CW. 4 Materiality
Piotr Staszkiewicz
Nov 2023
https://rpubs.com/staszkiewicz/Materiality_EN
Adding and subtracting variables (columns) and cases (rows) in a data frame
Data frame
Let’s build a zanyc frame with two vectors x => c(4,5,6), y => c(d,e,f) and add a column consisting of only 7 as a variable z
# Create a data frame
df <- data.frame(x = c(4, 5, 6), y = c('d', 'e', 'f'))
# Add a variable with a value of 7
df <- cbind(df, z = 7)
# Display the data frame
df## x y z
## 1 4 d 7
## 2 5 e 7
## 3 6 f 7Use rbind() to add rows Let’s add the third case consisting of three unary rows
df<-rbind(df,k=1)
df## x y z
## 1 4 d 7
## 2 5 e 7
## 3 6 f 7
## 4 1 1 1Let’s subtract this case
df<-df[-4,]
df## x y z
## 1 4 d 7
## 2 5 e 7
## 3 6 f 7adding columns/variables:
Method A df$name_new_column <- c(vector of data frame length)
Method B cbind() - column bind function (adds after columns) Method C
mutate()) from the dplyr library way D As a combination of
other columns in the frame way E As a conditional variable based on
other columns in the frame
# A
df$New <- c(5,4,5)
df## x y z New
## 1 4 d 7 5
## 2 5 e 7 4
## 3 6 f 7 5# B
# let's create a vector w
w<- c(1,1,12)
df1<- cbind(df,w)
df1## x y z New w
## 1 4 d 7 5 1
## 2 5 e 7 4 1
## 3 6 f 7 5 12#C
# Install the `dplyr` package if it is not already installed
#install.packages("dplyr")
# Load the `dplyr` package
library(dplyr)##
## Dołączanie pakietu: 'dplyr'## Następujące obiekty zostały zakryte z 'package:stats':
##
## filter, lag## Następujące obiekty zostały zakryte z 'package:base':
##
## intersect, setdiff, setequal, union# Create a data frame
df2 <- data.frame(x = c(1, 2, 3), y = c(4, 5, 6))
# Add a new column with the values 17
df2 <- mutate(df, muta = 17)
# Print the data frame
df2## x y z New muta
## 1 4 d 7 5 17
## 2 5 e 7 4 17
## 3 6 f 7 5 17#D
df$variable<- df$x+2
df## x y z New variable
## 1 4 d 7 5 6
## 2 5 e 7 4 7
## 3 6 f 7 5 8#E
# ifelse - if variable x has value 5 then layer 1 otherwise # 0 (method of generating zero-one variables)
df$variable2<- ifelse(df$x==5,1,0)
df## x y z New variable variable2
## 1 4 d 7 5 6 0
## 2 5 e 7 4 7 1
## 3 6 f 7 5 8 0subtracting columns of variables
Let’s remove the third column, for this we can use the
rm() function. This function removes the objects from the
global śreoodvix
# we remove the third column
df[-3]## x y New variable variable2
## 1 4 d 5 6 0
## 2 5 e 4 7 1
## 3 6 f 5 8 0Alternative methods of deleting variables using the
subset() function and using the variable name to be
deleted
# note as a general rule the minus sign deletes, the plus sign salvages
# deletion of variable y
subset(df, select = -y)## x z New variable variable2
## 1 4 7 5 6 0
## 2 5 7 4 7 1
## 3 6 7 5 8 0# compare
subset(df, select =y)## y
## 1 d
## 2 e
## 3 f# removal of variable z and y.
subset(df, select = -c(z,y))## x New variable variable2
## 1 4 5 6 0
## 2 5 4 7 1
## 3 6 5 8 0# by name reference remove variable x
df[, -which(names(df) == "x")]## y z New variable variable2
## 1 d 7 5 6 0
## 2 e 7 4 7 1
## 3 f 7 5 8 0Calculating materiality for a portfolio of entities
The task is to calculate the expected materiality for the entities banking entities in the US market. We will use primary data from the article Audit fee and banks’ communication sentiment. Economic Research-Ekonomska Istraživanja. https://doi.org/10.1080/1331677X.2021.1985567 Staszkiewicz and Karkowska (2021). The data are, as usual, available from the Essential (“Public Materials Public Materials”) file named Bank.cvs. Please download it to your computer and upload it to R. Please note that the data may be used after the class only for non-commercial purposes by indicating the original source.
