Principal Component Analysis and Cluster Analysis
Principal Component Analysis (PCA)
PCA is a mathematical method that uses an orthogonal transformation to convert a set of correlated variables into uncorrelated variables called the principal components. The first component has the highest variance (it captures the most variation in the data), followed by the second, third, and so on. The components must be uncorrelated (remember orthogonal direction). Normalizing data becomes extremely important when the predictors are measured in different units.
Read MoreScientific Method: Concepts, Steps, and Data Representation
Name: Fabian Pinto
Values: Responsibility
Attitude: Interest
Grade: 8-B
Date: 26/8/14
Key Scientific Concepts
1. Experiments
An experiment is a methodical process carried out to verify, establish, or falsify the validity of a hypothesis.
2. Observation
Observation involves systematic and recordable accounts of information.
3. Hypothesis
A hypothesis is an explanation of a phenomenon that can be tested to prove or disprove it.
4. Variable
A variable is a value that can change depending on conditions or information
Understanding Dimensional and Geometric Tolerances in Manufacturing
Dimensional Tolerances
Dimensional tolerances define the acceptable variation in the dimensions of a manufactured part. They are crucial for ensuring that parts fit and function correctly together.
Key Definitions:
- Shaft: Any cylindrical or prismatic part designed to fit inside another element.
- Hole: Any prismatic or cylindrical housing into which a shaft is inserted.
- Dimension or Measure: A numerical value expressing length or angle.
- Nominal Dimension: The theoretical value of a dimension, used as a
Measurement Principles and Uncertainty in Metrology
Measurement Principles and Uncertainty
1. Definition of Measurement
Measurement is the process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity.
2. Uncorrected, Corrected, and Final Results
- Uncorrected Result: The result of a measurement before correction for systematic error.
- Corrected Result: The result of a measurement after correction for systematic error.
- Complete Result: The result of a measurement after correction for systematic error, accompanied
Data Preparation: Editing, Coding, and Cleansing
Data Editing
Information gathered during data collection may lack uniformity. For example, data collected through questionnaires and schedules may have answers that are not marked in the proper places, or some questions may be left unanswered. Sometimes, information may be given in a form that needs reconstruction into a category designed for analysis, such as converting daily or monthly income into annual income. The researcher has to decide how to edit it.
Editing also ensures that data are relevant
Read MoreEconometric Modeling and Statistical Analysis in Economics
Properties of the Error Term in OLS
In Ordinary Least Squares (OLS) regression, two key properties of the error term are:
- Zero Conditional Mean: The expected value of the error term (u) is zero, given any value of the explanatory variable(s). While we cannot predict the specific value of the error for a single observation, we assume its probability distribution averages to zero.
- Homoscedasticity: The variance of the error term is constant for all values of the explanatory variable(s). This means the