Formulating Time Period Dummy Variables in Linear Regression Using R

Formulating Time Period Dummy Variable in Linear Regression

Introduction

Linear regression is a widely used statistical technique to model the relationship between a dependent variable and one or more independent variables. One of the challenges in linear regression is handling time period dummy variables, which are used to control for the effects of different time periods on the response variable.

In this article, we will explore how to formulate time period dummy variables in linear regression using R. We will discuss the different approaches to creating time period dummy variables and provide examples and code snippets to illustrate the concepts.

Time Period Dummy Variables

A time period dummy variable is a binary variable that takes on the value 1 for a specific time period and 0 otherwise. The purpose of these variables is to control for the effects of different time periods on the response variable.

For example, suppose we want to analyze the effect of temperature on sales. We can create two time period dummy variables: warm and cold. The warm variable takes on the value 1 if the temperature is above a certain threshold (e.g., 65°F) and 0 otherwise. The cold variable takes on the value 1 if the temperature is below the same threshold and 0 otherwise.

Approaches to Creating Time Period Dummy Variables

There are two main approaches to creating time period dummy variables:

Approach 1: One-Hot Encoding

One-hot encoding involves creating a new variable for each possible category in the independent variable. In this case, we can create three new variables: warm, cold, and other. The warm variable takes on the value 1 if the temperature is above 65°F and 0 otherwise. Similarly, the cold variable takes on the value 1 if the temperature is below 65°F and 0 otherwise.

One-hot encoding can be used to create time period dummy variables using R’s cut() function, as shown in the example code snippet:

# Create a vector of observation numbers
observationNumber <- 1:80

# Create a categorical variable for the temperature (one-hot encoded)
obsFactor <- cut(observationNumber, breaks = c(0, 55, 81), right = FALSE)

# Fit the linear regression model with one-hot encoding
fit <- lm(y ~ x * obsFactor)

In this example, obsFactor is a vector of length 80 that takes on the value 1 for temperatures above 65°F and 0 otherwise.

Approach 2: Dummy Variable with Coefficients

The second approach involves creating a dummy variable with coefficients. In this case, we can create a single dummy variable D_t that takes on the value 1 if the time period is above a certain threshold (e.g., 55) and 0 otherwise.

This approach can be used to create time period dummy variables using R’s lm() function, as shown in the example code snippet:

# Create a vector of observation numbers
observationNumber <- 1:80

# Create a categorical variable for the observation number (dummy variable)
obsFactor <- cut(observationNumber, breaks = c(0, 55, 81), right = FALSE)

# Fit the linear regression model with dummy variables
fit <- lm(y ~ x * obsFactor)

In this example, obsFactor is a vector of length 80 that takes on the value 1 for observations above 55 and 0 otherwise.

Interpreting Coefficients

Once we have created time period dummy variables using one of these approaches, we can interpret their coefficients in the linear regression model.

The coefficient for the D_t variable represents the change in the response variable for a one-unit increase in the time period, while holding all other independent variables constant. The coefficient for the product term x:obsFactor represents the change in the response variable for a one-unit increase in the independent variable x, while holding the time period dummy variable constant.

For example, if we have a linear regression model with coefficients:

Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.50959    0.04253 11.983   < 2e-16 ***
x         -0.02492    0.04194 -0.594    0.554    
obsFactor[55,81) -0.06357    0.09593 -0.663    0.510    
x:obsFactor[55,81)  0.07120    0.07371   0.966    0.337

We can interpret the coefficients as follows:

The coefficient for (Intercept) represents the expected value of the response variable when all other independent variables are held constant.
The coefficient for x represents the change in the response variable for a one-unit increase in the independent variable x, while holding the time period dummy variable constant.
The coefficient for obsFactor[55,81)} represents the change in the response variable for a one-unit increase in the time period, while holding all other independent variables constant.
The coefficient for x:obsFactor[55,81) represents the interaction between the independent variable x and the time period dummy variable.

Conclusion

In this article, we explored two approaches to creating time period dummy variables in linear regression using R. We discussed one-hot encoding and dummy variables with coefficients, and provided examples and code snippets to illustrate these concepts. By understanding how to create and interpret time period dummy variables, you can gain insights into the effects of different time periods on your response variable.

References

cut() function: https://www.rdocumentation.org/packages/stats/versions/4.0.2/topics/cut
lm() function: https://www.rdocumentation.org/packages/base/versions/3.6.1/functions/lm

Last modified on 2025-04-11