CH14-Assignment

Module 10 (Chapters 14) Assignment Problem 1 Cost Estimation. An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method 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 ($) 4 0 0 4000 450 5000 550 5400 600 5900 700 6400 C75 0 7000 a. Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume. The estimated regression equation that could be used to predict the total cost for a given production volume is y =7.6 x +1246.7 . There are two ways to find the estimated regression. One way is to use Excel to create a scatter plot, and under chart elements, you select 'more trendline options' and 'Display Equation on chart.' The other way is using the least squares method. You use the following formulas: b1 =∑( xi − x ˉ)( yi − y ˉ)/∑( xi − x ˉ)2. This will get you the slope. Then you find the y-intercept by using the following formula: b0= y ˉ− b 1 x ˉ. This will get you the estimated regression. b. What is the variable cost per unit produced? The variable cost per unit produced is 7.6 . To determine this, you need to find the slope of the data. To find the slope, use the following formula b1 =∑( xi − x ˉ)( yi − y ˉ)/∑( xi − x ˉ)2. c. Compute the coefficient of determination. What percentage of the variation in total cost can be explained by production volume? The coefficient of determination in percentage form is 95.86%. To calculate the coefficient of determination, you use the formula: Sum of Squares Regression / Sum of Squares Total. d. The company’s production schedule shows 500 units must be produced next month. Predict the total cost for this operation. The total cost of the company’s production schedule of 500 units is $5046.67 . To find this cost, you plug in the value of x, which is 500 units, into the estimated regression equation that we found in part A. y =7.6 (500) +1246.7 . Problem 2 College GPA and Salary. Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs (CivicScience)? Consider the college GPA and salary data (10 years after graduation) provided in the file GPASalary. http://tavana.us/rutgers/assignments/CH14-Assignment-Problem2-Data.xlsx GPA Salary 2.21 71000 2.28 49000

2.56 71000 2.58 63000 2.76 87000 2.85 97000 3.11 134000 3.35 130000 3.67 156000 3.69 161000 a. Develop a scatter diagram for these data with college GPA as the independent variable. What does the scatter diagram indicate about the relationship between the two variables? The scattergram shows a positive linear relationship. This indicates that the two variables are related, as we observe that people with a higher GPA are more likely to get a higher salary. To create a scatter plot, plug in the points that correspond to x and y values. b. Use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college GPA. The estimated regression equation is y= 72991x – 110210. There are two ways to find the estimated regression. One way is to use Excel to create a scatter plot, and under chart elements, you select 'more trendline options' and 'Display Equation on chart.' The other way is using the least squares method. You use the following formulas: b1 =∑( xi − x ˉ)( yi − y ˉ)/∑( xi − x ˉ)2. This will get you the slope. Then you find the y-intercept by using the following formula: b0= y ˉ− b 1 x ˉ. This will get you the estimated regression