Regression in Audit Paper

APPLICATION OF REGRESSION ANALYSIS IN AUDITING PROCEDURES 1
Application of Regression Analysis in Auditing Procedures
Marketa Kreuzingerova
Brescia University
Dr. Rohnn Sanderson
Business Statistics

Introduction
The purpose of this paper is to introduce the regression analysis as an auditing tool and
illustrate its usefulness in developing expectations in an audit engagement. Statistical procedures
in general have proven to be very useful in determining whether financial statements are
materially misstated, and the use of statistics in performing audit procedures is commonplace
among accounting firms. Naturally, statistics provide auditors with quantifiable data and
mathematical accuracy that cannot be achieved through performing tests on non-statistical basis,
which require only professional judgment.
For instance, auditors have the option of conducting tests of controls in either a statistical
or non-statistical manner. While the nature of certain engagements may allow for testing
controls solely on the basis of professional judgment, there is no doubt that the use of a statistical
sampling method, such as mean-per-unit estimation, provides a greater degree of substantial
appropriate evidence as to whether the population contains a material misstatement.
Consequently, the auditors achieve a higher level of assurance on the fair presentation of the
financial statements. Therefore, generalized audit software (GAS) employed by many accounting
firms contains a statistical package that includes tools for statistical analysis, such as random
number generators to be used in tests of controls2.
While the variety of statistical tools to be used for audit purposes is great, this paper
focuses on regression analysis as a cost-effective means of detecting material misstatements, or
simply deviations in client performance or operations.
First, it is important to understand the manner in which an audit is conducted. The steps
in a typical audit process constitute a planning stage, understanding the entity and its control

environment stage, risk assessment, performance of further audit procedures, a concluding stage,
and the issue of an opinion. Further audit procedures involve tests of controls, which assess
control risk of the entity, and substantive procedures, which limit detection risk of the
engagement. Substantive procedures take the form of analytical procedures and tests of details of
balances, classes of transactions, and disclosures. Because regression analysis is categorized as a
form of analytical procedures in professional accounting literature, the focus of this paper will be
on the understanding and performance of analytics2.
In general, analytical procedures provide auditors with assurance about the material
correctness of the financial statements by establishing and examining relationships between
financial and nonfinancial data pertaining to balance sheet and income statement accounts.
Examples of analytical procedures available to be used by the auditors consist of trend analysis,
ratio analysis, regression analysis, and reasonableness testing2.
Auditing standards AU 329, issued by the Public Company Accounting Oversight Board
(PCAOB), require the application of analytical procedures at two stages of the engagement. First,
analysis is critical in the risk assessment process of the audit; second, analytical procedures must
also be performed when the audit is nearing completion to substantiate the opinion being made.
Finally, auditors often employ analysis in substantive procedures; however, this step is not
required by the PCAOB1.
While regression is usually applied in a similar manner, the purpose of this form of
analysis differs with each stage of the engagement. If employed at the risk assessment stage,
regressions are run to help the auditors develop expectations about the client. In later stages,
either in substantive testing or at the completion point, regressions help in detecting actual
material misstatements in the account balances being tested2. Although substantiating account

balances represents a critical step in the audit process, the focus of this paper will be mainly on
the risk assessment stage.
In performing an engagement, auditors look to limit audit risk, which is the possibility of
issuing an unmodified opinion on materially misstated financials, to minimum levels. This
process involves assessing the inherent and control risk of the entity, which exist independently
of the audit. Based on the level of both risks, which together constitute the risk of material
misstatement, the auditors then perform further audit procedures to limit detection risk in a
manner that reduces the overall risk of the audit2.
As part of the risk assessment stage, auditors develop predictions about the trends that
can be reasonably expected in the year under the audit. Often, this involves comparisons to prior
years or industry averages. This process not only establishes the basis for risk assessment but
also helps the auditors obtain a better understanding of the environment the entity operates in2.
For instance, as referenced in Figure 1, they may be interested in the extent to which seasonal
factors affect the revenue streams of the client. Other relevant expectations may involve
projected growth in sales, expenses, and other accounts. While balance sheet items can be used
in this analysis, income statement items are more meaningful to the auditors as they cover a
period of time rather than a single balance1.
After developing their expectations, auditors usually establish a specific amount of
deviation that can be accepted without the need to assess the risk of material misstatement at a
higher level. Here, tolerable misstatements are introduced for each respective account.
Subsequent comparisons of expectations with collected data provide the auditors with evidence
as to whether the client’s operations follow the predicted trend. Based on the results, the auditors
decide on the appropriate course of the audit. First, if expectations are met, they may assess risk

of material misstatement at low levels and proceed with traditional further audit procedures. The
need for additional testing and a higher level of assessed audit risk arises when the results show
material deviations from expectations2.

