Questions:
1. The controller of the Connecticut Electronics Company believes that the identification of the variable and fixed components of the firm's costs will enable the firm to make better planning and control decisions. Among the costs the controller is concerned about is the behavior of indirect supplies expense. He believes that there is some correlation between the machine hours worked and the amount of indirect supplies used. A member of the controller's staff has suggested that a simple linear regression model be used to determine the cost behavior of indirect supplies. The regression equation shown below was developed from 40 pairs of observations using the method of least squares. The regression equation and related measures are
S = $200 + $4H
where S = total monthly costs of indirect supplies
H = machine hours per month
Standard error of the estimate (s,) = 100
Coefficient of determination (r2)= 0.7569
1. When a simple linear regression model is used to make inferences about a population relationship from sample data, what assumptions must be made before the inferences can be accepted as valid?
2. Assume the assumptions identified in part 1are satisfied for the indirect supplies expense of the company.
(a) Explain the meaning of "200" and "4" in the equation S = $200 + $4H.
(b) Calculate the estimated cost of indirect supplies if 900 machine hours are to be used during a month.
(c) In addition to the estimate for the cost of indirect supplies, the controller would like the range of values for the estimate if a 95 percent confidence interval is specified. He would use this range to judge whether the estimated costs indicated by the regression analysis were good enough for planning purposes. Calculate, for 900 machine hours, the range of the estimate for the cost of indirect supplies with a 95 percent confidence interval.
3. Explain briefly what the value of the coefficient of determination (r2)indicates in this case if the company wishes to predict the total cost of indirect supplies on the basis of estimated machine hours.
(CMA, adapted)