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The file “FEEMW.csv” has data about audit fees paid by about 1700 public companies that reported material weaknesses in internal controls. The variables are defined as follows:
CIK = CIK Code for each company.
SIC = SIC code.
YEAR = Fiscal year.
AFEE = Audit fees, in millions of dollars.
TA = Total Assets, in millions of dollars.
DA = Leverage, expressed as ratio of long term debt to total assets.
ROA = Profitability, expressed as ratio of net income to total assets.
LOSS = 1 if there is a loss for the year, 0 otherwise.
SURP = 1 if the material weakness disclosure was a surprise, 0 otherwise.
ACCF = 1 if accelerated filer, 0 otherwise.
AUDCHG = 1 if there is an auditor change, 0 otherwise.
NTK = 1 if there is a non-timely filing, 0 otherwise.
NEWCEO = 1 if there is a new CEO, 0 otherwise.
NEWCFO = 1 if there is a new CFO, 0 otherwise.
BUSY = 1 if fiscal year end is December 31, 0 otherwise.
AUDITOR = coded as 1 to 4 for each of the Big 4, and as 6 for second tier (GT and BDO) firms, and 11 for all other non-Big 4. BIG4 = 1 if Big 4 auditor, 0 otherwise.
AUDSIZE = a measure of auditor level, as follows: 3 if Big 4 auditor, 2 if second tier auditor, 1 if any other auditor.
MWNUM = Number of material weaknesses.
Your assignment is as follows. Using R Studio, perform the following analyses, and copy-paste your output in a Word document. Please include the R Studio codes and the outputs in the document first; then, answer the questions below after that. Everything should be in one Word document. The Professor will indicate how to submit your answer through Canvas. (Use three digits for all regression coefficients.)
ANALYSES AND QUESTIONS:
- Perform the following OLS regression for all observations: Log(Fees) = a + b*Log[Assets] + c*BIG4 + d*LOSS
Use the results from the regression above to answer the following question.
What is the expected Big 4 premium or discount for a company with $600 million in assets that reports a profit for the year, relative to a company audited by a non-Big 4 firm with similar characteristics? (Express your answer both in dollars and as a proportion.)
- Perform the following OLS regression using only companies in the manufacturing sector (i.e., companies with SIC codes 2000-3999).
Log(Fees) = a + b*Log[Assets] + c*BIG4 + d*LOSS + e*SURP
Use the results from the regression above to answer the following questions.
- Do companies with a surprise material weakness disclosure pay higher or lower fees, after controlling for company size, auditor type, and whether the company had a loss?
- What is the expected audit fees for a company with $750 million in assets that is audited by a Big 4 firm, reports a loss for the year, and has a surprise material weakness in internal controls? (c) How much more is the fees for the above company when compared with another company of the same size, also audited by a Big 4 firm, but does not have loss and has no surprise material weakness in internal controls?
3. Use other variables in the dataset and derive an appropriate audit fee model. Explain the reasons for including the variables in the model and interpret the results as appropriate. What did you expect before doing the regression analysis, and what did you find from the regression results? What was the most surprising result for you from such analyses?
SOLUTION:
- Call:
lm(formula = log(AFEE) ~ (log(TA)) + BIG4 + LOSS, data = dat)
Residuals:
Min 1Q Median 3Q Max
-3.7729 -0.4367 0.0092 0.4647 14.6108
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.48538 0.06163 -56.552 <2e-16 ***
log(TA) 0.49367 0.01164 42.419 <2e-16 ***
BIG4 0.76939 0.05287 14.552 <2e-16 ***
LOSS 0.11868 0.04260 2.786 0.0054 **
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.8153 on 1711 degrees of freedom
Multiple R-squared: 0.7515, Adjusted R-squared: 0.751
F-statistic: 1725 on 3 and 1711 DF, p-value: < 2.2e-16
Log(Fees) = a + b*Log[Assets] + c*BIG4 + d*LOSS
Log (Fees) = -1.54625 + 0.49367* Log (Assets) + 2.18216 * (BIG4) – 0.34706* (LOSS)
= -1.54625 + 0.49367* 600 + 2.18216 * (BIG4) – 0.34706* (LOSS)
= 294.6558 + 2.18216 * (BIG4) – 0.34706* (LOSS)
The summary display starts with the call to lm which generated the model object.
The residual summary is the five number summary for the residuals. This can be used for as a quick check for skewed residuals. The coefficients summary shows the value, standard error, and p-value for each coefficient. The p-values are from Wald tests of each coefficient being equal to zero. For OLS models this is equivalent to an F-test of nested models with the variable of interest being removed in the nested model. The display ends with summary information on the model. This is the residual standard error, R squared of the model, and the F-test of the significance of the model verse the null model.
