The slope coefficient is calculated by dividing the change in cost by the change in the cost driver. Here, $9,000 divided by 15,000 machine hours equals 0.6. This result indicates that for every machine hour added, the total cost increases by $0.60. This is a standard calculation used in high-low method cost estimation to determine the variable cost component.

The high-low method is a widely used analytical technique in cost accounting to separate mixed costs into their fixed and variable components. By focusing on the extreme data points—the highest and lowest activity levels—within a relevant range, accountants can calculate the variable cost per unit and subsequently determine the total fixed cost, assuming a linear cost behavior.

The third step in the quantitative estimation of a cost function involves gathering data for the dependent variable (the total cost) and the independent variable (the cost driver). This data is necessary to perform regression analysis or other statistical methods to determine the relationship between the cost and the activity level, allowing for the development of a reliable cost estimation model.

Cost estimation is a critical accounting technique used to predict future expenditures based on historical data, activity levels, and cost drivers. By applying various methods such as high-low analysis or regression, businesses can project future costs accurately, which is vital for budgeting, planning, and strategic decision-making within the organization.

The disturbance or residual term is calculated by subtracting the predicted value from the actual observed value. In this case, the calculation is 62 - 29 = 33. This value represents the portion of the actual cost that the regression model failed to explain, indicating the deviation of the observation from the regression line.

The quantitative analysis method, often involving techniques like simple or multiple regression analysis, uses historical data to mathematically estimate cost behavior. By minimizing the sum of squared errors, it provides a statistically sound and objective way to define the relationship between costs and activity levels, which is more rigorous than subjective estimation methods.

Goodness of fit is a statistical measure that describes how well a regression model captures the relationship between the independent variable (cost driver) and the dependent variable (cost). A high goodness of fit indicates that the cost driver is a strong predictor of the cost, meaning the model effectively explains the variation in the data.

The slope coefficient in a cost function represents the variable cost per unit of activity. It is calculated by dividing the change in total cost by the change in the activity level (in this case, machine hours). Using the provided figures: $7,000 / $18,000 = 0.3888... which rounds to 0.39. This value indicates the variable cost incurred for every additional machine hour utilized in the production process.

Economic plausibility requires that the relationship between a cost and its driver makes logical sense. A significant goodness of fit, typically measured by statistical tests like the p-value or R-squared, confirms that the observed correlation is not due to random chance. When the fit is significant, it provides empirical evidence that the chosen cost driver is a reliable predictor of the cost, supporting the validity of the cost function.

These are standard techniques used by management accountants to determine the relationship between costs and their drivers. The conference method relies on expert opinion, account analysis involves classifying accounts as fixed or variable based on experience, and quantitative analysis uses statistical tools like regression. Together, these methods allow organizations to estimate future costs, which is vital for budgeting, pricing strategies, and evaluating operational performance across different departments.