degree of freedom

简明释义

自由度

英英释义

例句

1.In this regression model, the degree of freedom 自由度 is equal to the number of observations minus one.

在这个回归模型中，自由度 degree of freedom 等于观察值的数量减去一。

2.The degree of freedom 自由度 of a t-distribution is crucial for determining critical values.

t分布的 自由度 degree of freedom 对于确定临界值至关重要。

3.When designing an experiment, it's important to calculate the degree of freedom 自由度 to determine the validity of your results.

在设计实验时，计算 自由度 degree of freedom 对于确定结果的有效性非常重要。

4.In statistical analysis, the number of independent values that can vary in an analysis is known as the degree of freedom 自由度.

在统计分析中，可以在分析中变化的独立值的数量被称为 自由度 degree of freedom.

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

机械系统中的 自由度 degree of freedom 决定了可能的运动数量。

作文

In the realm of science and mathematics, the concept of degree of freedom plays a crucial role in understanding various phenomena. Essentially, degree of freedom refers to the number of independent parameters or variables that can vary in a system without violating any constraints. This idea is prevalent in fields such as physics, statistics, and engineering, where it helps in analyzing systems and making predictions.For instance, consider a simple mechanical system like a pendulum. The pendulum can swing back and forth, and its motion can be described by several variables, such as the angle of displacement, the length of the string, and the mass of the bob. However, not all of these variables are independent. The length of the string is fixed, which means it does not contribute to the degree of freedom of the system. In this case, the degree of freedom would be one, as there is only one independent variable that can change—the angle of displacement.In statistics, the concept of degree of freedom is equally significant. When performing hypothesis tests or constructing confidence intervals, the degree of freedom affects the critical values from statistical distributions. For example, when estimating the variance of a sample, the formula includes a term that accounts for the degree of freedom. Specifically, if you have a sample size of n, the degree of freedom for variance estimation is n - 1. This adjustment is necessary because one parameter (the sample mean) is estimated from the data, thus reducing the number of independent pieces of information available.Moreover, in the context of social sciences, the degree of freedom can refer to the flexibility individuals or groups have in making choices or decisions. For example, a society with high degree of freedom allows its citizens to express their opinions, make personal choices, and pursue various paths without excessive restrictions. This sociopolitical aspect of degree of freedom highlights the importance of autonomy and self-determination in human behavior and societal development.Understanding the degree of freedom in various contexts enhances our ability to analyze complex systems effectively. In engineering design, for instance, knowing the degree of freedom helps engineers create structures that can withstand forces while maintaining stability. Similarly, in data analysis, recognizing the degree of freedom allows researchers to draw more accurate conclusions from their findings.In summary, the concept of degree of freedom is multifaceted and applicable across different disciplines. Whether in physics, statistics, or social sciences, it provides valuable insights into the behavior of systems and the limitations imposed by constraints. By grasping the nuances of degree of freedom, we can improve our analytical skills and foster a deeper understanding of the world around us. As we continue to explore new realms of knowledge, the significance of degree of freedom will undoubtedly remain a fundamental aspect of our inquiries and discoveries.

在科学和数学的领域中，自由度的概念在理解各种现象中起着至关重要的作用。本质上，自由度是指在不违反任何约束条件的情况下，系统中可以变化的独立参数或变量的数量。这个思想在物理学、统计学和工程等领域普遍存在，它帮助分析系统并做出预测。例如，考虑一个简单的机械系统，如摆。摆可以前后摆动，它的运动可以通过几个变量来描述，例如位移角、绳子的长度和摆锤的质量。然而，并不是所有这些变量都是独立的。绳子的长度是固定的，这意味着它不对系统的自由度产生影响。在这种情况下，自由度将为1，因为只有一个独立变量可以改变——位移角。在统计学中，自由度的概念同样重要。当进行假设检验或构建置信区间时，自由度会影响统计分布的临界值。例如，在估计样本方差时，公式中包含一个考虑自由度的项。具体来说，如果你有一个样本大小为n，则用于方差估计的自由度为n - 1。这个调整是必要的，因为一个参数（样本均值）是从数据中估计出来的，从而减少了可用的独立信息的数量。此外，在社会科学的背景下，自由度可以指个人或群体在做出选择或决策时的灵活性。例如，一个具有高自由度的社会允许其公民表达意见、做出个人选择，并在没有过多限制的情况下追求各种道路。这种自由度的社会政治方面突显了自主权和自我决策在人类行为和社会发展中的重要性。理解各种背景下的自由度增强了我们有效分析复杂系统的能力。在工程设计中，了解自由度帮助工程师创建能够承受力量同时保持稳定的结构。同样，在数据分析中，认识到自由度使研究人员能够从他们的发现中得出更准确的结论。总之，自由度的概念是多方面的，适用于不同的学科。无论是在物理学、统计学还是社会科学中，它都提供了对系统行为和约束所施加限制的宝贵见解。通过掌握自由度的细微差别，我们可以提高我们的分析能力，并加深对周围世界的理解。随着我们继续探索新的知识领域，自由度的重要性无疑将始终是我们探究和发现的基本方面。