Final answer:
To determine variable costs graphically, plot size against cost in a scatter plot, calculate the least-squares line's equation (ŷ = a + bx), where 'b' represents variable costs, and analyze the plot's slope. A correlation coefficient helps confirm the relationship's significance.
Step-by-step explanation:
Finding Variable Costs Using Graphical Method
To find variable costs (also known as b in the cost function equation) using the graphical method, you'll start by plotting a scatter plot with size (quantity produced or sold) as the independent variable on the x-axis and cost as the dependent variable on the y-axis. Then, inspect the plot to determine if there's a visible relationship between the variables; a clear upward trend suggests variable costs increase with output. To quantify this, calculate the least-squares line, which is the line of best fit that minimizes the sum of squared differences between observed and predicted values. The equation of this line is expressed in the form ŷ = a + bx, where 'a' represents fixed costs, and 'b' is the variable cost per unit of output.
Once you have the least-squares line, you can find the variable cost coefficient by looking at the slope of the line (b). This slope will show how much the cost increases for each additional unit produced, which is the variable cost per unit. If you've collected data on your company's output, total cost, marginal cost, average cost, variable cost, and average variable cost, you can create a table to assist in your graphical analysis. Determine the correlation coefficient to check the strength and significance of the relationship between size and cost. If the correlation coefficient is high and significant, the model is a good predictor of costs, and 'b' is a reliable measure of variable costs.
Note: When graphing, remember that lines for marginal, average, and average variable cost might appear almost flat compared to total, fixed, and variable costs due to the scale difference, making it difficult to accurately assess their values in the context of variable costs determination graphically.