Model the Next Expected Value in R Based on Values for Previous 3 Years

In this article, we will explore a common problem in data analysis and modeling: predicting future values based on historical data. We will use an example from the Stack Overflow community to demonstrate how to model the next expected value in R using linear regression.

Introduction

Predicting future values is a fundamental task in many fields, including finance, economics, and healthcare. In this article, we will focus on modeling the next expected value of a continuous variable based on its historical values for the previous three years. We will use a simple yet effective approach: linear regression with interaction terms.

Background

Linear regression is a widely used statistical technique for predicting a continuous outcome variable based on one or more predictor variables. In this article, we will assume that our outcome variable is a continuous value (e.g., sales revenue) and that we have three years of data to work with.

The basic idea behind linear regression is that the relationship between the outcome variable and each predictor variable can be represented by a straight line. By fitting this line to our historical data, we can estimate the expected value of the outcome variable for any given combination of predictor variables.

However, in many cases, the relationship between the outcome variable and one or more predictor variables is not linear. In these situations, we need to use more complex models that can capture non-linear relationships.

Preparing the Data

To begin with, our data needs to be in a tidy format, meaning that each observation has only two columns: one for the predictor variable(s) and one for the outcome variable.

The code snippet below shows how to convert our data from wide format (with separate columns for each year) to long format:

library(tidyverse)

# Convert data to long format
df_long <- df %>% 
  pivot_longer(-Area, names_to = 'Year') %>% 
  mutate(Year = as.numeric(Year))

This code uses the pivot_longer() function from the tidyverse package to convert our data from wide format to long format. The -Area argument specifies that we do not want to include the Area column in the pivot operation, and the names_to = 'Year' argument specifies that we want to rename the Year column to simply Year.

Fitting the Linear Model

Once our data is in long format, we can fit a linear model using the lm() function:

# Fit linear model with interaction terms
model <- lm(value ~ Area * Year, data = df_long)

In this code snippet, we use the lm() function to fit a linear model to our data. The value ~ Area * Year argument specifies that we want to predict the value variable based on both Area and Year. The data = df_long argument specifies that we want to use our data from long format.

Predicting Future Values

To predict future values, we need to create a new data frame with the desired predictor variables for each area in the next two years:

# Create new data frame with predicted values
newdata <- data.frame(Area = rep(c('AreaA', 'AreaB'), 2), 
                      Year = rep(2023:2024, each = 2))

newdata$value <- predict(model, newdata = newdata)

In this code snippet, we use the predict() function to generate predicted values for our data. The model argument specifies that we want to use our fitted model, and the newdata = newdata argument specifies that we want to use the new data frame with the desired predictor variables.

Displaying the Results

Finally, we can display the results in a wide format:

# Convert back to wide format
pivot_wider(bind_rows(df_long, newdata), names_from = Year, values_from = value)

In this code snippet, we use the pivot_wider() function from the tidyverse package to convert our data back to wide format. The bind_rows() argument specifies that we want to combine our original data with the predicted values in a new data frame, and the names_from = Year and values_from = value arguments specify that we want to include only the Year and value columns in the resulting data frame.

Conclusion

In this article, we demonstrated how to model the next expected value of a continuous variable based on its historical values for the previous three years using linear regression. We discussed the importance of preparing our data in a tidy format, fitting a suitable model, and displaying the results in a wide format.

We also touched on some common limitations and extensions of this approach, such as when to use non-linear models and how to handle additional predictor variables.

References

Crawley, M. J. (2005). The R book. University of Leicester.
Venables, W. S., & Chatfield, C. (2013). An introduction to the R programming language (2nd ed.). Springer.

Last modified on 2025-01-02