Project – Comparative Analysis of Multiple Linear Regression and Decision Tree Models in Predicting Households’ Expenditure Patterns in Nigeria 2003-2023

CHAPTER ONE

GENERAL INTRODUCTION

Research Topic: Comparative Analysis of Multiple Linear Regression and Decision Tree Models in Predicting Households’ Expenditure Patterns in Nigeria (2003–2023)

1.1 Background to the Study

Household expenditure is an important indicator of economic welfare, living standards, consumption behaviour, and the general economic conditions of a population. It refers to the amount of money households spend on goods and services to meet their daily needs, including food, housing, clothing, transportation, healthcare, education, communication, and other essential and non-essential items. The pattern of household expenditure provides information about how families allocate their financial resources among competing needs and how their consumption decisions respond to changes in income, prices, household size, and socioeconomic circumstances. According to Deaton and Muellbauer (1980), household consumption decisions can be understood through economic models that explain how consumers allocate limited resources among different goods and services. Similarly, the World Bank’s Living Standards Measurement Study programme emphasises the importance of household consumption and expenditure data in assessing living standards, poverty, and welfare in developing economies. In Nigeria, where households experience considerable differences in income, employment, family size, location, and access to essential services, understanding expenditure patterns is important for evaluating household welfare and supporting evidence-based economic planning. Consequently, the application of statistical models to predict household expenditure can provide useful insights into the factors associated with consumption behaviour and the allocation of household resources (Deaton & Zaidi, 2002; World Bank, n.d.).

Household expenditure patterns are influenced by several demographic, economic, and social characteristics that may interact in complex ways. Household income, the number of household members, the age and educational composition of the family, employment status, geographical location, and access to public services can all influence expenditure decisions. For example, a household with many dependants may allocate a greater proportion of its resources to food, education, healthcare, and transportation, while a household with higher disposable income may have greater capacity to spend on housing improvements, communication, recreation, and other discretionary goods. Deaton and Muellbauer (1980) demonstrated that consumer demand depends on prices, income, and preferences, while Deaton and Zaidi (2002) explained the importance of carefully measuring household consumption when assessing living standards and poverty. These relationships indicate that household expenditure is not determined by a single factor but rather by several variables that may have linear, nonlinear, or interacting effects. Therefore, statistical prediction models are useful for examining the contribution of different household characteristics and for estimating expenditure levels from observed demographic and socioeconomic information.

In Nigeria, household expenditure analysis is particularly relevant because economic conditions and access to resources differ across geographical areas and population groups. Households in urban centres may face relatively high expenditure on rent, transportation, utilities, and other services, while rural households may allocate a larger share of their resources to food production, agricultural inputs, and other location-specific needs. However, these differences cannot be assumed to apply uniformly to every household because consumption decisions are also influenced by income, household composition, employment, prices, and access to markets. The National Bureau of Statistics (NBS, 2006), in its report on consumption patterns in Nigeria, documented the collection of household information covering consumption expenditure, demographic characteristics, employment, housing, and other socioeconomic conditions. The Nigeria Living Standards Survey 2003–2004 also collected detailed household expenditure information, including a dataset containing annual household expenditure and associated household characteristics (NBS, 2003–2004). These official statistical resources demonstrate the importance of household-level data for examining consumption behaviour in Nigeria. Analysing such information through appropriate predictive models may help explain expenditure differences and improve the understanding of household economic welfare.

Multiple linear regression is one of the established statistical methods used to examine the relationship between a continuous outcome variable and two or more explanatory variables. In household expenditure analysis, the method can estimate the association between total household expenditure and factors such as household income, household size, education, employment, and location, while controlling for other included variables. The model expresses expenditure as a linear combination of explanatory variables and an error term, with coefficients indicating the estimated relationship between each predictor and expenditure under the model’s assumptions. Montgomery, Peck, and Vining (2021) explain that multiple regression is widely used for modelling relationships between a continuous response and several explanatory variables, including estimation, prediction, and the assessment of individual predictors. James, Witten, Hastie, and Tibshirani (2021) also describe linear regression as a foundational predictive method that can provide interpretable estimates of relationships between variables. In the Nigerian context, multiple linear regression may therefore provide a useful baseline for predicting household expenditure from available demographic and economic characteristics. However, its predictive performance may be affected when relationships are nonlinear, when explanatory variables interact, or when model assumptions are not adequately satisfied.

