degree of freedom

简明释义

自由度

英英释义

例句

1.When conducting an ANOVA test, the degree of freedom 自由度 is crucial for determining the F-value.

在进行方差分析时，自由度对确定F值至关重要。

2.In robotics, each joint contributes to the overall degree of freedom 自由度 of the robot arm.

在机器人技术中，每个关节都对机器人臂的整体自由度做出贡献。

3.In statistical analysis, increasing the sample size can improve the degree of freedom 自由度 for more accurate results.

在统计分析中，增加样本量可以提高自由度以获得更准确的结果。

4.The degree of freedom 自由度 of a dataset affects the reliability of the regression analysis.

数据集的自由度影响回归分析的可靠性。

5.The degree of freedom 自由度 in a mechanical system determines how many independent movements are possible.

机械系统中的自由度决定了可能的独立运动数量。

作文

In the realm of statistics and science, the concept of degree of freedom is pivotal for understanding various phenomena. It refers to the number of independent values or quantities that can vary in a statistical calculation. Essentially, it provides insight into how much flexibility we have when estimating parameters or fitting models. For instance, in a simple linear regression model, the degree of freedom helps determine how many data points are free to vary after accounting for the constraints imposed by the model. This is crucial in hypothesis testing, where we need to know how many values are available to estimate variance and make inferences about populations.The importance of degree of freedom extends beyond statistics; it plays a significant role in physics and engineering as well. In mechanics, the degree of freedom refers to the number of independent movements a system can undergo. For example, a robot arm may have several joints, each contributing to its overall degree of freedom. The more joints there are, the more complex the movements can be, allowing for greater versatility in tasks such as manufacturing or surgery.Moreover, in social sciences, the degree of freedom can denote the extent to which individuals can act independently within a given structure or society. It reflects the level of autonomy that people possess in making choices and decisions. High degree of freedom in this context suggests that individuals have ample opportunities to express themselves and pursue their goals without oppressive restrictions. Conversely, a low degree of freedom may indicate a constrained environment where personal choices are limited by societal norms or regulations.In everyday life, we often encounter situations where the degree of freedom affects our decision-making processes. For instance, when choosing a career path, individuals weigh their options based on the degree of freedom they perceive in that field. Some professions offer a high degree of freedom, allowing for creativity and innovation, while others may impose strict guidelines and limitations. This awareness can significantly influence one's satisfaction and success in their chosen career.Furthermore, the degree of freedom can also relate to personal relationships. In healthy relationships, both partners should feel a sense of degree of freedom to express their thoughts and feelings openly. This mutual respect fosters trust and understanding, ultimately strengthening the bond between individuals. On the other hand, relationships that lack this degree of freedom may lead to resentment and conflict, as one or both parties may feel stifled or controlled.In conclusion, the concept of degree of freedom is multifaceted and applies to various disciplines, from statistics to personal relationships. Understanding this term allows us to appreciate the balance between constraints and independence in different contexts. Whether we are analyzing data, designing mechanical systems, or navigating social dynamics, recognizing the degree of freedom available to us can enhance our decision-making and foster a deeper understanding of the world around us.

在统计和科学领域，自由度这一概念对于理解各种现象至关重要。它指的是在统计计算中可以变化的独立值或数量的数量。本质上，它提供了对我们在估计参数或拟合模型时拥有多少灵活性的洞察。例如，在简单线性回归模型中，自由度有助于确定在考虑模型施加的约束后，有多少数据点是可以自由变化的。这在假设检验中至关重要，因为我们需要知道有多少值可用于估计方差并对总体做出推断。自由度的重要性不仅限于统计学；它在物理和工程领域也起着重要作用。在力学中，自由度指的是一个系统可以经历的独立运动的数量。例如，一个机器人手臂可能有多个关节，每个关节都对其整体自由度产生贡献。关节越多，运动越复杂，从而在制造或外科手术等任务中允许更大的灵活性。此外，在社会科学中，自由度可以表示个人在特定结构或社会中能够独立行动的程度。它反映了人们在做出选择和决策时所拥有的自主权。高自由度在这个背景下表明，个人有充足的机会在没有压迫性限制的情况下表达自己并追求自己的目标。相反，低自由度可能意味着一个受限的环境，在这个环境中，个人选择受到社会规范或法规的限制。在日常生活中，我们经常遇到自由度影响我们决策过程的情况。例如，在选择职业道路时，个人根据他们认为在该领域的自由度来权衡选项。一些职业提供高自由度，允许创造力和创新，而其他职业可能施加严格的指导方针和限制。这种意识可以显著影响一个人在所选职业中的满意度和成功。此外，自由度还可以与个人关系相关。在健康的关系中，双方都应该感到有自由度可以开放地表达他们的思想和感受。这种相互尊重促进了信任和理解，最终增强了个体之间的纽带。另一方面，缺乏这种自由度的关系可能导致怨恨和冲突，因为一方或双方可能会感到被压制或控制。总之，自由度这一概念是多方面的，适用于从统计学到个人关系的各种学科。理解这个术语使我们能够欣赏不同背景下约束与独立之间的平衡。无论我们是在分析数据、设计机械系统还是导航社会动态，认识到我们所拥有的自由度可以增强我们的决策能力，并加深我们对周围世界的理解。