Question

In: Statistics and Probability

An important application of regression analysis in accounting is in the estimation of cost. By collecting...

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 ($)
400 4,700
450 5,700
550 6,100
600 6,600
700 7,100
750 7,700
  1. Compute b1 and b0 (to 1 decimal).
    b1
    b0

    Complete the estimated regression equation (to 1 decimal).
    = + x
  2. What is the variable cost per unit produced (to 1 decimal)?

  3. Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1.
    r2 =

    What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
    %
  4. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?

Solutions

Expert Solution

(a)

(i)

From the given data, the following statistics are calculated:

X Y XY X2 Y2
400 4700 1880000 160000 22090000
450 5700 2565000 202500 32490000
550 6100 3355000 302500 37210000
600 6600 3960000 360000 43560000
700 7100 4970000 490000 50410000
750 7700 5775000 562500 59290000
Total = 3450 37900 22505000 2077500 245050000

Slope b1 is given by:

y - Intercept b0 is given by:

So,

Answer is:

b1 = 7.6

b0 = 1946.7

(ii)

The Estimated Regression Equation is given by:

(b)

Variable cost per unit produced = 7.60

(c)

Correlation Coefficient (r) is got as follows:

Coefficient of Determination (R2) is given by:

R2 = 0.97912 = 0.959

(d)

The percentage of the variation in total cost can be explained by the production volume = 95.9 %

(e)
For x = 500, we get:

So,

Answer is:

5747


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