Cost Behavior Analysis; Correlation Analysis; Standard Error of the Estimate. Randal Company manufactures a wide range of electrical products at several different plant locations. Due to fluctuations, its Franklin plant has been experiencing difficulties in estimating the level of monthly overhead.

Management needs more accurate estimates to plan its operational and financial needs. A trade associa¬ tion publication indicates that for companies like Randal, overhead tends to vary with direct labor hours. Based on this information, one member of the accounting staff proposes that the overhead cost behavior pat¬ tern be determined in order to calculate the overhead cost in relation to budgeted direct labor hours. Another member of the accounting staff suggests that a good starting place for determining the cost behavior pattern of the overhead cost would be an analysis of historical data to provide a basis for estimating future overhead costs.

Direct labor hours and the respective factory overhead costs for the past three years are as follows:

19A 19B 19C Direct Factory Direct Factory Direct Factory Labor Overhead Labor Overhead Labor Overhead Month Hours Costs Hours Costs Hours Costs January.

2,000

$8,500 2,100

$8,700 2,000

$8,600 February.

2,400 9,900 2,300 9,300 2,300 9,300 March.

2,200 8,950 2,200 9,300 2,300 9,400 April.

2,300 9,000 2,200 8,700 2,200 8,700 May.

2,000 8,150 2,000 8,000 2,000 8,100 June.

1,900 7,550 1,800 7,650 1,800 7,600 July.

1,400 7,050 1,200 6,750 1,300 7,000 August.

1,000 6,450 1,300 7,100 1,200 6,900 September.

1,200 6,900 1,500 7,350 1,300 7,100 October.

1,700 7,500 1,700 7,250 1,800 7,500 November.

1,600 7,150 1,500 7,100 1,500 7,000 December.

1,900 7,800 1,800 7,500 1,900 7,600 Required:

(1) Compute the amount of fixed factory overhead and the variable cost rate, using the method of least squares. (Round fixed factory overhead to the nearest dollar and the variable cost rate to the nearest cent.)

(2) Compute the coefficient of correlation, r, and the coefficient of determination, r2, for factory overhead costs and direct labor hours. (Round to four decimal places.)

(3) Compute the standard error of the estimate. (Round to the nearest dollar.)

(4) Compute the 95% confidence interval for factory overhead costs at the 2,200-direct-labor-hour level of activity. (Assume that the sample size is sufficiently large that the normal probability distribution can be assumed and that the correction factor for small samples can be omitted. Round to the nearest dollar.)