# Regression Analysis for Unit Cost and Budgeting

**Publication:**The Journal of Bank Cost & Management Accounting

**Date:**January 1, 1993

**Volume/issue:**Vol. 6, No. 3

## Article excerpt

INTRODUCTION

Understanding and analyzing costs is an essential element of bank cost accounting. With the increasing pressure from non-bank competitors that don't have the immense cost structure of traditional banks along with other market conditions imposed on the banking industry, managing and controlling costs will take on an even higher priority. Banks that understand and manage costs will be the survivors.

Regression analysis is a relatively simple quantitative technique that can be used to better understand and analyze the trend in costs, especially unit cost. Regression techniques enhance the presentation quality of graphs, thereby giving bank managers a better understanding of cost trends. This article will graphically illustrate the power of regression analysis in analyzing costs, discuss regression caveats, and suggest ways of using regression techniques in budgeting.

REGRESSION GRAPHS

Unit cost analysis is a common method to examine expense efficiencies, especially in a production environment. Unit cost analysis involves the ratio of costs (numerator) to some kind of production (denominator).

There are many applications within banking, such as check and loan processing, that are ideally suited for unit cost analysis.

A useful tool to help analyze and illustrate unit cost trends involves using graphs. Table I (page 6) summarizes the expenses and production results for a hypothetical production department for the past twelve quarters. (Table I omitted) The unit cost is a function of the dollars spent divided by the items produced.

Figure I (page 7) graphically illustrates the quarterly unit cost. (Figure I omitted) From a management perspective, the critical issue when examining a history of unit cost is the trend direction. Are unit costs going down or are they going up? On a casual visual inspection of Figure I, it would appear that the unit costs are somewhat erratic. Unit costs vary from a low of $1.84 in quarter eight to a high of $2.39 in quarter eleven. It is difficult to tell, however, the eight to a high of $2.39 in quarter eleven. It is difficult to tell, however, the true trend direction of the unit costs depicted in Figure I.

Many of the questions about the unit cost trend can be answered by examining Figure II (page 9). (Figure II omitted) By using the least squares regression method, Figure II incorporates a line that smoothes the various high and low points of the data and presents a clear trend line. The trend line in Figure II is moving in a definite upward direction. This is extremely useful information to know since management now has a much better idea of the true trend direction.

Table II (pages 10 and 11) summarizes the data used to calculate not only the unit cost results but also the regression line. (Table II omitted) The steps used to generate a regression line are:

1. Determine the X and Y variables. In this example, the X variable is the quarter and the Y variable is the unit cost.

2. Solve for the values of X times Y, X squared, and Y squared for each time period used in the analysis.

3. Solve for the slope of the regression line (variable b) by using this equation:

(Equation omitted)

4. Solve for the Y intercept (variable a) using the following equation:

a = The mean of Y - (b * the mean of X)

5. Finally, the regression estimate is solved by using this equation:

Regression Estimate = a + (b * X variable)

It is highly recommended that these calculations be completed on an electronic spreadsheet to facilitate sensitivity analysis.

REGRESSION CAVEATS

Although regression analysis is a very useful tool, it must be used with caution. Below is a summary of some potential problems that can arise when using regression estimates to analyze trends:

1. Data points used in analysis: The regression line in Figure II is treading upward, which means that unit costs are increasing based upon the twelve quarters of data. …