# z bazowych funkcji systemu wczytamy klasyczny plik z csv ale w taki sposób
# że wybierzemy z okienka umiejscowienie pliku na włanym komuterze
# dlaego zagnieżdzamy polecenie "file.choose()"
bank <- read.csv("Cw2/Bank.csv")Relevance Introduction
In the original language of the standard there are two terms materiality and significance. Both are translated into Polish as materiality, which gives rise to numerous interpretation perplexities. Lets return to the original meaning of materiality as significance – it is the probability of an event, a term primarily All statistics use the term to describe whether an event (e.g., a test of a test) is likely or nearly impossible. It is expressed as a percentage. Materiality in the sense of accounitng materiality is a concept used in auditing and is defined as an error, omission or an error, omission or misstatement whose occurrence alters the decision to use financial statements. It is expressed in monetary value. Despite many similarities, they are different concepts and should not be should not be equated.
The auditing standards do not specify how materiality should be measured in the accounting materiality sense and leave this concept as a blanket standard to be defined by the auditor in the course of the audit. In the following materiality will be understood as materiality in the sense of auditing.
Dimensions and calculation of materiality
Since materiality is an undefined concept practice has developed its measurement.
Dimensions of materiality:
Information is material
if its omission or misrepresentation misrepresentation could influence the economic decision of a user of financial statements.
- An error of substance, omission, or misstatement has both a quantitative as well as quantitative.
(3) No matter how the auditor determines the level of materiality –. always that level will be treated as professional judgment.
(4) The materiality level primarily affects:
The identification of areas of risk
The type and extent of audit testing
Formulation of opinions.
In practice, materiality is determined as a fraction of a stable position The following are some of the key considerations that should be taken into account in determining materiality
| Scope | |||
|---|---|---|---|
| Net profit | 5–10% | ||
| Sales revenues | 0.5–1% | ||
| Net equity | 3–7% | ||
The following coefficients were calculated for the period from the beginning of the year to the end of the year.
The above-mentioned ratios are different for different audit firms and result The above coefficients are different for different audit firms and result from their own internal control system, audit methodology, and The level of civil residual risk insurance.
Control parameters
During the audit it may turn out that the auditor found small errors (trivial error), whether the error will be taken into account in the overall The steering parameter called the minimum error shown in the statement of unadjusted audit differences, calculated The second control parameter is the error in the summary of audit differences.
The second control parameter is the tolerable error, which is a value of aggregate error, which size does not cause modification of opinions, typically it is 70-80% of significance.
Fixed significance test