Decision tree models provide an alternative approach to predicting household expenditure by dividing observations into groups based on the values of explanatory variables. Rather than requiring one overall linear relationship between predictors and expenditure, a regression tree repeatedly splits the dataset into smaller, more homogeneous groups and predicts the outcome using the observations within each terminal group. For example, a tree may identify different expenditure patterns among households according to income level, household size, employment status, or urban and rural residence. Breiman, Friedman, Olshen, and Stone (1984) established the Classification and Regression Trees (CART) framework, which provides a systematic approach to constructing trees for classification and continuous-outcome prediction. James et al. (2021) similarly explain that tree-based methods can capture nonlinear relationships and interactions between explanatory variables without requiring them to be specified in advance in the same way as conventional linear models. This flexibility makes decision trees relevant to household expenditure prediction, where the effect of income or household size may vary across different groups. Nevertheless, tree models can be sensitive to changes in training data and may overfit if their complexity is not controlled, making proper validation essential when comparing their predictive performance with multiple linear regression.

The comparison of multiple linear regression and decision tree models is important because a model that explains relationships clearly does not necessarily provide the most accurate predictions for new observations. Multiple linear regression is generally valued for its interpretability and ability to estimate the separate associations between explanatory variables and household expenditure. Decision trees, on the other hand, can represent nonlinear patterns and interactions through a sequence of decision rules, potentially improving predictions when the underlying relationships are complex. However, the relative performance of these models depends on the characteristics of the data, the variables included, the quality of the observations, and the methods used to assess predictive accuracy. James et al. (2021) explain that predictive models should be evaluated using suitable validation procedures rather than selected solely on their performance on the training data. Kuhn and Johnson (2013) also emphasise the importance of resampling, model tuning, and performance evaluation when developing predictive models. A comparative analysis of the two methods can therefore establish whether the additional flexibility of a decision tree produces better household expenditure predictions than a conventional linear model, or whether the simpler regression model performs equally well or better.

The period from 2003 to 2023 is significant for examining Nigerian household expenditure because it covers substantial changes in economic conditions, prices, consumption opportunities, and household welfare. During these two decades, Nigeria experienced changes in economic growth, employment conditions, food prices, transportation costs, exchange-rate movements, and access to consumer goods and services. The global financial crisis, the 2016 recession, the COVID-19 pandemic, and subsequent domestic economic adjustments affected household purchasing power and expenditure decisions in different ways. The National Bureau of Statistics (NBS, 2019) documented household living conditions and consumption-related information through the Nigeria Living Standards Survey 2018–2019, while the NBS and World Bank’s General Household Survey–Panel programme provided longitudinal information on household welfare and socioeconomic outcomes. These sources demonstrate the importance of examining household expenditure across different periods and economic circumstances. However, the period should not be treated as a single continuous dataset without checking comparability: household surveys conducted in different years may differ in sampling design, expenditure recall periods, price reference periods, and questionnaire structure. Accordingly, the study must identify the relevant datasets, establish which variables can be harmonised, and use comparable expenditure measures before fitting and comparing the predictive models.

