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

Data Collection Definitions

• Primary data: Data personally collected by you. Examples include traffic counts, pedestrian counts, environmental indexes, questionnaires, or land use surveys.
• Secondary data: Data collected by someone else. This can be found in books, on the internet, or in academic journals.
• Census: A detailed, compulsory survey carried out by nearly all countries every 10 years.

Primary Data Analysis

Advantages

• It is up to date (current).
• You know how the data has been collected.
• Includes data relevant to coursework.
• Only covers your study area.
• Collected in the format that you want.

Disadvantages

• Data may include personal bias.
• Collection can be time-consuming.
• Can be expensive to collect.
• Hard to study temporal changes.
• Some data might be unavailable

1. The t-test is never valid if the sample size is small, say less than 30. (TRUE OR FALSE)

It can be valid if the sample is approximately normal.

2. The results of an observational study indicate that people who use vitamin supplements get fewer colds than people who don't. However, we can't conclude that vitamin supplements prevent colds because this type of study does not allow us to infer causation. (TRUE OR FALSE)

Only experimental designs can infer causation because it allows us to create treatment groups that are very similar.

3. A survey was administered to a random sample of college students. Both males and females were surveyed, and one question asked was "How much are you willing to spend on a stereo system (in dollars)?" An analysis

Polygon Interior Angles Theorem

The sum of the measures of interior angles of an n-gon is (n-2)x180

Interior angles of a quadrilateral:

The sum of the measures of the interior angles of a quadrilateral is 360^o

Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.

Angles have to measure up to 360. 360/n (n=#of sides)

Theorems

If a quadrilateral is a parallelogram, then its opposite sides are congruent

If a quadrilateral is a parallelogram, then its opposite angles are congruent

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary

If a quadrilateral is a parallelogram, then its diagonal bisects each other

If both pairs of opposite sides of a quadrilateral

Econometric Notation: Residuals and Estimates

Residuals are denoted by e (Sample Regression Function, SRF) and the true error term by u (Population Regression Function, PRF).

• Coefficients: Estimated coefficients (e.g., $\hat{\beta}_0$ and $\hat{\beta}_1$) in the SRF are denoted with hats (caps). True coefficients ($\beta_0, \beta_1$) in the PRF are without hats.
• Dependent Variable: The predicted value $\hat{Y}_t$ (the value derived from the regression equation without the residual) is denoted with a hat. The actual observed value $Y_t$ (which includes the residual or error term) is without a hat.

Fundamentals of Hypothesis Testing

Hypothesis testing makes inferences about the validity of specific economic (or other) theories from a sample of the... Continue reading "Econometric Hypothesis Testing and Regression Model Specification" »

MATLAB Cable Tension and Cost Optimization

This script calculates cable tensions and optimizes costs for a structural system by iterating through coordinate positions.

Initialization

ACMatrix = zeros(51,51);
ABMatrix = zeros(51,51);
ADMatrix = zeros(51,51);
CostMatrix = zeros(51,51);
countery = 0;
MinCost = 1;

A = [6 2 1]';
B = [3.5 0 -0.5]';
D = [0 -1 5.5]';
F = -[160 20 -30]';

rab = B - A;
rad = D - A;
ead = rad/norm(rad);
eab = rab/norm(rab);

Iterative Calculation

The following loop calculates tensions and costs across a range of Y and Z coordinates:

• C: Point position of the system.
• Tensions: Solved using the unit vector matrix.
• Cost: Calculated based on cable length and tension.

for y = 1:.1:6
    countery = countery + 1;
    counterz = 0;

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Cost Tool Information

The Cost Tool provides the following information:

• Manufacturer
• Overall Cost (Total)
• Profit Percentage
• Overall Weight
• SKU Number
• Shipping Location (Town and State)

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Discount Guidelines

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Accounting Fundamentals: Key Concepts & Transactions

Essential Accounting Terminology

Core Concepts

• Accounting: Practice, activity, action.
• Accountancy: Theory, technique.
• Accountant: Person, profession.
• Account: Record, ledger, report, put the $ on.

Key Roles and Statements

Roles

• CFO: Chief Financial Officer.
• Accountant
• Bookkeeper

Financial Statements

• Balance Sheet: Financial statement showing the financial situation of the company.
• Profit & Loss Statement: Financial statement to show the profit earned or losses incurred in a determinate period.

Debits, Credits, and Balances

• DEBIT: When you move the $ out.
• CREDIT: Transfer the $ to another account.
• To Debit Account: To take $ out of account.

Assets and Liabilities

Assets

• Assets: Any property owned by a person or firm.
• Intangible Asset: Asset that you cannot

What is Statistics?

Statistics is a set of tools designed to analyze data and deduce information about a population from a given sample.

The Three-Step Process of Statistics

1. Sampling and Design of the Experiment: Take a sample (or many) from the population, make observations about the sample, and turn them into numerical data.
2. Descriptive Statistics: Analyze the data to get information about the sample.
3. Statistical Inference: From the data, deduce information about the whole population.

Context is Crucial

The context of a statistical study is crucial in interpreting the results. A population is a set of individuals (people, cases, etc.) that we want to analyze. A sample is a subset of the population. A variable is an aspect or characteristic of the... Continue reading "Statistics: A Guide to Data Analysis and Population Inference" »

Frequency Tables for Data Organization

A frequency table is the easiest way to organize data. To construct a frequency table from the data, essentially we have to count how many times each event occurs among the data. Depending on the type of variable, we can add more or less information to the frequency table.

• Absolute frequency: Count how many times each value appears in the table.
• Relative frequency: Count how many times each value appears in the table, divided by the size of the sample.
• Cumulative absolute frequency: The sum of all previous absolute frequencies (e.g., how many people own 3 cars or less?).
• Cumulative relative frequency: The sum of all previous relative frequencies (e.g., what proportion of people own 3 cars or less?).

Discrete