Statistics: Scope, Applications, and Techniques
Scope of Statistics
Through statistical analysis, business executives gain insights into market trends, customer demands, and purchasing patterns. This knowledge guides product development, marketing strategies, and customer relationship management, ensuring sustained growth and competitiveness.
Statistics is the discipline that concerns the interpretation, analysis, organization, collection, and presentation of data. The scope of Statistics is very immense, the application of statistics goes into
Read MoreFinancial Calculations and Analysis
2) Compound Interest
$1000 for 3 years at 10% per year compound interest F = P(1 + i)^N = 1000(1 + 0.10)^3 = $1331 | $1000 for one year at 1% per month: $1000(1.01)^12 = $1,126.83 | for one year at 12% annual: $1000(1.12) = 1,120 | at 0.2% per week three years 1000(1.002) 52*3 = 1,365.73 |
2) Bond Valuation
$1000 state govt. bond is issued in 1865. It carries an annual interest rate of 24%. How much is the fair market value of the bond 128 years late in 1993? Compound: 1000(1.24)^128 = 908 T Simple
Read MoreBest Management Practices and Timber Harvesting in the Southern US
Best Management Practices
BMPs are non-regulatory, but:
- Failure to apply voluntary BMPs could lead to mandatory forest practice laws later.
- Help maintain “public license.”
Voluntary BMPs are effectively mandatory in many states because of:
- Forest certification (SFI, SFC, Tree Farm)
- Professional certifications (Georgia master timber harvester)
- Tax incentives programs
- Timber sales on public land
- Water quality laws
SMZs:
- Perennial streams: 50 sq ft. basal area and 50% canopy cover.
- Intermittent streams: 25 sq
ANOVA, Chi-Square, and Non-Parametric Statistics: A Comprehensive Guide
Between: each participant goes through a level of the IV. 2-way participants exposed to one level or both IVs, 3-way etc..
Within (repeated measures): all participants exposed to all levels and combinations
1-way ANOVA (1 iv and 1 outcome/dv) : null= means are the same (same as t-test) Exp /omnibus/=they differ
You can manipulate more than one independent variable
and is an extension of t-test.
Pairwise t-tests can’t look at several independent variables
and inflate the Type I error rate. (FW
A Deep Dive into Subspaces, Vector Spaces, and Their Applications in Linear Algebra
What is a Subspace of R^n?
A set U of vectors in R^n is called a subspace of R^n if it satisfies the following properties:
- The zero vector 0-> ∈ U.
- If x-> ∈ U and y-> ∈ U, then x->+y-> ∈ U.
- If x-> ∈ U, then ax-> ∈ U for every real number a.
Any subspace of R^n other than {0} or R^n is called a proper subspace.
Why is a Plane Through the Origin a Subspace of R^3?
Every plane M through the origin in R^3 has equation ax + by + cz = 0 where a, b, and c are not all zero. Here
n-
Read MoreDeterminants, Eigenvalues, and Linear Dynamical Systems in Linear Algebra
Determinants and Invertibility
What is the Determinant of a Matrix?
The determinant of a matrix is a scalar value that provides information about the matrix’s invertibility. Only square matrices have determinants.
Calculating Determinants
For a 2×2 matrix A = [a b; c d], the determinant is calculated as det(A) = ad – bc.
For 3×3 matrices and larger, methods like cofactor expansion or row reduction are used.
Determinants and Row Operations
Elementary row operations affect the determinant as follows:
- Interchanging