The application of predictive modelling to household expenditure is also relevant to poverty assessment, social protection, public expenditure planning, and the design of economic interventions. Reliable predictions can help researchers and policymakers identify household characteristics associated with high expenditure needs, examine differences between population groups, and understand how consumption patterns vary with socioeconomic circumstances. Deaton and Zaidi (2002) emphasised that careful measurement of household consumption expenditure is central to welfare comparisons, while the World Bank’s Living Standards Measurement Study programme supports the collection and analysis of household data for evidence-based development research. In Nigeria, the NBS’s General Household Survey–Panel Wave 5, conducted in 2023–2024, continued the collection of household-level information on expenditure, income-generating activities, food consumption, assets, and socioeconomic conditions (NBS & World Bank, 2024). These data resources illustrate the continuing relevance of household expenditure analysis. Against this background, the present study will compare multiple linear regression and decision tree models for predicting household expenditure patterns in Nigeria over the period 2003–2023. By evaluating the two models using comparable data and appropriate predictive accuracy measures, the study seeks to identify which method provides more reliable predictions and to establish the practical strengths and limitations of each approach.

1.2 Statement of the Problem

Household expenditure is an important measure of living standards and economic welfare, yet predicting how much households spend and how they allocate their resources remains a challenging task in an economy characterised by differences in income, household size, employment, location, and access to essential services. In Nigeria, household expenditure patterns are particularly important because changes in food prices, housing costs, transportation expenses, healthcare needs, and educational costs may affect households differently depending on their socioeconomic circumstances. The National Bureau of Statistics (NBS, 2019) reported substantial differences in the composition of household consumption expenditure, with food accounting for 56.65% of total household expenditure nationally in 2019. This illustrates the importance of understanding how households distribute their financial resources among competing needs. However, describing expenditure patterns is different from accurately predicting household expenditure using available socioeconomic information. The central problem is therefore the need for a reliable statistical approach that can predict household expenditure and capture the differences that exist among households in Nigeria.

A second problem concerns the limitations that may arise when a single predictive method is used to represent household expenditure behaviour. Multiple linear regression provides an interpretable framework for estimating the relationship between household expenditure and explanatory variables such as income, household size, education, employment, and location. However, the model may not adequately capture complex nonlinear relationships or interactions unless these are explicitly incorporated into its specification. Decision tree models offer an alternative by dividing households into groups according to relevant characteristics, allowing different expenditure patterns to emerge across different groups. Nevertheless, decision trees may be sensitive to the observations used to construct them and may overfit the training data if their complexity is not controlled. Montgomery et al. (2021) discuss the role of regression in statistical modelling, while Breiman et al. (1984) establish the principles of regression tree construction. The problem requiring investigation is which of these two approaches provides more accurate and reliable predictions of household expenditure when applied to Nigerian household data.

Another important problem relates to the availability, consistency, and comparability of household expenditure data covering the period 2003–2023. Nigeria’s household surveys have been conducted at different times and may differ in sampling design, questionnaire structure, expenditure reference periods, and the variables collected. The Nigeria Living Standards Survey 2003–2004 provides detailed household expenditure information, while the 2018–2019 Nigeria Living Standards Survey covers food and non-food expenditure, household characteristics, assets, employment, and other welfare indicators (NBS, 2003–2004; NBS, 2019). The existence of these datasets provides an opportunity for empirical analysis, but it does not automatically establish that observations from different survey rounds can be combined into one directly comparable dataset. Differences in survey methodology and the monetary value of expenditure across years must be addressed to avoid misleading predictions. The study must therefore establish a defensible data structure, identify comparable variables, and determine whether expenditure values require appropriate price adjustment before the two models are estimated and evaluated.

Furthermore, there is a need for empirical evidence on the relative predictive performance of multiple linear regression and decision tree models when applied to Nigerian household expenditure patterns. Although both approaches are established statistical and machine-learning methods, their comparative performance depends on the nature of the dataset, the selected explanatory variables, model complexity, and the validation procedure. James et al. (2021) emphasise the importance of assessing predictive models using observations not used to fit the models, while Kuhn and Johnson (2013) discuss the role of resampling and model evaluation in developing reliable predictive systems. Without a systematic comparison using the same data, comparable predictors, and consistent evaluation measures, it is difficult to determine which model offers better predictive performance for Nigerian households. Consequently, this study will compare multiple linear regression and decision tree models using appropriate validation procedures and predictive accuracy measures to establish their relative performance in predicting household expenditure patterns in Nigeria from 2003 to 2023.

