Final answer:
The quantitative method missing from the student's list is the least squares regression method, which complements the high-low and scatter plot methods to separate mixed costs into fixed and variable components, providing critical insights for business cost analysis.
Step-by-step explanation:
The three quantitative methods of separating a mixed cost into its fixed and variable components are the high-low method, the scatter plot method, and the least squares regression method. Firms must understand the breakdown of total costs into fixed costs and variable costs as these measures offer unique insights that can aid in cost analysis and business strategy. The high-low method uses the highest and lowest activity levels to estimate variable and fixed costs, while the scatter plot method graphically represents the relationship between cost and activity level to visually assess the behavior of costs. The least squares regression method provides a more statistically accurate way to determine the fixed and variable cost components by fitting a line that minimizes the sum of the squared differences between the estimated costs and the actual costs.