Question

1. 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	5,000
450	6,000
550	6,400
600	6,900
700	7,400
750	8,000

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)?
   $

2.

Consider the following data for a dependent variable y and two independent variables, x₁and x₂; for these data SST = 15,029.6, and SSR = 13,917.

x 1	x 2	y
30	12	95
46	10	109
24	18	112
50	17	179
40	5	95
52	19	175
74	7	171
37	13	118
59	14	143
77	16	211

Round your answers to three decimal places.

a. Compute R².

b. Compute R_a².

Answer 1

The statistical software output for this problem is :

1)

(a)

b1 = 7.6

b0 = 2246.7

= 2246.7 + 7.6 x

(b)

Variable cost = $ 7.6

(c)

r ² = 0.959

95.9%

(d)

$ 6047

2)

R-squared: 0.926
R-squared (adjusted): 0.905