It should also be noted that materiality is referred to as Planing materiality in English. This is because it is determined on the basis of initial financial statements (or a forecast thereof) prior to audit testing. After completing the audit procedures, and before issuing audit procedures and before issuing an opinion, the auditor must update his materiality assessment on the based on the revised financial statements. While this is formally a a continuing obligation, however, in practice it is performed prior to planning and before issuing the opinion.
Illustrative example
We are going to count the materiality for US banks. First, let us
generate the necessary data frame. For this we will use the
tidyverse library. If someone does not have has it on your
machine you should install it by using install.library()
function. Lets choose the following variables (columns of our database)
database) namely: CIK_Code,
Companyx,Auditorx,Audit_Fees_USDx,Year_Ended_Datex,Revenue_USDx_N,Earnings_USDx_N,Assets_USDx_N,
Total_Equity
Once the data is loaded, lets use the colnames command
to see what data we have available
colnames(bank)## [1] "CIK_Code" "Year_Ended"
## [3] "Companyx" "Tickerx"
## [5] "Marketx" "IRS_Number"
## [7] "Bus_Street_1x" "Bus_Street_2x"
## [9] "Cityx" "Countyx"
## [11] "State_Codex" "State_Namex"
## [13] "Region" "Zipx"
## [15] "Bus_Phonex" "Incorporation_State_Code"
## [17] "Parent_CIKx" "Parent_Namex"
## [19] "SIC_Codex" "SIC_Descriptionx"
## [21] "NAICS_Codex" "NAICS_Descriptionx"
## [23] "Filer_Actx" "Auditorx"
## [25] "Auditor_Keyx" "Audit_Fees_USDx"
## [27] "Audit_Related_FeesUSD" "Benefit_Plan_Related_Fees_USD"
## [29] "FISDI_Fees_USD" "Tax_Related_Fees_USD"
## [31] "Tax_Related_Fees__ComplianceUSD" "Tax_Related_Fees__NonComplianc"
## [33] "OtherMisc_Fees_USD" "Total_Non_Audit_Fees_USD"
## [35] "Total_Fees_USDx" "Currency"
## [37] "Fees_Include_Subsidiaries" "Fees_Included_In_Parent_Filings"
## [39] "Restatement" "Year_Ended_Datex"
## [41] "Year_Ended_Month_Ideal" "Fiscal_Year_Ends_Currently_Repo"
## [43] "Sourcex" "Source_Datex"
## [45] "Stock_Price_USDx" "Stock_Price_Datex"
## [47] "Market_Cap_USDx" "Market_Cap_USDx_N"
## [49] "Finacls_Datex" "Revenue_USDx"
## [51] "Revenue_USDx_N" "Earnings_USDx"
## [53] "Earnings_USDx_N" "Book_Value_USDx"
## [55] "Book_Value_USDx_N" "Assets_USDx"
## [57] "Assets_USDx_N" "State_Region"
## [59] "Audit_Opinion_Key" "Auditor_City"
## [61] "Auditor_State_Code" "Auditor_State_Name"
## [63] "Auditor_State_Region" "Year_Ended_Ideal"
## [65] "Month_Ended_Ideal" "Signature_Date"
## [67] "Sourcey" "Source_Datey"
## [69] "Going_Concern" "Going_Concern_Issue_Key_List"
## [71] "Going_Concern_Issue_Phrase_List" "Accounting_Basis"
## [73] "Is_Integrated_Audit" "Is_Additiol_Opinion"
## [75] "Additiol_Sigture_Date_1" "Additiol_Sigture_Date_2"
## [77] "Additiol_Sigture_Date_3" "Additiol_Sigture_Date_4"
## [79] "Additiol_Sigture_Date_5" "Filer_Status"
## [81] "Fees_Fiscal_Year_Ended" "Audit_Fees_USDy"
## [83] "NonAudit_Fees_USD" "Total_Fees_USDy"
## [85] "Stock_Price_USDy" "Stock_Price_Datey"
## [87] "Market_Cap_USDy" "Fincials_Datey"
## [89] "Revenue_USDy" "Earnings_USDy"
## [91] "Book_Value_USDy" "Assets_USDy"
## [93] "Country_of_Headquarters" "Company_Common_Name"
## [95] "Total_Assets" "Total_Equity"
## [97] "ROA" "Net_Interest_Margin_Total_"
## [99] "Fee_Revenue_" "Efficiency_Ratio_"
## [101] "Operating_Leverage" "Labor_And_Related_Expense"
## [103] "Noninterest_IncomeOp_Inc" "Net_Loans__PeriodPeriod"
## [105] "Deposits__PeriodPeriod" "Loan_Loss_Provision__of_Loans"
## [107] "Nonperforming_Loans__of_Loans" "Tier_1_RiskAdjusted_Capital_Rat"
## [109] "EOP_LoansEOP_Deposits" "Securities__Avg_Earning_Assets"
## [111] "Going_Convern_Value" "isdup"
## [113] "dup" "suma_Poz"
## [115] "SumaNegat" "Rel_Poz"
## [117] "Rel_Neg" "Total_Words"
