # p value for T test 

# Other items also can be checked by 
data.frame(model.linr.cars$MSE,           # Mean square error 
           model.linr.cars$R.square,      # R^2 
           model.linr.cars$Adj.R.square,  # Adjusted R^2 
           model.linr.cars$F_statistic,   # F statistics of estimators
           model.linr.cars$p_value.F)     # p value for F test 

# You could also look at the fitted values and residuals like this:
# head(model.linr.cars$fitted.values)       # Look at the first 6 fitted values
# head(model.linr.cars$residuals)           # Look at the first 6 residuals

1. Conducting multiple linear regression with linr on your data

# Here we use the R build-in dataset mtcars as an example:
# fit a linear model with disp as outcome and mpg, wt, carb as predictors
model.linr.mtcars <- linr(disp ~ mpg + wt + carb, data = mtcars)

Then you could check items generated by linr as follows:

model.linr.mtcars$Call                      # This is how your model looks like
data.frame(model.linr.mtcars$coefficients,  # Coefficient estimators
           model.linr.mtcars$std.error,     # Standard error of estimators
           model.linr.mtcars$T_statistic,   # T statistics of estimators
           model.linr.mtcars$p_value.T)     # p value for T test 

# Other items also can be checked by 
data.frame(model.linr.mtcars$MSE,           # Mean square error 
           model.linr.mtcars$R.square,      # R^2 
           model.linr.mtcars$Adj.R.square,  # Adjusted R^2 
           model.linr.mtcars$F_statistic,   # F statistics of estimators
           model.linr.mtcars$p_value.F)     # p value for F test 

# You could also look at the fitted values and residuals like this:
# head(model.linr.mtcars$fitted.values)       # Look at the first 6 fitted values
# head(model.linr.mtcars$residuals)           # Look at the first 6 residuals

Correctness Checking

To check the correctness of function linr, we compare its outputs with stats::lm function

See more test for correctness and function efficiency in vignette("Efficiency_tests", package = "linr"

# simple example for checking correctness. See more tests in vignette.
model.lm <- lm(y ~ x)
all(c(all.equal(model.lm$coefficients, model.linr$coefficients), 
      all.equal(model.lm$fitted.values, model.linr$fitted.values),
      all.equal(model.lm$residuals, model.linr$residuals)))

model.lm.mul <- lm(Y ~ X)
all(c(all.equal(model.lm.mul$coefficients, model.linr.mul$coefficients), 
      all.equal(model.lm.mul$fitted.values, model.linr.mul$fitted.values),
      all.equal(model.lm.mul$residuals, model.linr.mul$residuals)))

model.lm.cars <- lm(dist ~ speed, data = cars) 
all(c(all.equal(model.lm.cars$coefficients, model.linr.cars$coefficients), 
      all.equal(model.lm.cars$fitted.values, model.linr.cars$fitted.values),
      all.equal(model.lm.cars$residuals, model.linr.cars$residuals)))

model.lm.mtcars <- lm(disp ~ mpg + wt + carb, data = mtcars)
all(c(all.equal(model.lm.mul$coefficients, model.linr.mul$coefficients), 
      all.equal(model.lm.mul$fitted.values, model.linr.mul$fitted.values),
      all.equal(model.lm.mul$residuals, model.linr.mul$residuals)))

Useful links:

• Github page

• Report bug

SelinaSong0412/linr documentation built on Dec. 18, 2021, 1:04 p.m.