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Question

oard/execute/content/file?cmd=view&content;_id--64 20491&course-id;=-20882_1 SHOW ALL OF YOUR WORK CHAPTER 13-Simple Linear Regression # 12-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 Cost (units)Total Cost (S) 400 450 550 600 700 750 4000 5000 5400 5900 6400 7000 Use these data to calculate and interpret the linear correlation coefficient. Use these data to develop an estimated regression equation that could be used to predict total cost for a given production volume. What is the variable cost per unit produced? What is the fixed cost for this manufacturing process? (i.e., interpret the regression coefficients) (a) (b) (c) (d) Compute and interpret the coefficient of determination. the (e) The company's production schedule shows 500 units must be produced next month. Predict the total cost for this operation. MacBook Pro

Explanation / Answer

Solution:

a. Correlation(r) = N?XY - (?X)(?Y) / Sqrt([N?X2- (?X)2][N?Y2- (?Y)2])

Correlation (r) = [6*20090000- (3450)(33700)]/Sqrt([6*2077500 - (3450)^2][6*194930000-(33700)^2]

Correlation (r) = 0.9791

There is strong and positive relationship between production costs and total cost.

b. Slope (b) = (N x ?XY - (?X/N)(?Y/N)) / (N x ?X2- (?X)2)

Slope (b) = (6*20090000) - (3450/6)(33700/6)/(6*2077500-(3450)^2)

Slope (b) = 7.6

Intercept (a) = (?Y/N) - b*(?Y/N)

Intercept (a) =(33700/6) - 7.6*(3450/6)

Intercept (a) = 1246.67

The estimated regression equation is Y = 1246.67 + 7.6X

c. The variable cost per unit produced is 7.6. For every additional increase in production cost, total cost increases by 7.6

The fixed cost is 1246.67. The total cost is 1246.67 when there is no production cost.

d. Coefficient of determination, r-square= (0.9791)^2 = 0.9587

95.87% of the total variation is explained by the regression model.

e. When X = 500, total cost would be

Y = 1246.67 + 7.6 (500)

Y = 5047

X Y XY X^2 Y^2 400 4000 1600000 160000 16000000 450 5000 2250000 202500 25000000 550 5400 2970000 302500 29160000 600 5900 3540000 360000 34810000 700 6400 4480000 490000 40960000 750 7000 5250000 562500 49000000 Sum = 3450 33700 20090000 2077500 194930000

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