1.3 Objectives of the Study

The main objective of this study is to comparatively analyse multiple linear regression and decision tree models in predicting households’ expenditure patterns in Nigeria from 2003 to 2023.

The specific objectives are to:

1. Examine the patterns and distribution of household expenditure in Nigeria during the period 2003–2023.

2. Develop a multiple linear regression model for predicting household expenditure using selected demographic and socioeconomic variables.

3. Develop a decision tree model for predicting household expenditure using the same or comparable explanatory variables.

4. Compare the predictive accuracy and performance of the multiple linear regression and decision tree models to identify the more suitable approach for the available Nigerian household expenditure data.

1.4 Research Questions

The study will be guided by the following research questions:

1. What are the patterns and distribution of household expenditure in Nigeria during the period 2003–2023?

2. How effectively can multiple linear regression predict household expenditure using selected demographic and socioeconomic variables?

3. How effectively can a decision tree model predict household expenditure using the same or comparable explanatory variables?

4. Is there a statistically significant difference in the predictive accuracy of multiple linear regression and decision tree models for Nigerian household expenditure data?

1.5 Research Hypothesis

The following null hypothesis will be tested at the 5% level of significance.

H₀: There is no statistically significant difference between the predictive accuracy of multiple linear regression and decision tree models in predicting household expenditure patterns in Nigeria.

The hypothesis will be tested using a suitable procedure based on the prediction errors generated by both models on the same validation observations. The choice of test will depend on the structure of the validation data and the assumptions of the selected procedure.

1.6 Significance of the Study

The findings of this study are expected to be useful to economic policymakers, government agencies, researchers, development institutions, statisticians, and other stakeholders interested in household welfare and predictive modelling.

Government and economic policymakers: The study may provide evidence on the usefulness of predictive models for estimating household expenditure and understanding differences in consumption needs. Such information may support the design of poverty-reduction programmes, social protection interventions, and household welfare policies. Deaton and Zaidi (2002) emphasised the importance of reliable household consumption measures for assessing living standards and comparing welfare across populations.

National Bureau of Statistics: The study may demonstrate the value of statistical modelling in analysing household expenditure data and identifying the variables associated with expenditure differences. Its findings may provide methodological insights for future household survey analysis, particularly in relation to predictive accuracy and the comparability of expenditure measures. The NBS (2019) highlighted the importance of household expenditure information for understanding consumption patterns and living conditions in Nigeria.

Researchers and statisticians: The study will contribute to the application of statistical and machine-learning methods in household economic research. By comparing multiple linear regression and decision tree models, it may help researchers understand the circumstances under which a conventional regression model or a tree-based approach performs better. James et al. (2021) provide a methodological foundation for comparing predictive approaches and evaluating their performance on data not used for model fitting.

Development organisations: Organisations concerned with poverty, food security, and social welfare may find the results useful when considering methods for estimating household expenditure from socioeconomic characteristics. The findings may help inform the selection of predictive approaches for future research and programme assessment, subject to the quality and representativeness of the underlying data.

Households and the general public: Although the study will not directly determine household income or reduce expenditure, its findings may improve understanding of the socioeconomic characteristics associated with household spending. This may contribute to wider discussions about household welfare, consumption needs, and the distribution of economic resources.

Students and future researchers: The study may serve as a reference for further research in statistics, economics, data science, econometrics, and machine learning. It may also provide a basis for extending the comparison to additional models, such as random forests, gradient boosting, or other predictive methods, in subsequent studies. Breiman (2001) provides an important foundation for understanding the development of ensemble tree methods beyond a single decision tree.

1.7 Scope of the Study

The study will focus on the comparative analysis of multiple linear regression and decision tree models in predicting household expenditure patterns in Nigeria from 2003 to 2023.

Geographical scope: The study will cover Nigeria, using suitable household expenditure datasets collected by recognised statistical institutions.

Temporal scope: The study will cover the period 2003–2023. The researcher will identify the survey rounds and observations available within this period and establish whether the data can be harmonised for comparative analysis.

