covariance

Covariance

Covariance 是一个统计学和概率论中的重要概念，通常用于描述两个随机变量之间的关系。它可以是名词形式，表示两个变量间的协方差值。该词没有形容词形式，但相关的形容词如“covariant”用于描述与协方差相关的情况。

词语辨析

在统计学中，covariance 和其它相似的概念（如correlation）有不同的含义。协方差是一个衡量两个变量如何一起变化的指标，而相关性则是标准化后的协方差，表示变量间的线性关系强度。

词汇扩充

• Variance (方差)：衡量单一变量的离散程度。
• Correlation (相关性)：标准化的协方差。
• Covariant (协变的)：与协方差相关的属性或变量。

近义词

No direct synonyms, but related terms include association (关联) and relationship (关系).

反义词

No direct antonyms, but one could argue that independence (独立性) is an opposite concept, as it suggests no relationship between variables.

柯林斯词典定义

Covariance is defined as a measure of the relationship between two variables, representing how much they change together.

牛津词典定义

Covariance refers to a statistical measure that indicates the extent to which two variables change in tandem.

用法

在数据分析、金融、工程等领域，covariance 被广泛应用于风险评估和模式识别。

例句

• The covariance between the two stocks is positive, indicating they tend to move together.

  这两只股票之间的协方差是正的，表明它们倾向于一起波动。

• Understanding covariance is crucial for portfolio diversification.

  理解协方差对于投资组合的多样化至关重要。

• Researchers often calculate the covariance to assess the relationship between variables.

  研究人员通常计算协方差来评估变量之间的关系。

• A high covariance value suggests a strong relationship between the two variables.

  高协方差值表明两个变量之间的关系很强。

• The covariance matrix is used in multivariate statistics.

  协方差矩阵用于多变量统计分析。

• To find the covariance, you need the means of both variables.

  要计算协方差，你需要两个变量的均值。

• The negative covariance indicates that the variables move in opposite directions.

  负的协方差表明变量朝相反方向移动。

• In finance, covariance helps in assessing the risk of asset pairs.

  在金融中，协方差有助于评估资产对的风险。

• The covariance of the dataset was calculated using Excel.

  数据集的协方差是通过Excel计算的。

• Positive covariance means that an increase in one variable will likely increase the other.

  正协方差意味着一个变量的增加可能会使另一个变量增加。

• When analyzing data, covariance provides insights into variable relationships.

  在分析数据时，协方差提供了变量关系的洞察。

• The covariance can be affected by the scale of the variables.

  协方差可能受到变量尺度的影响。

• In a regression analysis, covariance plays a crucial role.

  在回归分析中，协方差起着至关重要的作用。

• The formula for calculating covariance involves the mean of both variables.

  计算协方差的公式涉及两个变量的均值。

• Understanding the covariance helps in predictive modeling.

  理解协方差有助于预测建模。

• Different datasets can yield different covariance values.

  不同的数据集可能会产生不同的协方差值。

• In machine learning, covariance matrices are often used for dimensionality reduction.

  在机器学习中，协方差矩阵常用于降维。

• Analyzing covariance can help identify trends in data.

  分析协方差可以帮助识别数据中的趋势。

• High covariance is often a sign of a strong underlying relationship.

  高协方差通常是潜在强关系的迹象。