1. ACCT: 742-Advanced Auditing
SAS 56-Analytical Procedures (AU 329)
Regression Analysis and Other Analytical Procedures

2. SAS 56: ANALYTICAL PROCEDURES (AU 329)
“Analytical procedures are an important part of the audit process and consist of evaluation of financial information made by a study of plausible relationships among both financial and non-financial data. Analytical procedures range from simple comparisons to the use of complex models involving many relationships and elements of data. A basic premise underlying the application of analytical procedures is that plausible relationships among data may reasonably be expected to exist and continue in the absence of known conditions to the contrary.” [AU ]

3. Analytical procedures are used for the following purposes:
To assist the auditor in planning the nature, timing, and extent of other auditing procedures
As a substantive test to obtain evidential matter about particular assertions related to account balances or classes of transactions
As an overall review of the financial information in the final review stage of the audit

4. Timing and Purposes of Analytical Procedures-Planning Phase
(Required)
Purpose
Understand client’s
industry and business
Primary purpose
Assess going concern
Secondary purpose
Indicate possible misstatements
(attention directing)
Primary purpose
Reduce detailed tests
Secondary purpose

5. Timing and Purposes of Analytical Procedures-Testing Phase
(Recommended)
Understand client’s
industry and business
Assess going concern
Indicate possible misstatements
(attention directing)
Secondary purpose
Reduce detailed tests
Primary purpose

6. Timing and Purposes of Analytical Procedures-Completion Phase
(Required)
Understand client’s
industry and business
Assess going concern
Secondary purpose
Indicate possible misstatements
(attention directing)
Primary purpose
Reduce detailed tests

7. Five Types of Analytical Procedures
Compare client and industry data.
Compare client data with similar prior period data.
Compare client data with client-determined expected results.
Compare client data with auditor-determined expected results.
Compare client data with expected results, using non-financial data.

8. Some Specific Examples of Analytical Procedures
Ratio Analysis (Financial and Non-financial data)
Common-Size Statements
Trend Analysis
Regression Analysis
Time Series Regression
Cross-Sectional Regression
Discriminant Analysis
Bankruptcy Models (Altman Z-factor)
Digital Analysis
Intelligent Agents and Expert Systems
Non-financial ratios: number of units produces vs. production costs, miles traveled (gross tonnage hauled) by a trucking company vs. fuel expenses.
Time Series Regression: Prediction of the current year sales by month based on a two-or three year history of the monthly relationship of sales to cost of sales.
Cross-Sectional Regression: Prediction of an amount, such as account balance, based on independently predicting variables from the same period: data from other firms, the industry, or across different units of the client’s business, such as sales branches or inventory locations. For example, auditor cannot economically observe inventory at each location of a client that has 600 retail outlets. Regression analysis can be used to identify locations that seem out of line with the other stores. Inventory amounts at each store may be predicted base on the sales, floor space, and price-level index at each location.

9. Altman Z-factor Z = 1.2*X1 + 1.4*X2 + 3.3*X3 + 0.6*X4 + 1.0*X5
Z = discriminant or credit score
X1 = (working capital)/(total assets)
X2 = (retained earnings)/(total assets)
X3 = (earnings before interest and taxes)/(total assets)
X4 = (market value of equity)/(book value of total debt)
X5 = sales/(total assets)
Z < 1.81: Company will go bankrupt within a year or two.
2.675 > Z>1.81: Company will probably go bankrupt, but there is a chance it will not.
2.676 <Z< 2.99: Company will probably not go bankrupt, but there is a chance it will.
Z > 2.99: Company will not go bankrupt.

