Notes, summaries, assignments, exams, and problems for Mathematics

Sample Size Calculation

To find what n must be:

n ≥ (Z_1-α/2 / MOE)² * p(1-p)

Wald Confidence Interval

SE^ = sqrt((p^ * (1 – p)) / n)

Odds Ratio Analysis

Calculated by criss-cross of 2x2 table.

Example: The odds for someone to smoke ≥ 5 cigarettes and have lung cancer is 3.40 times that of someone who smokes < 5 cigarettes daily to have lung cancer.

Fisher's Exact Test

Used when cell frequencies are < 5 in a 2x2 table. Tests for independence.

• H₀: Odds ratio = 1
• H_A: Odds ratio ≠ 1

Chi-Square Test of Independence

• H₀: The two variables are independent.
• H_A: The two variables are not independent.

Logit Model

To find the number of odds used in the model, find all combinations of levels (e.g., a 2x3 model has 6 combinations).

Exp(estimate) = odds for... Continue reading "Statistical Analysis Cheat Sheet: Formulas and Methods" »

Gross Income and Business Deductions

Gross Income: Includes revenue from sales, services, rents, dividends, interest, etc. Exclusions include life insurance proceeds and municipal bond interest. Expenses associated with the production of tax-exempt income are not deductible.

Deductions Above the Line (for AGI)

Deductions for Adjusted Gross Income (AGI) include business expenses, rental expenses, self-employed health insurance, and IRA contributions.

• Ordinary & Necessary Test: An expense must be customary and appropriate for the business.
• Meals Deduction: Can deduct 50% of meals if the expense is ordinary, necessary, and reasonable, the employee is present, the person eating is a current or potential client, and the meal is purchased separately

Introduction to Data Analytics

Types of Data Analytics

• Descriptive: Analyzes past trends.
• Predictive: Applies past trends to current data to understand the future.
• Prescriptive: Suggests actions and outlines potential impacts.

Project Stages

1. Problem Specification:
   1. Understand the Problem Statement.
   2. Define the Project Scope.
2. Data Gathering & Preprocessing:
   1. Define a system for data collection.
   2. Clean data with data processing.
3. Descriptive Analytics:
   1. Perform Exploratory Data Analysis (EDA).
   2. Get a basic understanding of the dataset.
   3. Answer initial assumptions about the data.
4. Machine Learning:
   1. Apply correct ML models depending on the scope/nature of the data and project.
   2. Train the ML model to assess its performance.
5. Deployment:
   1. Consult with project stakeholders on

Time Series Analysis

Identifying Trends

• Upward trend: Data increases over time.
• Downward trend: Data decreases over time.
• Stationary trend: No clear increase or decrease.

Smoothing Data (Reducing Fluctuations)

• 3-point moving mean: Average of 3 consecutive values.
• 5-point moving mean: Average of 5 consecutive values.

Seasonal Indices (SI)

Formula:

Seasonal Index = Actual Value ÷ Trend Value

• SI > 1 → Above-average season.
• SI < 1 → Below-average season.

Deseasonalising Data

Formula:

Deseasonalised Value = Actual Value ÷ Seasonal Index

Regression Line (Trend Line)

Equation of the line:

y = mx + c

• m = gradient (rate of change).
• c = y-intercept (starting value).

Bivariate Data Analysis

Types of Correlation

• Positive → Both variables increase together.
• Negative

Residual claim: shareholders get only what is left-over after everyone has been paid. Discount rate: the rate at which present and future values are traded off. Future value of cash flow: C x (1+ r)^n. R= (FV/PV)^1/n - 1. Present value= C/(1+ r)^n. Compound interest: exponential growth in wealth, initial amount of money + the interest that has been added the previous years. Perpetuity, Growing Perpetuity, Annuity: multiple payments overtime, same amount, regular interest. NPV: the difference between and investment's value and its cost. Positive NPV=investment yes; NPV=0 project earns the required rate. . IRR measures the average return on the investment: accept project if IRR is greater than the discount rate(minimum return you want). Payback

This table provides a structured reference for key settings and functional components within SAP Treasury and Risk Management.

Lease Accounting: Vehicle Leases and Journal Entries

Today is May 31, X1, and we lease three vehicles to visit our factories for €120,000. The contractual conditions are as follows:

• The term of the lease is 4 years.
• The payments (€35,000 each) are annual and will be made on May 31. An additional €1,000 will be added as a purchase option in the final payment.
• Effective interest rate: 6.75%
• The estimated useful life for each vehicle is 8 years.

Lease Amortization Schedule

Journal Entries for Lease Transactions

May 31, X1: Initial Lease Recognition

Statistical Goals

• Describe: Explain what's happening in the data (e.g., mean, mode, average, minimum, variation).
• Explore: Understand how different variables relate to each other.
• Draw Inference: Test hypotheses or theories to make generalizations. Important: Correlation doesn't equal causation.
• Predict: Forecast future outcomes (e.g., weather networks).
• Draw Causal Inference: Determine cause-and-effect relationships, which requires experiments.

Variables in Statistics

Variable Types

1. Categorical (e.g., color, name, religion) vs. Numerical (Discrete: whole numbers OR Continuous: decimals, e.g., movie ranking).
2. • Nominal: Categories with no inherent order.
   • Ordinal: Categories with a meaningful order.
   • Interval: Ordered, equal intervals, but zero is arbitrary

CME 315 Midterm 1 Cheat Sheet

MATLAB General Setup and Output

f = @(x) <expression>;

x = linspace(startValue, endValue, numberOfPoints);
x = startValue:spacing:endValue;
y = f(x);

.*    ./    .^

plot(x,y,'LineWidth',1.5)
fplot(f,[a b])
hold on
yline(0,'--')
plot(xPoint,f(xPoint),'ro')
xlabel('Variable (units)')
ylabel('Function (units)')
legend('Curve','Location','best')
grid on

fprintf('Result = %.6f units\n',result)
fprintf('Residual = %.3e\n',residual)
fprintf('Iterations = %d\n',iter)

SAP S/4HANA Financial and Treasury Functions

The following table details various aspects, components, and features related to SAP S/4HANA, particularly focusing on Cash Management and Treasury functions.