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Difference between Space and Subspace
This tutorial explains the difference between space and subspace. What is space? The most simple example of space is the two-dimensional space, \( \mathbb{R}^2 \). You can visualize it as the xy-coordinate plane. \( \mathbb{R}^2 \) is a vector space...
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Linear Subspace
A linear subspace or vector subspace is a vector space that is a subset of some larger vector space. To be considered a linear subspace, a vector set needs to meet the following 3 requirements. For instance, if we say...
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Vector and Arrow in Space
This tutorial provides examples to explain vectors and arrows in space (vector visualization). It includes 2 and 3-dimension vectors as well as vector addition and subtraction. Example 1: 2 dimension vectors \( \vec{V_1} =(3, 2 ) = \left[\begin{array}{ccc}3\\2 \end{array}\right]\) Note...
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Orthonormal Vectors: Definitions and Examples
Two Orthogonal Vectors Definition: Two vectors are orthogonal if they are perpendicular to each other. That is, the dot product of the two vectors is zero. The following is an example of two orthonormal vectors. \( \vec{V_1} =\left[\begin{array}{ccc}1\\0\\-1\end{array}\right]\), \( \vec{V_2}...
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Changing Reference Level in Dummy Coding in R
You can change the reference level in dummy coding in R by using the following R code. contr.treatment(total_levels, base = Number_reference_level) Step 1: Prepare Data The following R code generates a sample data. X Y 1 1 -0.56047565 2 2...
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Dummy and Contrast Codings in R
“Dummy” or “treatment” coding is to create dichotomous variables where each level of the categorical variable is contrasted to a specified reference level. Basic Syntax of Dummy and Contrast Coding 1. Dummy Coding The following is the syntax to do dummy...
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Quartile: Definition and Example
Definition of Quartile A quartile is a statistic describing how a set of data points are divided into 4 groups. Quartiles split a set of data by using 3 points: the lower quartile (Q1), the median (Q2), and the upper...
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Difference between Descriptive Statistics and Inferential Statistics
Descriptive statistics aim to summarize the characteristics of a given data set. In contrast, inferential statistics aim to use a sample of data to draw inferences about the whole population (i.e., hypothesis testing). Types of Descriptive Statistics 1. Measures of Central Tendency...
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Difference between Sample and Population
A population is the entire group of individuals about whom you want to draw conclusions. In contrast, a sample is the subset of the same entire group. Example 1 of sample and population You would like to study if students like...
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Calculate Population Variance in Excel
You can use the VARP, VAR.P, or VARPA functions in Excel to calculate population variance. Data Example The following is the data example for population variance. Example of VARP() Type =VARP(B2:B12) in a cell in Excel to calculate population variance. The population variance is 46.23. Example...
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