## [119] "Rel_total" "Poz_to_Neg"
## [121] "Poz_to_ALL" "Poz_toAllMinus_NegToAll"
## [123] "X_merge_sentiment" "id"
## [125] "bank_name" "Moodyslong_d"
## [127] "Moodysshort_d" "SPshort_d"
## [129] "SPlong_d" "SPlong_f"
## [131] "SPshort_f" "Moodyslong_f"
## [133] "Fitchlong_f" "CIK_Code_2"
## [135] "X_merge" "sd_ROA"
## [137] "ZSCORE" "Audit_B4"
## [139] "Audit_Opininon_GC" "sentiment"
## [141] "audit_fee" "noaudit_fee"
## [143] "size" "loans_growth"
## [145] "npl" "crisis"
## [147] "integ_sen_B4" "integ_sen_aud_fee"
## [149] "integ_sen_cris" "NAICS"
## [151] "audit_fee_u" "noaudit_fee_u"
## [153] "inter_sent_size" "inter_sent_loans"
## [155] "inter_sent_npl" "mean_ROA"
## [157] "ZSCORE_5" "adj_ROA"
## [159] "LEV" "audit_ta"
## [161] "nonaudit_ta" "audit_earn"
## [163] "nonaudit_earn" "totfee_ln"
## [165] "lev_p25y" "lev_p50y"
## [167] "lev_p75y" "lev_p25yy"
## [169] "lev_p50yy" "lev_p75yy"
## [171] "GegraphicalMatch" "State_Namex1"
## [173] "Audit4_sent" "Audit4_size"
## [175] "post_crisis" "Audit4_pcrisis"
## [177] "Audit4_zscore" "Audit4_loan_depo"
## [179] "Audit4_llp" "Audit4_opinion"
## [181] "Auditor_1" "Auditor_10"
## [183] "Auditor_10a" "sent_Audit4"
## [185] "sent_opinion" "sent_size"
## [187] "sent_zscore" "sent_loan_depo"
## [189] "sent_llp" "sent_pcrisis"
## [191] "sentiment_growth" "totfee_ln_growth"
## [193] "average_sentiment" "nyear"
## [195] "X_est_IVall" "X_est_IVall_cencored"
## [197] "censor"And then lets generate the data frame needed for further analysis
calling it $PM$ and let’s see the first records using the
head function
library(tidyverse) #invoce library## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ readr 2.1.4
## ✔ ggplot2 3.4.2 ✔ stringr 1.5.0
## ✔ lubridate 1.9.3 ✔ tibble 3.2.1
## ✔ purrr 1.0.1 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsPM<- bank %>% select(CIK_Code, Companyx,Auditorx,Audit_Fees_USDx,Year_Ended_Datex,Revenue_USDx_N,Earnings_USDx_N,Assets_USDx_N, Total_Equity )
# Let us see what we got
head(PM)## CIK_Code Companyx Auditorx Audit_Fees_USDx Year_Ended_Datex
## 1 7789 ASSOCIATED BANC-CORP KPMG LLP 288000 12/31/2000
## 2 7789 ASSOCIATED BANC-CORP KPMG LLP 405700 12/31/2001
## 3 7789 ASSOCIATED BANC-CORP KPMG LLP 403100 12/31/2002
## 4 7789 ASSOCIATED BANC-CORP KPMG LLP 380120 12/31/2003
## 5 7789 ASSOCIATED BANC-CORP KPMG LLP 842700 12/31/2004
## 6 7789 ASSOCIATED BANC-CORP KPMG LLP 725000 12/31/2005
## Revenue_USDx_N Earnings_USDx_N Assets_USDx_N Total_Equity
## 1 1123002000 167983000 13128394000 968696000
## 2 1076225000 179522000 13604374000 1070416000
## 3 1012841000 210719000 15043275000 1272183000
## 4 973799000 228657000 15247894000 1348427000
## 5 977369000 258286000 20520136000 2017419000
## 6 1385111000 320161000 22100082000 2324978000Now we can enrich our framework with additional columns showing materiality ranges that we will take into account. To build the ranges we can use new columns by generating them according to the PM-dollar sign rule `PM$name_column<- [what it has]’. For example, in Table 1 we have a value of profit n etto from 5-10%. In view of the above, let’s mash up two columns and see them:
PM$ER_0.05<- (PM$Earnings_USDx_N)*0.05
PM$ER_0.1<- (PM$Earnings_USDx_N)*0.10
head(PM %>% select(ER_0.05,ER_0.1))## ER_0.05 ER_0.1
## 1 8399150 16798300
## 2 8976100 17952200
## 3 10535950 21071900
## 4 11432850 22865700
## 5 12914300 25828600
## 6 16008050 32016100Since we already know how to build new data let’s generate all the columns, just as as we did for the results, for assets, capital, and income.
