Understanding Statistical Significance and Portfolio Diversification in Finance
Understanding Statistical Significance in Regression Analysis
Recall that the probability of rejecting a correct null hypothesis is equal to the size of the test, denoted α. The possibility of rejecting a correct null hypothesis arises from the fact that test statistics are assumed to follow a random distribution, and hence they will take on extreme values that fall in the rejection region some of the time by chance alone. A consequence of this is that it will almost always be possible to find significant
Proof of Triangle Congruence: SAS Postulate
Theorem 8: Triangle Congruence via SAS Postulate
Statements
- In \( \triangle ABC \leftrightarrow \triangle GET \)
- i) \( BC = WE \)
- ii) \( \angle B = \angle GET \)
- iii) \( BA = GE \)
Understanding Lines and Angles in Analytic Geometry
Length of a Segment from a Point to a Line
The shortest distance from a point P (x1, y1) to a line Ax + By + C = 0 is given by the following expression:
In this expression, (x,y) represent the point from which we want to measure the distance, and A, B, and C are the coefficients of the line.
The conditions to consider are the following:
- If the value of C is not equal to 0, the sign of the radical is the opposite of C.
- If C=0 and B is not equal to 0, the radical will have the same sign as B.
- If C=B=0,
Understanding Surveying Levels and Measurement Errors
Components of a Surveying Level
The image below illustrates the components of a typical surveying level:
- Ocular
- Reticulum Focus
- Image Focus
- ASA (presumably a brand or model designation) dismantled, with screws
- RS232 serial interface
- Leveling mechanism
- Screw
- Lens with electronic distance meter (EDM) integrated
- Exit measurement beam
- Display
- Spherical level
- Keyboard
- Trigger button
- Switch
- Fine measurement, horizontal
Types of Surveying Levels
Levels can be classified as follows:
- Tilt Levels: These levels are adjusted
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