10. Altman Z-factor Calculation
Use this website for a company's data:
Use 10-K from SEC and stock price for the day from
You may have to go to Google to search for the sicker symbol of your company
In millions except stock price
QualComm Inc. (QCOM)
Delta Ailines (DAL)
AAPL (Apple Computers)
2009
Stock Price (March 22, 2010) $ $ $
Number of Common Shares
1,674
Current Assets
13,574
7,741
36,265
Current Liabilites
2,948
9,797.00
19,282
Working Capital
10,626
(2,056)
16,983
Total Assets
28,903
43,539
53,851
MValue of Equity
67,429
10,389
$ ,204.07
BV of Total Debt
7,550
43,294
26,019
Retained Earnings
11,792
(10,019)
19,538
EBIT
1,052
(1,581)
7,984
Sales
2,670
28,063
36,537
Z-factor
6.58
0.29
6.72

11. Regression Analysis
Regression analysis is a statistical technique used to describe the relationship between the account being audited and other possible predictive factors.
Regression analysis helps
Determine whether there is a relationship between the dependent and independent variables
Determine whether a “significant difference” has occurred
Simple Linear Regression (Time-series & Cross-Sectional Analysis)
Multiple Regression (Time-series & Cross-Sectional Analysis)

12. Regression Analysis: Data Requirements
Accuracy and honesty in recording data
Accounting transactions should be properly accrued
Data should be adjusted for economies of scale or learning effects.
Changes in the nature of production process should be properly taken into consideration.
Variable level of activity is required.

13. Some Examples of Regression Analysis Applications
Monthly sales based on cost of sales and selling expense
Airline and truck company fuel expense based on miles driven and fuel cost per gallon
Maintenance expense based on production levels
Overhead cost based on machine hours and labor hours used
Inventory at each location of a retail company based on store sales, store square footage, regional economic data, and type of store location

14. Linear Regression Model
yi = a + bxi + ei
yi = dependent variable at time ‘i’ or location ‘i’
xi = independent variable at time ‘i’ or location ‘i’
ei = Error term that incorporates (1) the effects of omitted variables, and (2) model errors caused by nonlinear relationships between x and y.
‘a’ and ‘b’ are estimated by minimizing the sum of the squared terms (Ordinary Least Squares, OLS, technique)
Minimize: (ei)2= (yi – a - bxi)2

15. Regression Line: y = a + bx Scatter Graph
ei = (yi-y)
Minimize variance S(ei)2 a

16. Assumptions
Linear relationship between the dependent variable and the independent variable(s).
E(ei) = 0, i.e., Sei = 0.
Variance of ei is constant for all t, and does not depend on the independent variables.
Covariance(ei, ej) = 0, for all i, j where i  j.
The independent variables are uncorrelated.
ei ~ N(0, se).

17. E(ei) = 0, i.e., Sei = 0.
Sei = 0 ei

18. Variance of ei is constant for all i

19. Four Criteria For Evaluating Regression Results
Plausibility of relationship between the dependent variable and the independent variables.
Goodness of fit measured by R2 (Coefficient of determination) and F statistic.
Confidence placed on the parameters of the regression model.
Specification Tests – Critical assumptions have been met.

20. Goodness of fit Measured by Coefficient of Determination
R2 (Coefficient of Determination) represents the percentage of variance explained in the dependent variable through the independent variables.
Value: 1>R2>0
If R2 = 0.85, it means 85% of variance is explained by the independent variable(s)

21. Significance of the Coefficients
Y = a + bx
Is ‘a’ different from zero? Determines if there is a constant term.
Is ‘b’ different from zero? Determines if there is a linear relationship.
We use t-statistics to test for their significance
ta = (a – 0)/sa, sa is the standard deviation of ‘a’
tb = (a – 0)/sb , sb is the standard deviation for ‘b’
As a rule of thumb, for a large sample size, if t is greater than 2 then we consider the coefficient to be different from zero.

22. Standard Error of the Regression and Standard deviations of a and b
The standard error of the regression
where n is the number of data points and k is number of unknown parameters in the model.
The standard deviation of b, the coefficient of the independent variable:

23. Standard Deviation of the parameter a
The standard error of the constant term, a:

24. Predictions from the Regression Equation
Prediction: yf from regression line = a + bxf. The standard error Sf for yf is given by:
The t statistic for the test of significance is:

25. 95% Confidence Intervals
Confidence interval for coefficient a:
= [ a ± t.95 sa]
Confidence interval for coefficient b:
= [ b ± t.95 sb]
Confidence interval for the predicted value :
= [ ± t.95 sf]