Data Analysis

Statistical data analysis from descriptive to inferential, covers the univariate and multivariate analysis of the data, exploratory analysis, and visualization of the data

Backward Deletion Method Step by Step in R

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Introduction to Backward Deletion Method

With many predictor variables, one can create the most statistically significant model from the data. There are two main choices: forward stepwise regression and backward deletion method.
In Forward Stepwise Regression: Start with the single best variable and add more variables to build your model into a more complex form.

In Backward Deletion (Backward Selection) Regression: put all the variables in the model and reduce the model by removing variables until you are left with only significant terms.

Backward Deletion method (Step by Step Procedure)

Let’s start with a big model and trim it until you get the best (most statistically significant) regression model. This drop1() command can examine a linear model and determine the effect of removing each one from the existing model. Complete the following steps to perform a backward deletion. Note that the model has different R packages for the Backward and Forward Selection of predictors.

Step 1: (Full Model)

Step 1: To start, create a “full” model (all variables at once in the model). It would be tedious to enter all the variables in the model, one can use the shortcut, the dot notation.

mod <- lm(mpg ~., data = mtcars)

Step 2: Formula Function

Step 2: Let’s use the formula() function to see the response and predictor variables used in Step 1.

formula(mod)
Backward Deletion Method

Step 3: Drop1 Function

Step 3: Let’s use the drop1() function to see which term (predictor) should be deleted from the model

drop1(mod)

Step 4: Remove the Term

Step 4: Look to remove the term with the lowest AIC value. Re-form the model without the variable that is non-significant or has the lowest AIC value. The simplest way to do this is to copy the model formula in the clipboard, paste it into a new command, and edit out the term you do not want

mod1 <- lm(mpg ~ ., data = mtcars)

Step 5: Examine the Effect

Step 5: Examine the effect of dropping another term by running the drop1() command once more:

drop1(mod1)

If you see any variable having the lowest AIC value, if found, remove the variable and carry out this process repeatedly until you have a model that you are happy with.

FAQS about Backward Deletion Method in R

  1. Write a step-by-step procedure to perform the Backward Deletion Method in r.
  2. How one can examine the effect of dropping the term from the model?
  3. What is the use of the formula function term in lm() model?
  4. What is the use of drop1() function in r?

Learn more about lm() function

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Performing Linear Regression in R: A Quick Reference

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Introduction to Performing Linear Regression in R

Regression is to build a function of independent variables (also known as predictors, regressors, explanatory variables, and features) to predict a dependent variable (also called a response, target, and regressand). Here we will focus on performing linear regression in R Language.

Linear regression is to predict response with a linear function of predictors as $$y=\beta_0+\beta_1x_1+\beta_2x_2+\cdots + \beta_kx_k,$$ where $x_1, x_2, \cdots, x_k$ are predictors and $y$ is the response to predict.

Before performing the regression analysis it will be very helpful to computer the coefficient of correlation between dependent variable and independent variable and also better to draw the scatter diagram.

Performing Linear Regression in R

Load the mtcars data, and check the data structure using str().

str(mtcars)

You have data stored in some external file such as CSV, then you can use read.csv() function to load the data in R. To learn about importing data files in R follow the link: Import Data files in R

Let us want to check the impact of weight (wt) on miles per gallon (mpg) and test the significance of the regression coefficient and other statistics to see the goodness of our fitted model 

mod <- lm(mpg ~ wt, data = mtcars)
summary(mod)
Performing Linear Regression in R Estimation and Testing

Now look at the objects of results stored in mod

names(mod)

Getting Coefficients and Different Regression Statistics

Let us get the coefficients of the fitted regression model in R

mod$coef
coef(mod)

To obtain the confidence intervals of the estimated coefficients, one can use the confint() 

confint(mod)

Fitted values from the regression model can be obtained by using fitted()

mod$fitted
fitted(mod)

The residuals can be obtained for the regression model using residual() function

mod$resid
resid(mod)

One can check the formula used to perform the simple/ multiple regression. It will tell you which variable is used as a response and others as explanatory variables.

formula (mod)

Graphical Representation of Relationship

To graphically visualize the relationship between variables or pairs of variables one can use plot() or pair() functions. Let us draw the scatter diagram between the dependent variable mpg and the explanatory variable wt using the plot() function.

plot(mpg ~ wt, data = mtcars)
Scatter Plot and Performing Linear Regression in R

One can add a best-fitted line to the scatter plot. For this purpose use abline() with an object having the class lm such as mod in this case

abline(mod)

There are many other functions and R packages to perform linear regression models in the R Language.

