Managerial, or cost, accountants often use simple regression models to assess th

Question

Managerial, or cost, accountants often use simple regression models to assess the relationshipbetween an organization’s costs and its production (or output). The table below contains the production,in units of output, and costs, in actual dollars, for S-E Enterprises during each month of 2016:

In addition, for production, the standard deviation equals approximately 149.7473 units, and thecovariance between production and costs equals approximately 1,495,454.55.

a. Estimate the straight-line simple regression (or Y^) equation that can be used to predict monthly costs given units produced.

b. Interpret the value of the estimated intercept.

c. Interpret the value of the estimated slope coefficient for units produced.

d. Which estimated value, the intercept or the slope coefficient, represents fixed costs in accounting?

e. Which estimated value, the intercept or the slope coefficient, represents variable costs in accounting?

MONTH PRODUCTION COSTS January 800 $93,000 February 1,100 $114,000 March 1,200 $119,000 April 950 $103,000 May 1,300 $126,000 June 1,250 $124,000 July 1,000 $107,000 August 1,050 $110,000 September 1,000 $105,000 October 900 $100,000 November 1,050 $110,000 December 1,200 $119,500

Explanation / Answer

Result:

In addition, for production, the standard deviation equals approximately 149.7473 units, and the covariance between production and costs equals approximately 1,495,454.55.

Cost = 39,739.8649+66.6892*production

b. Interpret the value of the estimated intercept.

When there is no production the fixed cost is $39,739.8649.

c. Interpret the value of the estimated slope coefficient for units produced.

When there is increase in one unit of production, the cost increases by $66.6892.

d. Which estimated value, the intercept or the slope coefficient, represents fixed costs in accounting?

The intercept represents fixed costs in accounting.

e. Which estimated value, the intercept or the slope coefficient, represents variable costs in accounting?

The slope coefficient represents variable costs in accounting.

Regression Analysis

r²

0.995

n

12

r

0.998

k

1

Std. Error

708.896

Dep. Var.

COSTS

ANOVA table

Source

SS

df

MS

F

p-value

Regression

1,097,037,162.1622

1  

1,097,037,162.1622

2183.01

4.86E-13

Residual

5,025,337.8378

10  

502,533.7838

Total

1,102,062,500.0000

11  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=10)

p-value

95% lower

95% upper

Intercept

39,739.8649

1,536.1873

25.869

1.71E-10

36,317.0262

43,162.7035

PRODUCTION

66.6892

1.4273

46.723

4.86E-13

63.5089

69.8695

Regression Analysis

r²

0.995

n

12

r

0.998

k

1

Std. Error

708.896

Dep. Var.

COSTS

ANOVA table

Source

SS

df

MS

F

p-value

Regression

1,097,037,162.1622

1  

1,097,037,162.1622

2183.01

4.86E-13

Residual

5,025,337.8378

10  

502,533.7838

Total

1,102,062,500.0000

11  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=10)

p-value

95% lower

95% upper

Intercept

39,739.8649

1,536.1873

25.869

1.71E-10

36,317.0262

43,162.7035

PRODUCTION

66.6892

1.4273

46.723

4.86E-13

63.5089

69.8695

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