doorMarco Taboga, PhD
Een ontwerpmatrix is eenMatrixmet gegevens over meerdere kenmerken van meerdere personen of objecten. Elke rij komt overeen met een individu en elke kolom met een kenmerk.
De ontwerpmatrix is een fundamenteel wiskundig object in regressieanalyse, bijvoorbeeld inlineaire regressiemodellenen inlogit-modellen. Het wordt vaak aangeduid met een hoofdletter
.
Inhoudsopgave
Voorbeelden
Hoe de ontwerpmatrix wordt gedefinieerd in lineaire regressies
Rang van de ontwerpmatrix
(Video) #TheIdentityRe-designMatrix #EnterTheMatrix designer Identitieies for the futureMeer details
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Voorbeelden
We geven hier enkele voorbeelden van ontwerpmatrices.
VoorbeeldAls we de lengte en het gewicht van vijf individuen meten, kunnen we de metingen verzamelen in een ontwerpmatrix met vijf rijen en twee kolommen. Elke rij komt overeen met een van de tien individuen, de eerste kolom bevat de lengtemetingen en de tweede vermeldt de gewichten:
waargeeft de hoogte van de-de individuele enhaar gewicht.
VoorbeeldAls we de gegevens over het bruto binnenlands product (bbp) van vier landen in drie opeenvolgende jaren verzamelen, dan is de ontwerpmatrix deMatrix
waar bijv.is het BBP van het derde land in het tweede jaar.
Hoe de ontwerpmatrix wordt gedefinieerd in lineaire regressies
Beschouw de lineaire regressie
waaris de afhankelijke variabele,is eenvector die deverklarende variabelen (regressors),is een
vector van regressiecoëfficiënten,is de foutterm en die zijn erobservaties (
).
Zo observeren wekenmerken, vervat in de vector van regressors, voor elk van dewaarnemingen.
Alle waarnemingen kunnen worden verzameld in de ontwerpmatrix
waarduidt de-de ingang van de vector, dat is de-de regressor.
We kunnen op dezelfde manier de observaties van de afhankelijke variabele en de fouttermen in tweeën stapelen
vectoren:
De ontwerpmatrix hebben gedefinieerden de twee vectorenEn, kunnen we de regressievergelijkingen in matrixvorm schrijven:
Hierdoor kunnen we gebruikenmatrixalgebraom een schatter van de regressiecoëfficiënten te vinden(zie delezing over lineaire regressieom te zien hoe).
Rang van de ontwerpmatrix
In de meeste statistische modellen is de ontwerpmatrix vereistvolledige rang, dat wil zeggen, de kolommen moeten zijnlineair onafhankelijk(zie bijv. denormaal lineair regressiemodel). Wanneer aan deze eis niet wordt voldaan, spreken we van multicollineariteit in de ontwerpmatrix (ziedeze lezingvoor details).
Er zijn echter ook regressiemodellen waarbij de ontwerpmatrix rang-deficiënt kan zijn (d.w.z. niet volledig gerangschikt), bijvoorbeeld deRidge-regressiemodel.
Meer details
Zie de lezing oplineaire regressiemodellenvoor meer details.
Blijf de woordenlijst lezen
Vorige invoer:Cross-covariantiematrix
Volgende invoer:Discrete willekeurige variabele
Hoe te citeren
Graag citeren als:
Taboga, Marco (2021). "Ontwerpmatrix", Lezingen over kansrekening en wiskundige statistiek. Kindle Directe publicatie. Online bijlage. https://www.statlect.com/glossary/design-matrix.
FAQs
How does a competitive matrix help determine a competitive advantage for a business? ›
Competitive matrices are used to facilitate the process of comparing your business with other industry competitors. They help you take advantage of strengths and opportunities, while identifying weaknesses and threats before they become detrimental.
How do you prepare a competitive matrix? ›- List the features of your brand. In a lefthand column of your competitive matrix, you can list factors you use to target customers, such as: ...
- List the competitors of your brand. ...
- Rank your brand against your competitors.
The score is the result of weight multiplied by rating. Each company receives a score on each factor. Total score is simply the sum of all individual score for the company. The firm that receives the highest total score is relatively stronger than its competitors.
What is a competitor pricing matrix? ›Competitive positioning matrix
If you're analyzing price and quality, you'll place low price and low quality on the lower left, and high price and high quality on the upper right. The other two quadrants will be low price and high quality, and high price and low quality.
To measure your competitive advantage, you need to use metrics and benchmarks that reflect your goals and performance. For example, you can use market share, customer satisfaction, retention, loyalty, profitability or growth as indicators of your competitive position.
What is the purpose of the competition matrix? ›A competitive matrix is an analysis tool that helps you establish your company's competitive advantage. It provides an easy-to-read portrait of your competitive landscape and your position in the marketplace. The matrix can be just a simple chart.
What are the key success factors matrix? ›- Product range and quality.
- Customer service.
- Brand equity and reputation.
- Marketing and innovation.
- Management and HR competency.
However, critical success factors in a CPM include both internal and external issues; therefore, the ratings refer to strengths and weaknesses, where 4 = major strength, 3 = minor strength, 2 = minor weakness, and 1 = major weakness.
Why is the competitive profile matrix important? ›The matrix identifies a firm's key competitors and compares them using industry's critical success factors. The analysis also reveals company's relative strengths and weaknesses against its competitors, so a company would know, which areas it should improve and, which areas to protect.
What is an average competitive profile matrix? ›The average weighted score for CPM matrix is 2.5 any company total weighted score fall below 2.5 consider as weak. The company total weighted score higher then 2.5 is consider as strong in position. The other dimension of CPM is the firm with higher total weighted score considered as the winner among the competitors.
How to analyze CPM matrix? ›
The Competitive Profile Matrix
The first step is to draw up a list of critical success factors in your industry. These might include pricing, market share, brand reputation, a strong online presence, customer loyalty and a wide range of products. The exact list will vary depending on your industry, Marketing91 says.
Scoring competitors is often subjective. Once you have finished scoring every competitor for every critical success factor, you need to multiply the weight of each attribute by the score given to each competitor in the CPM. The result of this calculation will give you the weighted score for each competitor.
What are the three types of competitive pricing strategy explain? ›The three main types of competitive pricing are: Low price - When you set the prices lower than your competitors. High price - When you set the prices higher than your competitors. Matched price - When you align your prices with your competitors.
How do you calculate competitors pricing? ›You take the price of your product, divide it by the average competitor market price, and multiply that by 100. You should have one of these three results. If it is over 100, that means your product has a higher price than your competitors. If it is 100, that means your product has the same price as your competitors.
What is the advantage of competitive advantage in the business? ›The purpose of having a competitive advantage is to distinguish a company from its competitors by offering something different and of superior value to its customers. Competitive advantage also means the business can outperform its competition in the market and make a higher profit.
In what ways does a competitive advantage benefit a business? ›A competitive advantage is what sets a company apart from its competitors, in the eyes of its consumers. These advantages allow a company to achieve and maintain superior margins, a better growth profile, or greater loyalty among current customers.
What are competitive advantage factors in space matrix? ›- Market share (small to large) ...
- Product quality (inferior to superior) ...
- Product life cycle (late to early) ...
- Product replacement cycle (variable to fixed) ...
- Customer loyalty (low to high) ...
- Competition's capacity utilisation (low to high) ...
- Technological know-how (low to high)