FAQS about Performing Linear Regression Models in R

  1. What is the use of abline() function in R?
  2. How a simple linear regression model can be visualized in R?
  3. How one can obtain fitted/predicted values of the simple linear regression model in R?
  4. Write a command that saves the residuals of lm() model in a variable.
  5. State the step-by-step procedure of performing linear regression in R.

To learn more about the lm() function in R

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Some Descriptive Statistics in R: A Comprehensive R Tutorial

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Descriptive Statistics in R

There are numerous functions in the R language that are used to computer descriptive statistics. Here, we will consider the data mtcars to get descriptive statistics in R. You can use a dataset of your own choice. To learn about what are descriptive statistics, read the different posts from the Basic Statistics Section.

Getting Dataset Information in R

Before performing any descriptive or inferential statistics, it is better to get some basic information about the data. It will help to understand the mode (type) of variables in the datasets.

# attach the mtcars datasets
attach(mtcars)

# data structure
str(mtcars)

You will see the dataset mtcars contains 32 observations and 11 variables.

It is also best to inspect the first and last rows of the dataset.

# for the first six rows
head(mtcars)

# for the last six rows
tail(mtcars)

Getting Numerical Descriptive Statistics in R

To get a quick overview of the dataset, the summary( ) function can also be used. We can use the summary( ) function separately for each of the variables in the dataset.

summary(mtcars)
summary(mpg)
summary(gear)
Some Descriptive Statistics in R

Note that the summary( ) the function provides five-number summary statistics (minimum, first quartile, median, third quartile, and maximum) and an average value of the variable used as the argument. Note the difference between the output of the following code.

summary(cyl)
summary( factor(cyl) )

Remember that if for a certain variable, the datatype is defined or changed R will automatically choose an appropriate descriptive statistics in R. If categorical variables are defined as a factor, the summary( ) function will result in a frequency table.

Some other functions can be used instead of summary() function.

# average value
mean(mpg)
# median value
median(mpg)
# minimum value
min(mpg)
# maximum value
max(mpg)
# Quatiles, percentiles, deciles
quantile(mpg)
quantile(mpg, probs=c(10, 20, 30, 70, 90))
# variance and standard deviation
var(mpg)
sd(mpg)
# Inter-quartile range
IQR(mpg)
# Range
range(mpg)

Creating a Frequency Table in R

We can produce a frequency table and a relative frequency table for any categorical variable.

freq <- table(cyl); freq
rf <- prop.table(freq)

barplot(freq)
barplot(rf)
pie(freq)
pie(rf)
Barplot and Pie chart Some Descriptive Statistics in R

Creating a Contingency Table (Cross-Tabulation)

The contingency table can be used to summarize the relationship between two categorical variables. The xtab( ) or table( ) functions can be used to produce cross-tabulation (contingency table).

xtabs(~cyl + gear, data = mtcars)
table(cyl, gear)

Finding a Correlation between Variables

The cor( ) function can be used to find the degree of relationship between variables using Pearson’s method.

cor(mpg, wt)

However, if variables are heavily skewed, the non-parametric method Spearman’s correlation can be used.

cor(mpg, wt, method = "spearman")

The scatter plot can be drawn using plot( ) a function.

plot(mpg ~ wt)

FAQs about Descriptive Statistics in R

  1. How to check the data types of different variables/columns in R?
  2. What is the use of str() function in R?
  3. What is the use of head() and tail() functions in R?
  4. How numerical statistics of a variable or data set can be obtained in R?
  5. What is the use of summary() function in R?
  6. How summary() function can be used to perform descriptive statistics of a categorical variable in R?
  7. How to produce a frequency table in R?
  8. What is the use of xtab() function in R?
  9. What is the use cor(), plot(), and pie() functions, explain with the help of examples.
  10. What functions are used to compute, mean, median, standard deviation, variance, Quantiles, and IQR.

Learn more about plot( ) function: plot( ) function

Visit: Learn Basic Statistics