Analysis
To illustrate the application of regression analysis in the risk assessment process of an
audit engagement, several models will be developed based on data gathered from the Securities
and Exchange Commission’s Electronic Data Gathering, Analysis, and Retrieval (EDGAR)
database3. The data presented below summarizes the operations of SnapOn Tools, Inc., a 2.4
billion dollar company specializing in tool and equipment manufacturing and distribution.
Known for its high-end products, lifetime warranties, and exceptional customer service, SnapOn
Tools, Inc. has been in business since the year 1920. Since then, it has grown into a publicly-
traded corporation that employs over 11,000 people4 and generates over 400 million dollars in
net earnings per year3.
For the purpose of this analysis, income statement data reflecting operations during the
years 2010 to 2014 was gathered from the Securities and Exchange Commission. Net sales, cost
of goods sold, gross profit, and other figures were extracted from EDGAR’s financial statements
to reflect quarterly reported results of SnapOn Tools, Inc. in these respective periods3. Because
the following illustration focuses on the risk assessment stage of the audit process, the regression
analysis performed will be centered around developing and subsequently confirming
expectations. As described above, auditors develop expectations about factors such as the client’s
operating environment and the projected earnings figures for the year under the audit.
In our analysis of SnapOn Tools, Inc., the primary interest was in assessing whether the
company’s revenue streams are subject to seasonality; this is a critical feature of the concept of
revenue generation that can affect a company’s earnings substantially and therefore is of great
interest to the auditors in developing expectations.

Figure 1
Figure 2

As illustrated in Figures 1 and 2, the relationship of net sales and time was analyzed by
running a regression line where net sales represented the dependent variable and time constituted
the independent variable. Focusing on our coefficient of determination value, as highlighted in
Figure 1, we can see that the time variable is responsible for roughly 90 percent of the variation
in net sales. When examining the regression line, we do not observe any apparent seasonal trend
that would affect the data set. The presence of seasonality can further be tested by including
additional time factors in the analysis. For SnapOn Tools, Inc., the regression was expanded to
include a time variable consisting of quarterly data from the second, third, and fourth quarters.
Figure 3
Examining the data acquired from the new regression model, we can see that the
coefficient of determination has not changed by a significant amount. In fact, we have
recognized a mere 4 percent increase in the coefficient as a result of including the additional

quarterly time variables. Consequently, we can conclude that adding seasonal variables
contributes minimally to the explanation of variability in net sales over time. Therefore,
seasonality does not represent a significant factor in the analysis of net sales and its impact on
change in net sales figures can be disregarded. This conclusion is further supported by the
regression model in Figure 4, which does not reflect any apparent seasonality in the trend of the
graph.
Figure 4
Applying this information to the development of expectations, the auditors can conclude
that it is reasonable not to expect seasonal fluctuations in net sales figures. Later in the audit
process, this expectation will either be confirmed or denied by comparisons to actual data. If
fluctuations in data are apparent when performing substantive procedures, it is possible that a

misstatement has occurred, and the auditors will take special caution when dealing with the
account balance in question.
Further, expectations can be developed regarding specific balances of accounts. For
SnapOn Tools, Inc., the quarterly gross profit figures for the years 2010 through 2014 were
selected to illustrate how specific expectations are made, how they assist auditors in assessing
the risk of material misstatement, and what effect they have on other stages of the audit process.
Again, the analysis starts with the regression model, where gross profit represents the
dependent variable and the time trend is the independent variable. First of all, the coefficient of
determination in Figure 5 indicates that about 94 percent of the variability in gross profit is
caused by the time factor; therefore, a very strong relationship exists between the variables. Also,
the time coefficient suggests that gross profit grows by approximately 5.5 units (measured in
millions of dollars) every period.
Figure 5

Figure 6 provides us with additional information about the trend that gross profit
followed from 2010 to 2014. Based on the relationship gross profit has with net sales, it is
reasonable to expect gross profit to follow a trend similar to the one depicted in Figure 2, where
net sales were analyzed. Comparing the two figures, we can see that the fluctuations as well as
their extent are relatively comparable, which substantiates the relationship between these two
income statement accounts.
Figure 6
As mentioned above, auditors performing risk assessments not only develop expectations
but also estimate acceptable deviations at the given level of material misstatement risk. The
amount of acceptable deviation is determined based on the extent to which auditors wish to limit
the overall audit risk. While the level of acceptable risk can vary with the nature of every client,
auditors generally desire to assess the overall risk as low. In regression analysis, the level of risk

