covariances

简明释义

英[ˌkəʊvəˈraɪənsɪz]美[ˌkoʊvəˈraɪənsɪz]

n. [数]协方差；共分散（covariance 的复数形式）

英英释义

单词用法

同义词

反义词

例句

1.The matrix of covariances 协方差 is essential for understanding the spread of data in multivariate analysis.

在多变量分析中，covariances 协方差矩阵对于理解数据的分布至关重要。

2.Calculating the covariances 协方差 between stock returns can help investors diversify their portfolios.

计算股票收益之间的covariances 协方差可以帮助投资者实现投资组合的多样化。

3.In statistics, we often analyze the covariances 协方差 between different variables to understand their relationships.

在统计学中，我们经常分析不同变量之间的covariances 协方差以理解它们的关系。

4.The covariances 协方差 of the two datasets indicated a strong positive correlation.

这两个数据集的covariances 协方差显示出强正相关性。

5.Researchers often use covariances 协方差 to assess the impact of one variable on another.

研究人员通常使用covariances 协方差来评估一个变量对另一个变量的影响。

作文

In the field of statistics and data analysis, the term covariances refers to a measure that indicates the extent to which two random variables change in tandem. Understanding covariances is crucial for researchers and analysts who aim to identify relationships between different variables in their data sets. For instance, when studying the relationship between hours studied and exam scores, researchers may calculate the covariances to determine whether students who study more tend to score higher. This statistical measure helps in understanding how two variables can influence each other, providing insights that are essential for making informed decisions based on data.The concept of covariances can be further explained through its mathematical formulation. The covariance between two variables X and Y is calculated using the formula: Cov(X,Y) = E[(X - μ_X)(Y - μ_Y)], where E represents the expected value, and μ_X and μ_Y are the means of variables X and Y, respectively. A positive covariance indicates that as one variable increases, the other tends to increase as well, while a negative covariance suggests that an increase in one variable may lead to a decrease in the other. If the covariance is close to zero, it implies that there is little to no linear relationship between the variables.In practical applications, covariances play a significant role in various fields such as finance, economics, and social sciences. For example, in finance, investors often look at the covariances between different assets to construct diversified portfolios. By understanding how the returns of different stocks move together, investors can mitigate risks and optimize their investment strategies. Similarly, in economics, policymakers may analyze the covariances between economic indicators, such as inflation rates and unemployment rates, to make informed decisions that affect the economy as a whole.Moreover, the study of covariances extends beyond simple pairwise analysis. In multivariate statistics, the concept is expanded to consider the covariance matrix, which contains the covariances between all pairs of variables in a dataset. This matrix is fundamental in techniques such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), which are used for dimensionality reduction and classification tasks, respectively. By examining the covariance matrix, researchers can identify patterns and correlations among multiple variables, leading to deeper insights into the underlying structure of the data.In conclusion, the understanding of covariances is vital for anyone engaged in data analysis. Whether in academia or industry, knowing how to interpret and apply covariances can enhance the quality of research and decision-making processes. As data continues to grow in complexity, the ability to analyze covariances will remain an essential skill for extracting meaningful information from datasets. By mastering this concept, individuals can contribute significantly to their respective fields, leveraging data to drive innovation and improve outcomes.

在统计学和数据分析领域，术语协方差指的是一种度量，表示两个随机变量共同变化的程度。理解协方差对于研究人员和分析师来说至关重要，他们旨在识别数据集中不同变量之间的关系。例如，在研究学习时间与考试成绩之间的关系时，研究人员可能会计算协方差以确定学习更多的学生是否倾向于获得更高的分数。这一统计度量有助于理解两个变量如何相互影响，为基于数据做出明智决策提供了必要的见解。协方差的概念可以通过其数学公式进一步解释。两个变量X和Y之间的协方差通过以下公式计算：Cov(X,Y) = E[(X - μ_X)(Y - μ_Y)]，其中E代表期望值，μ_X和μ_Y分别是变量X和Y的均值。正的协方差表明，当一个变量增加时，另一个变量也倾向于增加，而负的协方差则表明一个变量的增加可能导致另一个变量的减少。如果协方差接近零，则意味着变量之间几乎没有线性关系。在实际应用中，协方差在金融、经济学和社会科学等多个领域发挥着重要作用。例如，在金融领域，投资者通常会查看不同资产之间的协方差来构建多样化的投资组合。通过了解不同股票的回报如何共同波动，投资者可以降低风险并优化投资策略。同样，在经济学中，政策制定者可能会分析经济指标之间的协方差，例如通货膨胀率和失业率，以做出影响整个经济的明智决策。此外，协方差的研究不仅限于简单的成对分析。在多元统计中，这个概念扩展到考虑协方差矩阵，该矩阵包含数据集中所有变量对之间的协方差。这个矩阵在主成分分析（PCA）和线性判别分析（LDA）等技术中是基础，这些技术用于降维和分类任务。通过检查协方差矩阵，研究人员可以识别多个变量之间的模式和相关性，从而深入洞察数据的潜在结构。总之，理解协方差对于从事数据分析的任何人来说都是至关重要的。无论是在学术界还是行业中，知道如何解释和应用协方差可以提高研究和决策过程的质量。随着数据复杂性的不断增长，分析协方差的能力将仍然是从数据集中提取有意义信息的基本技能。通过掌握这一概念，个人可以对各自的领域做出重要贡献，利用数据推动创新并改善结果。