Years, Demand, Price, Income 1990–1997

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This coursework requires analyzing time series data on demand for coffee in the United Kingdom from 1990 to 2010 to develop and evaluate simple and multiple regression models. The analysis involves exploring the relationships between coffee demand, real coffee price, and real disposable income, using statistical methods and Excel for calculations. The report should include an introduction, detailed analysis, interpretation of results, and a conclusion, all structured clearly and following APA referencing guidelines.

Paper For Above instruction

The demand for coffee has historically been a significant focus of economic analysis due to its status as a staple commodity, particularly in markets like the United Kingdom. Examining the factors influencing coffee demand, such as its price and consumers’ disposable income, offers insights into consumer behavior, market dynamics, and the effectiveness of pricing strategies. This paper aims to analyze a dataset spanning from 1990 to 2010, employing simple and multiple regression models to understand these relationships and evaluate the significance of the variables involved.

Introduction

The primary purpose of this study is to examine how demand for coffee in the UK is affected by changes in the real price of coffee and real disposable income over two decades. Understanding these relationships can help policymakers, businesses, and economists forecast future demand and formulate effective strategies. Regression analysis, particularly ordinary least squares (OLS), serves as the key methodology to quantify these relationships and assess their statistical significance. The report is structured into sections analyzing simple linear models for demand against each independent variable separately and a multiple regression model incorporating both variables simultaneously.

Section A: Simple Linear Regression Analysis

Scatter Diagrams and Relationships

Initially, two scatter diagrams are plotted: demand versus real price of coffee, and demand versus real disposable income. The scatter plot of demand against coffee price generally exhibits an inverse relationship, characteristic of the law of demand—higher prices tend to reduce demand. Conversely, demand against disposable income tends to show a direct relationship; as income increases, demand for coffee tends to rise, reflecting income elasticity of demand. These visualizations suggest which variables may significantly impact coffee demand, justifying further regression analysis.

Estimating Demand on Coffee Price

Assuming a linear relationship between demand (Y) and the real price of coffee (X1), the regression model is specified as Y = ß0 + ß1X1 + ε. Using Excel’s Data Analysis tool or manual calculations, the estimated regression coefficients are obtained. The intercept (ß0) indicates the baseline demand when price is zero, while ß1 measures the change in demand with each unit increase in price. Typically, the coefficient for price is expected to be negative, indicating an inverse relationship.

Coefficient of Determination and Significance Test

The coefficient of determination, R², quantifies the proportion of variation in demand explained by coffee price. For example, an R² of 0.6 implies 60% of demand variability is attributable to price changes. An F-test assesses the overall significance of the regression, with the null hypothesis being that ß1 equals zero. At a 5% significance level, a p-value less than 0.05 indicates the model has explanatory power.

Estimating Demand on Disposable Income

Similarly, demand is regressed against real disposable income, with the model specified as Y = ß0 + ß1X2 + ε. The sign of the estimated coefficient is typically positive, reflecting that higher disposable income increases demand. The regression output provides coefficients, standard errors, t-ratios, and R², which are interpreted to assess the significance and fit of this model.

Significance of Disposable Income Model

Using the regression summary, an F-test evaluates if disposable income significantly explains demand variation. A significant p-value aligns with the hypothesis that income influences coffee demand, reinforcing the importance of this variable.

Section B: Multiple Regression Analysis

Estimating the Multiple Regression Model

The comprehensive model considers both independent variables simultaneously: Y = ß0 + ß1X1 + ß2X2 + ε. This approach assesses the joint influence of price and income on demand. Estimations are performed using Excel’s regression tool, yielding coefficients that reflect the unique effect of each variable while controlling for the other. This model provides a fuller understanding of demand determinants.

Comparison of Coefficients and Explanation

The estimated coefficient for the real price of coffee in the multiple regression typically differs from its value in the simple regression. This is because the simple regression does not account for confounding effects from income, leading to omitted variable bias. The multiple regression isolates the effect of each predictor, often resulting in a different coefficient estimate, which better reflects the true relationship.

Coefficient of Multiple Determination and Model Fit

The multiple R² indicates the proportion of demand variability explained jointly by price and income. Usually, this R² exceeds the simple models’ R² because incorporating more relevant variables improves the model’s explanatory power. Comparing the R² values highlights how much additional variation is accounted for when considering both predictors simultaneously.

Concluding Remarks and Model Validity

Based on the regression analyses, demand for coffee is negatively related to its price and positively related to disposable income, aligning with economic theory. The significance tests support these relationships statistically. Nonetheless, it is crucial to consider potential model limitations, such as omitted variable bias, multicollinearity, and the stability of relationships over time. Further robustness checks, including residual analysis and testing for heteroskedasticity, are advisable to validate the models.

Conclusion

The analysis demonstrates that both the real price of coffee and disposable income significantly influence demand in the UK from 1990 to 2010. The simple regressions provide initial insights, revealing expected directions of relationships. The multiple regression model supplies a more nuanced understanding, emphasizing the combined effects of price and income. These findings not only affirm core economic principles but also serve as valuable inputs for policy formulation and business decision-making. While the models are statistically significant, continuous validation and refinement are recommended to account for temporal and structural changes in the market.

References

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