Regression Analysis: Let X Be The Cups Of Coffee Sold And Y

regression Analysislet X Be The Cups Of Coffee Soldand Y Be The Uti

Let X be the number of cups of coffee sold and Y be the utility expenses. The data for each month from January to December has been analyzed to establish a regression relationship between these variables. The regression line is given by the equation Y = a + bX, where a is the fixed cost and b is the variable cost per cup. Based on the calculations provided, b = 0.04, and a = 62.61. This implies that the variable cost per cup of coffee is approximately $0.04. The fixed cost is estimated at $62.61 by regression analysis.

Additionally, the high-low method was employed to estimate the variable and fixed costs. The high-low method identified a variable cost per cup of approximately $0.04, consistent with the regression method. The fixed cost calculated via the high-low method was approximately $45. The regression method is generally considered more reliable than the high-low method because it utilizes all data points rather than just the extreme values, providing a more comprehensive analysis of costs associated with coffee sales and utility expenses.

This analysis underscores that while the variable cost per cup remains consistent between methods, the fixed cost estimates differ, primarily because the high-low method relies only on the highest and lowest data points. The regression approach's advantage over the high-low method emphasizes its suitability for costs analysis, especially when detailed and accurate estimates are required in managerial decision-making within microeconomics contexts (McEachern, 2020).

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The regression analysis conducted to evaluate the relationship between coffee sales and utility expenses highlights the importance of choosing appropriate methods for cost estimation. The regression line Y = 62.61 + 0.04X suggests that for each additional cup of coffee sold, utility expenses increase by approximately $0.04, with a fixed utility cost of about $62.61. This estimation accounts for all data points, providing a comprehensive understanding of cost behavior, beneficial for managerial and economic decision-making.

In contrast, the high-low method simplifies cost estimation by only considering the months with the highest and lowest sales figures. It estimates the variable cost per cup as $0.04 and fixed costs at approximately $45. However, this approach can lead to inaccurate cost estimations because it ignores the variability across all months. Particularly, fixed costs derived from the high-low method tend to be less precise as they depend solely on two extreme data points, possibly exaggerating or underestimating the actual fixed costs.

The use of regression analysis over the high-low method aligns with best practices in managerial accounting and microeconomics analysis, emphasizing the importance of leveraging all available data to produce more reliable and valid cost estimates. Regression analysis captures the nuanced relationship between sales and expenses, accommodating fluctuations and patterns that simple methods might overlook (McEachern, 2020).

Furthermore, understanding the nuances of cost behaviors is critical for effective decision-making. For example, fixed costs, such as rent or salaries, remain constant regardless of sales volume, whereas variable costs, like utility expenses per unit, change proportionally with output. Accurate estimation of these costs enables managers to optimize pricing, production, and sales strategies, ultimately enhancing profitability and efficiency in microeconomic operations.

Regression analysis also provides statistical measures, such as the coefficient of determination, which indicates how well the model explains the variability in utility expenses based on coffee sales. This insight is valuable for predicting future costs and planning accordingly. In addition, it can inform broader economic policies or business strategies tailored to the specific cost structures of firms dealing in consumer goods like coffee.

In conclusion, the comparison between regression and high-low methods underscores the importance of comprehensive data analysis in microeconomic cost management. The regression method's reliance on all data points makes it superior for accurate cost estimation, which is essential for informed decision-making, effective resource allocation, and strategic planning in microeconomics contexts (McEachern, 2020).

References

• McEachern, W. A. (2020). ECON MACRO 3. Cengage Learning.
• McEachern, W. A. (2020). ECON MICRO 3. Cengage Learning.