Case 3: High-Low Method And Regression Analysis

Case3: High-low method and regression analysis. Mars Co A Cooperativ

Analyze the relationship between weekly order volume and total costs for Mars Co., a cooperative of local farms. Using the first 12 weeks of data, plot the relationship, estimate cost equations through high-low and regression methods, determine whether the cooperative broke even, and predict the number of orders needed for next season. Additionally, evaluate the regression line's plausibility, goodness of fit, and statistical significance, and compare the two estimation methods.

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The agricultural sector faces unique challenges in cost analysis due to the variability in production and demand. For cooperatives like Mars Co., which supplies fresh produce through a seasonal club, understanding cost behavior is vital for financial planning and sustainability. The first step involves analyzing the relationship between the number of weekly orders and total weekly costs, which can be achieved through data visualization. Plotting weekly total costs against the number of orders helps identify whether costs behave in a linear fashion—a prerequisite for applying simple cost estimation techniques such as the high-low method and regression analysis.

Using the data provided over 12 weeks, the initial task is to plot this relationship. The weekly total costs and the number of orders serve as the variables of interest. A scatter plot typically reveals the nature of the relationship; a linear pattern suggests that costs increase proportionally with orders, up to a point. For a more precise analysis, the high-low method provides a straightforward means to estimate fixed and variable costs. This method involves identifying the weeks with the highest and lowest order volumes, then calculating the slope (variable cost per order) and intercept (fixed costs).

To implement the high-low method, suppose that the week with the highest orders was Week X with Y total costs, and the week with the lowest orders was Week Z with W total costs. The variable cost per order is estimated as:

Variable Cost (VC) = (Cost at high activity - Cost at low activity) / (High orders - Low orders)

Once VC is known, fixed costs (FC) are determined by plugging these values into the cost equation derived from either the high or low point:

Cost = FC + VC * Number of Orders

The regression analysis refines this estimate by fitting a line that minimizes the sum of squared differences between observed and predicted costs. Using statistical software, we can determine the regression equation of the form:

Weekly total costs = A + ($B × Number of orders)

where A represents the fixed costs and B indicates the variable cost per order, estimated through least squares regression.

To evaluate whether Mars Co. broke even during the season, we consider both the fixed membership fee and variable costs. Revenue per family from membership fees is $100, and the price per order is $40. The total revenue is then calculated as:

Total Revenue = Number of Families × ($100 membership fee + $40 per order)

For 500 families, this is:

Revenue = 500 × ($100 + $40 × Average Orders per Family)

Assuming an average number of orders (which needs to be estimated), the break-even point is where total revenue equals total costs. The total costs include fixed and variable components, estimated via the regression or high-low method.

By using the estimated cost function, the number of orders required to break even can be calculated. Next season, with 500 families, costs are expected to be similar, assuming no changes in prices or costs. The break-even number of orders per week is obtained by setting the total revenue equal to total costs and solving for the number of orders. Specifically, the required weekly orders to break even satisfy:

Revenue = Total costs

or:

500 × ($100 + $40 × Orders) = Estimated Total Costs

which simplifies to a formula that calculates the minimum number of weekly orders to cover all costs and generate no profit or loss.

Finally, the regression line's effectiveness and appropriateness are assessed through criteria such as economic plausibility—i.e., whether the estimated costs make sense in the real-world context—goodness of fit measures like R-squared, and the statistical significance of the independent variable (orders). Comparing the high-low estimate with the regression line reveals whether the simpler high-low method provides a sufficiently accurate approximation or if the regression method offers a more precise understanding of cost behavior.

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