A budget is an expression of management’s expectations and goals concerning future revenues and costs. To increase their effectiveness, many budgets are flexible, including allowances for the effect of variation in uncontrolled variables. For example, the costs and revenues of many production plants are greatly affected by the number of units produced by the plant during the budget period, and this may be beyond a plant manager’s control. Standard cost-accounting procedures can be used to adjust the direct-cost parts of the budget for the level of production, but it is often more difficult to handle overhead. In many cases, statistical methods are used to estimate the relationship between overhead (y) and the level of production (x) using historical data. As a simple example, consider the historical data for a certain plant:

a. Construct a scatterplot of y versus x.

b. Find the least-squares regression line relating overhead costs to production.

c. Graph the regression line on the scatterplot.

Production (in 10,000) units: 5 6 7 8 9 10 11 Overhead costs (in $1000): 12 11.5 14 15 15.4 15.3 17.5