Content scope: The dependent variable will be household expenditure, preferably measured as total household consumption expenditure or another clearly defined expenditure aggregate. The explanatory variables may include household size, household income, educational attainment, employment status, household composition, geographical location, and other socioeconomic characteristics available in the selected datasets.

Methodological scope: The study will employ multiple linear regression and a regression decision tree. Both models will be developed using the same target variable and comparable explanatory variables. Model performance will be assessed using appropriate predictive accuracy measures, including mean absolute error (MAE), root mean squared error (RMSE), and, where suitable, mean absolute percentage error (MAPE).

The comparison will use an appropriate training and validation procedure. Where several survey rounds are combined, the study will account for differences in survey design and expenditure measurement. Monetary expenditure values from different years will be adjusted for price changes where necessary and where defensible price indices are available.

1.8 Limitations of the Study

One possible limitation is the availability of comparable household expenditure data for every year between 2003 and 2023. Nigeria’s major household expenditure surveys were conducted in specific survey rounds rather than necessarily providing directly comparable annual household-level observations throughout the entire period. The Nigeria Living Standards Survey 2003–2004 and the 2018–2019 survey provide important household-level data, but the compatibility of their variables and measurement procedures must be verified before they are combined (NBS, 2003–2004; NBS, 2019).

Another limitation concerns differences in the measurement of household expenditure. Expenditure recorded in nominal monetary values in different years may not be directly comparable because of inflation and changes in the cost of living. Failure to adjust appropriately for price changes could lead the models to predict differences that partly reflect changes in the price level rather than changes in real consumption.

The study may also be affected by missing observations, measurement errors, and differences in household survey design. Multiple linear regression can be sensitive to influential observations and violations of its modelling assumptions, while decision trees may overfit the training sample if their depth and complexity are not controlled. Montgomery et al. (2021) and Breiman et al. (1984) provide the methodological foundations for understanding these respective modelling approaches.

Finally, the results may depend on the selected explanatory variables and the method used to evaluate predictive accuracy. A model that performs well on the training data may not necessarily perform well on new observations. James et al. (2021) therefore emphasise the importance of validation and the careful assessment of prediction errors. The study will interpret its findings in light of these limitations and avoid claiming that superior predictive performance automatically establishes causal relationships between household characteristics and expenditure.

1.9 Operational Definition of Terms

Household expenditure: The total amount spent by a household on goods and services during a specified reference period, measured according to the expenditure definition adopted in the selected dataset.

Expenditure patterns: The distribution and allocation of household spending across categories such as food, housing, transportation, education, healthcare, and other consumption needs.

Multiple linear regression: A statistical modelling technique used to estimate the relationship between a continuous dependent variable and two or more explanatory variables.

Decision tree model: A predictive method that divides observations into groups using successive rules based on explanatory variables. For continuous household expenditure, the study will use a regression tree.

Predictive accuracy: The degree to which a model’s predicted expenditure values correspond to actual observed expenditure values in validation data.

Dependent variable: The outcome variable being predicted. In this study, it is the selected measure of household expenditure.

Explanatory variables: The household characteristics used to predict expenditure, potentially including income, household size, employment status, educational attainment, and location.

Training data: The portion of the dataset used to estimate or fit a predictive model.

Validation data: Observations used to evaluate predictive performance on data not used to fit the model.

Mean Absolute Error (MAE): The average absolute difference between actual and predicted expenditure values.

Root Mean Squared Error (RMSE): The square root of the average squared prediction errors. It penalises larger errors more heavily than MAE.

Overfitting: A situation in which a model fits the training observations closely but performs poorly on new or unseen observations.

Household socioeconomic characteristics: Economic and social attributes of household members, including income, employment, education, household composition, and residential location.

Comparative predictive analysis: The systematic evaluation of two or more predictive models using consistent data, validation procedures, and performance measures.

Project – Comparative Analysis of Multiple Linear Regression and Decision Tree Models in Predicting Households’ Expenditure Patterns in Nigeria 2003-2023