directly relates to the confidence interval of the model. Generally, the lower the confidence
interval, the narrower the range of values to be accepted, and the greater the ability of the
auditors to assess the overall risk of material misstatement at low levels.
Therefore, auditors restrict the confidence range to reflect their desired level of assurance
as to whether material misstatements exist in the respective account. Focusing on Figure 7, we
are presented with a 95 percent confidence interval, which provides us with a relatively high
probability that the actual gross profit values will fall within the established value range.
However, such a wide confidence interval provides only limited assurance as to the
appropriateness of actual gross profit data.
Figure 7
Using the coefficients of each variable and the confidence interval, we can develop
expectations as to the range within which actual gross profit figures should fall for every quarter.
Taking the data from Figure 7 and re-structuring it into tabular format, we can gain better
understanding of the meaning of the data. When multiplied with the respective time factor, the
time coefficient provides us with a time value that helps us generate the mean gross profit figure
earned every quarter. For instance, the average value for first quarter is obtained by adding the

constant coefficient, 292.221, to the product of the time coefficient and the time factor, 5.48466
and 1, respectively.
Similarly, we apply the same technique to generate gross profit values that constitute the
95 percent confidence interval. Using both the lower-interval coefficients, 284.196 and 4.81474,
and higher-interval coefficients, 300.246 and 6.15458, we can construct a clear range of values
that is expected to approximate actual gross profit earnings of the company.
Actual
Within
Range
1 297.48$ 288.80$ 306.15$ 287.60$ N
2 302.96$ 293.60$ 312.30$ 303.80$ Y
3 308.44$ 298.40$ 318.45$ 301.20$ Y
4 313.92$ 303.20$ 324.60$ 318.50$ Y
5 319.40$ 308.00$ 330.75$ 330.60$ Y
6 324.88$ 312.80$ 336.90$ 342.20$ N
7 330.36$ 317.60$ 343.05$ 329.30$ Y
8 335.84$ 322.40$ 349.20$ 335.80$ Y
9 341.32$ 327.20$ 355.35$ 347.70$ Y
10 346.80$ 332.00$ 361.50$ 349.90$ Y
11 352.28$ 336.80$ 367.65$ 340.40$ Y
12 357.76$ 341.60$ 373.80$ 352.00$ Y
13 363.24$ 346.40$ 379.95$ 356.90$ Y
14 368.72$ 351.20$ 386.10$ 373.20$ Y
15 374.20$ 356.00$ 392.25$ 364.30$ Y
16 379.68$ 360.80$ 398.40$ 378.50$ Y
17 385.16$ 365.60$ 404.55$ 378.70$ Y
18 390.64$ 370.40$ 410.70$ 400.40$ Y
19 396.12$ 375.20$ 416.85$ 393.90$ Y
20 401.60$ 380.00$ 423.00$ 411.30$ Y
Figure 8
Quarter Mean Low High
This step concludes the estimation stage of the risk assessment process; the auditors are
now ready to perform comparisons of actual data to the models they have developed, and use the
results to evaluate the level of risk of material misstatement. As illustrated in Figure 8, auditors
usually face two types of results when comparing real-world data with client expectations. First,

it is apparent from our model that SnapOn Tools, Inc.’s gross profit values mostly follow the
growth trend predicted by the regression analysis. Second, we encounter a few outliers in our
data that do not copy the expected trend. Consequently, the auditors can take different courses of
action depending on the results of the comparison stage of the analysis.
As auditors complete the risk assessment process, they evaluate results obtained from the
regression analysis and take steps that will complement their goal of restricting the overall audit
risk to minimum levels. If data obtained from the client does not deviate from the developed
model, auditors will abandon the risk assessment stage and perform traditional further audit
procedures as planned, while leaving the assessed material misstatement risk at the planned
level.
If deviations are detected, the auditors must determine whether these deviations are
material in either their amount or nature. Material differences can have substantial effect on the
entire audit process as auditors will need to re-assess the overall level of material misstatement
risk to reflect the deviations encountered. Depending on the impact of the deviation, the
responses may vary from revising the audit program and performing additional substantive
procedures to withdrawing from the engagement.
Conclusion
The purpose of this paper was to illustrate the potential of regression analysis in assessing
the risk of material misstatement when performing an audit engagement. While regression
analysis is not widely used by the auditing profession, it represents a source of information that
can prove critical in several stages of the audit process, and as such should not be overlooked in
performing auditing procedures as a whole.

References
1. American Institute of Certified Public Accountants (2002). AU Section 329. Retrieved April
22, 2015, from http://pcaobus.org/Standards/Auditing/Pages/AU329.aspx
2. Whittington, O. Ray, & Pany, Kurt (2014). Principles of Auditing & Other assurance
Services. 19th Edition pp 137-154
3. Electronic Data Gathering, Analysis, and Retrieval (2012, Feb 12). U.S. Securities and
Exchange Commission. Retrieved April 15, 2015, from http://www.sec.gov/edgar.shtml
4. Snap-on (2015, Mar 2). Wikipedia. Retrieved April 22, 2015 from
http://en.wikipedia.org/wiki/Snap-on

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