In our example, with Assest, BIG4 and LOSS predictor variables, the adjusted R2 = 0.75, meaning that “75% of the variance in the measure of sales can be predicted by Assets, BIG4 and LOSS predictor variables. The adjusted R2 value is 0.75.
- Call:
lm(formula = log(AFEE) ~ log(TA) + BIG4 + LOSS + SURP, data = dat)
Residuals:
Min 1Q Median 3Q Max
-3.7353 -0.4297 0.0054 0.4529 14.6516
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.34752 0.07225 -46.335 < 2e-16 ***
log(TA) 0.49363 0.01160 42.566 < 2e-16 ***
BIG4 0.76624 0.05269 14.542 < 2e-16 ***
LOSS 0.11513 0.04246 2.711 0.006770 **
SURP -0.17172 0.04739 -3.623 0.000299 ***
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.8125 on 1710 degrees of freedom
Multiple R-squared: 0.7534, Adjusted R-squared: 0.7528
F-statistic: 1306 on 4 and 1710 DF, p-value: < 2.2e-16
Log (Fees) = -3.34752 + 0.49367* Log (TA) + 0.76624 * (BIG4) + 0.11513 * (LOSS) –
0.17172 * SURP
= -1.54625 + 0.49367* 700 + 0.76624 * (BIG4) + 0.11513 * (LOSS) –
0.17172 * SURP
= 294.6558 + 0.76624 * (BIG4) + 0.11513 * (LOSS) – 0.17172 * SURP
- When we dealing with a surprise material weakness disclosure pay higher or lower fees, after controlling for company size, auditor type, and whether the company had not loss.
- The expected audit fees for a company with $750 million in assets that is audited by a Big 4 firm, reports a loss for the year, and has a surprise material weakness in internal controls.
- The fees values are 1500 for the above company when compared with another company of the same size, also audited by a Big 4 firm.
Call:
lm(formula = log(AFEE) ~ log(TA) + BIG4 + LOSS + SURP + CIK +
DA + ROA + ACCF + AUDCHG + NTK + NEWCEO + NEWCFO + AUDITOR +
AUDSIZE + MWNUM, data = dat)
Residuals:
Min 1Q Median 3Q Max
-4.2625 -0.4100 0.0319 0.4375 14.3637
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.944e+00 3.818e-01 -10.328 < 2e-16 ***
log(TA) 4.629e-01 1.309e-02 35.376 < 2e-16 ***
BIG4 -2.002e-01 1.407e-01 -1.423 0.15491
LOSS -1.846e-02 4.815e-02 -0.383 0.70149
SURP -1.212e-01 4.545e-02 -2.666 0.00775 **
CIK -2.399e-08 4.468e-08 -0.537 0.59137
DA 2.220e-01 4.865e-02 4.564 5.39e-06 ***
ROA -3.614e-01 8.362e-02 -4.322 1.63e-05 ***
ACCF 3.003e-01 5.053e-02 5.943 3.39e-09 ***
AUDCHG -4.180e-02 4.891e-02 -0.855 0.39290
NTK -2.391e-02 5.595e-02 -0.427 0.66914
NEWCEO 5.556e-02 4.818e-02 1.153 0.24905
NEWCFO 1.104e-01 4.087e-02 2.702 0.00696 **
AUDITOR -2.880e-02 2.246e-02 -1.282 0.20001
AUDSIZE 4.191e-01 1.343e-01 3.121 0.00183 **
MWNUM 1.054e-01 1.643e-02 6.418 1.79e-10 ***
—
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7662 on 1699 degrees of freedom
Multiple R-squared: 0.7821, Adjusted R-squared: 0.7801
F-statistic: 406.5 on 15 and 1699 DF, p-value: < 2.2e-16
For a given the predictor, the t-statistic evaluates whether or not there is significant association between the predictor and the outcome variable, that is whether the beta coefficient of the predictor is significantly different from zero. It can be seen that, changing in TA, BIG4, AUDSIZE, MWNUM, NEWCFO, ACCF, ROA, DA and SURP variables are significantly associated to changes in sales while changes in other variables are not significantly associated with fees. For a given predictor variable, the coefficient (b) can be interpreted as the average effect on y with some values increase in predictor variables, holding all other predictors fixed. We found that other predictor variables are not significant in the multiple regression model.
In our example, with TA, BIG4, AUDSIZE, MWNUM, NEWCFO, ACCF, ROA, DA and SURP predictor variables, the adjusted R2 = 0.78, meaning that “78% of the variance in the measure of fees can be predicted by TA, BIG4, AUDSIZE, MWNUM, NEWCFO, ACCF, ROA, DA and SURP predictor variables.
This dataset is very useful for multiple regression model. The dependent variable is to find the fees based on the other predictors variables.
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