# for assets
PM$TAS_0.001<- (PM$Assets_USDx_N)*0.001
PM$TAS_0.01<- (PM$Assets_USDx_N)*0.010
# for revenue 0.5-1%
PM$REV_0.005<- PM$Revenue_USDx_N*0.005
PM$REV_0.01<- PM$Revenue_USDx_N*0.01
# for equity 3--7%
PM$EQU_0.03<- PM$Total_Equity*0.03
PM$EQU_0.07<- PM$Total_Equity*0.07
# let us see upadted dataframe
head(PM)## CIK_Code Companyx Auditorx Audit_Fees_USDx Year_Ended_Datex
## 1 7789 ASSOCIATED BANC-CORP KPMG LLP 288000 12/31/2000
## 2 7789 ASSOCIATED BANC-CORP KPMG LLP 405700 12/31/2001
## 3 7789 ASSOCIATED BANC-CORP KPMG LLP 403100 12/31/2002
## 4 7789 ASSOCIATED BANC-CORP KPMG LLP 380120 12/31/2003
## 5 7789 ASSOCIATED BANC-CORP KPMG LLP 842700 12/31/2004
## 6 7789 ASSOCIATED BANC-CORP KPMG LLP 725000 12/31/2005
## Revenue_USDx_N Earnings_USDx_N Assets_USDx_N Total_Equity ER_0.05 ER_0.1
## 1 1123002000 167983000 13128394000 968696000 8399150 16798300
## 2 1076225000 179522000 13604374000 1070416000 8976100 17952200
## 3 1012841000 210719000 15043275000 1272183000 10535950 21071900
## 4 973799000 228657000 15247894000 1348427000 11432850 22865700
## 5 977369000 258286000 20520136000 2017419000 12914300 25828600
## 6 1385111000 320161000 22100082000 2324978000 16008050 32016100
## TAS_0.001 TAS_0.01 REV_0.005 REV_0.01 EQU_0.03 EQU_0.07
## 1 13128394 131283940 5615010 11230020 29060880 67808720
## 2 13604374 136043740 5381125 10762250 32112480 74929120
## 3 15043275 150432750 5064205 10128410 38165490 89052810
## 4 15247894 152478940 4868995 9737990 40452810 94389890
## 5 20520136 205201360 4886845 9773690 60522570 141219330
## 6 22100082 221000820 6925555 13851110 69749340 162748460There is no method to explicitly select a value from the possible ranges. As a rule, negative values are not taken into account, and the final selection is the auditor’s professional judgement. auditor. This judgment must be documented in the working papers. Hence, the institution of judgment is not arbitrariness, but a choice in the inflicted scope. The formulation of judgment requires consideration of information quantitative and qualitative (e.g. characteristics of the entity). In our case, banks are supervised by a regulatory requirement thus the typical starting point will be equity.
It is also worth noting that the choice of base for analysis is not necessarily random, and relates to the relationship with the ultimate shareholder. More about who it is, how it is analyzed etc. here Staszkiewicz and Szelągowska (2019), although again this is an item more for hobbyists. Returning to thoughts in industrial companies the typical decision path is the following:
profit - refers to a distributed shareholder living off dividends, because then the most important annual income in addition to unrealized capital gain, is the declared dividend. dividend.
Equity - rather to majority shareholder concentrated, because it shows the linear (book) value of assets under their control. control.
Earnings - in case of expected acquisitions, mergers, change of significant shareholding, because it shows market share.
total assets - rarely rather for “too big to fail” illustrates the impact of social and systemic impact of entities,
Task 1
As an example, let’s try to count istonity as a weighted average of the ranges indicated in Table 1 for all entities in individual years. Let’s generate a new variable called PM
sr<- apply(PM[10:17], 1, mean, na.omit=T) #mean by rows
PM$PM <-sr
head(PM)## CIK_Code Companyx Auditorx Audit_Fees_USDx Year_Ended_Datex
## 1 7789 ASSOCIATED BANC-CORP KPMG LLP 288000 12/31/2000
## 2 7789 ASSOCIATED BANC-CORP KPMG LLP 405700 12/31/2001
## 3 7789 ASSOCIATED BANC-CORP KPMG LLP 403100 12/31/2002
## 4 7789 ASSOCIATED BANC-CORP KPMG LLP 380120 12/31/2003
## 5 7789 ASSOCIATED BANC-CORP KPMG LLP 842700 12/31/2004
## 6 7789 ASSOCIATED BANC-CORP KPMG LLP 725000 12/31/2005
## Revenue_USDx_N Earnings_USDx_N Assets_USDx_N Total_Equity ER_0.05 ER_0.1
## 1 1123002000 167983000 13128394000 968696000 8399150 16798300
## 2 1076225000 179522000 13604374000 1070416000 8976100 17952200
## 3 1012841000 210719000 15043275000 1272183000 10535950 21071900
## 4 973799000 228657000 15247894000 1348427000 11432850 22865700
## 5 977369000 258286000 20520136000 2017419000 12914300 25828600
## 6 1385111000 320161000 22100082000 2324978000 16008050 32016100
## TAS_0.001 TAS_0.01 REV_0.005 REV_0.01 EQU_0.03 EQU_0.07 PM
## 1 13128394 131283940 5615010 11230020 29060880 67808720 35415552
## 2 13604374 136043740 5381125 10762250 32112480 74929120 37470174
## 3 15043275 150432750 5064205 10128410 38165490 89052810 42436849
## 4 15247894 152478940 4868995 9737990 40452810 94389890 43934384
## 5 20520136 205201360 4886845 9773690 60522570 141219330 60108354
## 6 22100082 221000820 6925555 13851110 69749340 162748460 68049940Lets determine the materialtiy distribution in our population (# xlim=c(100,150700000),)
hist(PM$PM,
freq = T,
main="Histogram ",
xlab="Materiality",
border="blue",
col="green",
las=1,
breaks=20000)
min(PM$PM,na.rm=T) # minimum value of materiality## [1] -2187282max(PM$PM, na.rm=T) # maximum value of materiality## [1] 6845808375And now we’re still going to have a third column that shows us the contribution of , and in the auditor’s remuneration to materiality. What can we conclude from such a distribution we can conclude?
