An important application of regression analysis in accounting is in the estimation of cost. Bycollecting data on volume and cost and using the least squares meathod to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.Production Volume (units) Total Cost ($)400 4000450 5000550 5400600 5900700 6400750 7000A. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.B. What is the variable cost per unit produced?C. Compute the coefficient of determination. What percentage of the variation in total cost can be explaned by production volume?D. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this opperation?
Question
An important application of regression analysis in accounting is in the estimation of cost. Bycollecting data on volume and cost and using the least squares meathod to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.Production Volume (units) Total Cost ($)400 4000450 5000550 5400600 5900700 6400750 7000A. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.B. What is the variable cost per unit produced?C. Compute the coefficient of determination. What percentage of the variation in total cost can be explaned by production volume?D. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this opperation?
Solution
A. To develop an estimated regression equation, we first need to find the slope (b1) and the y-intercept (b0) of the regression line. The slope can be calculated using the formula:
b1 = Σ[(xi - x̄)(yi - ȳ)] / Σ[(xi - x̄)^2]
where xi and yi are the individual x and y data points, and x̄ and ȳ are the means of the x and y data points respectively.
The y-intercept can be calculated using the formula:
b0 = ȳ - b1*x̄
After calculating these values, the estimated regression equation will be:
y = b0 + b1*x
B. The variable cost per unit produced is represented by the slope of the regression line (b1).
C. The coefficient of determination (R^2) can be calculated using the formula:
R^2 = Σ[(ŷi - ȳ)^2] / Σ[(yi - ȳ)^2]
where ŷi is the predicted y value for each x data point. The R^2 value represents the proportion of the variance in the dependent variable (total cost) that is predictable from the independent variable (production volume).
D. To estimate the total cost for producing 500 units, we can substitute x = 500 into the regression equation:
y = b0 + b1*500
Please note that the actual calculations depend on the specific data points provided, which are not included in your question.
Similar Questions
What is the primary use of regression analysis?*Analyzing financial trendsAssessing financial statementsPredictive modeling and risk assessmentCalculating financial ratios
2 / 2I am doing research on this topic: "A Study on the Environmental Impact of Maritime Transportation and Measure to Reduce its Carbon Footprint." I want to use regression analysis to analyse my data using the variables below. 1). Carbon Emissions - dependent variable2). Technological Innovation - independent variableGive me a sample table
Fundamentals of Cost and Management Accounting (Study Text) 165 | P a g e Example Company A produces a single product with the following budget: Selling price Rs 10 Direct materials Rs 3 per unit Direct wages Rs 2 per unit Variable production overhead Re 1 per unit Fixed production overhead Rs 10,000 per month. The fixed overhead absorption rate is based on volume of 5,000 units per month. There was production of 6000units i.e 4,800 units were sold and 1200 units left in closing stock. Prepare the profit statement for the month under absorption costing.
In order to analyze sales as a function of advertising expenses, the sales manager developed a simple regression model. The model included the following equation, which was based on 32 monthly observations of sales and advertising expenses with a related coefficient of determination of .90.Sales = $10,000 + (2.5 × Advertising expenses)If the advertising expenses in 1 month amounted to $1,000, the related point estimate of sales would be
Cost-volume-profit analysis is used to:a.Determine the selling price of a productb.Analyze the relationship between costs, volume, and profitc.Calculate the breakeven pointd.Prepare the budget for a companyClear my choice
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.