PM$AFR<- PM$Audit_Fees_USDx/PM$PM
hist(PM$AFR)
summary(PM$AFR, na.omit=T)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -0.43106 0.03657 0.05612 0.06966 0.08350 1.46075 102Task 2
Let us calculate in how many cases materiality is greater than the
fee of the auditor’s fee. We check how many entities we have in our
database. We apply the Hmisc() library and the desribe
function to understand our data.
library(Hmisc)##
## Dołączanie pakietu: 'Hmisc'## Następujące obiekty zostały zakryte z 'package:dplyr':
##
## src, summarize## Następujące obiekty zostały zakryte z 'package:base':
##
## format.pval, units# let us describe materiality
describe(PM$PM)## PM$PM
## n missing distinct Info Mean Gmd .05 .10
## 5254 102 5254 1 58400064 109091292 545349 817624
## .25 .50 .75 .90 .95
## 1432811 2924430 8938676 32513831 77318372
##
## lowest : -2187280 45102 51890.4 77399 80998.1
## highest: 6222180000 6266840000 6359390000 6624250000 6845810000# let us understand the relation of the matieriality to audit fee
describe(PM$AFR)## PM$AFR
## n missing distinct Info Mean Gmd .05 .10
## 5254 102 5232 1 0.06966 0.05324 0.01361 0.02142
## .25 .50 .75 .90 .95
## 0.03657 0.05612 0.08350 0.12183 0.15548
##
## lowest : -0.431064 0 0.000520695 0.000584316 0.000639326
## highest: 0.912027 0.937462 1.00802 1.2141 1.46075All our observations in the database are 5356 as the result
nrow(PM) hence 5352 as the result
nrow(PM[PM$PM>PM$Audit_Fees_USDx, ]).
Task 3
Calculate the parameters of the significance model in the population
\[ PM = a_{0}+a_{1}x_{1}+a_{2}x_{2}+... a_{n}x_{n}+ error \]
Withlet the first, second, and third non-dependent variables be: total assets, capital, and result.
model<-lm(PM$PM~PM$Assets_USDx_N+PM$Total_Equity+PM$Earnings_USDx_N)Let us summarize the model:
summary(model)##
## Call:
## lm(formula = PM$PM ~ PM$Assets_USDx_N + PM$Total_Equity + PM$Earnings_USDx_N)
##
## Residuals:
## Min 1Q Median 3Q Max
## -121975562 -133433 -110813 -83837 80521989
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.089e+05 5.721e+04 1.904 0.057 .
## PM$Assets_USDx_N 1.565e-03 1.966e-06 795.860 <2e-16 ***
## PM$Total_Equity 1.151e-02 1.966e-05 585.535 <2e-16 ***
## PM$Earnings_USDx_N 2.047e-02 5.943e-05 344.441 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4109000 on 5250 degrees of freedom
## (102 obserwacje zostały skasowane z uwagi na braki w nich zawarte)
## Multiple R-squared: 0.9999, Adjusted R-squared: 0.9999
## F-statistic: 1.965e+07 on 3 and 5250 DF, p-value: < 2.2e-16And some plots:
plot(model)
Additional independent analysis
Based on the American significance value model, determine the expected significance for WIG index companies, and the average for the index.
Independent work assignments
Great Pleasure p. 130
Blue Caffee p. 146
Application of AI in auditing p. 163
## To read:
Blokdijk et al. (2003), DeZoort, Harrison, and Taylor (2006), Martinov and Roebuck (1998)