square sum of residues

简明释义

残差平方和

英英释义

例句

1.In statistical analysis, we often calculate the square sum of residues 残差平方和 to assess the model's fit.

在统计分析中，我们经常计算残差平方和 square sum of residues 来评估模型的拟合度。

2.When fitting a curve, we analyze the square sum of residues 残差平方和 to improve accuracy.

在拟合曲线时，我们分析残差平方和 square sum of residues 以提高准确性。

3.Minimizing the square sum of residues 残差平方和 is a common objective in optimization problems.

最小化残差平方和 square sum of residues 是优化问题中的一个常见目标。

4.The square sum of residues 残差平方和 can indicate whether our model is underfitting or overfitting the data.

残差平方和 square sum of residues 可以指示我们的模型是欠拟合还是过拟合数据。

5.The square sum of residues 残差平方和 helps in determining how well the regression line approximates the real data points.

残差平方和 square sum of residues 有助于确定回归线与真实数据点的拟合程度。

作文

In the realm of mathematics, particularly in number theory, the concept of residues plays a significant role. When we talk about the square sum of residues (残余的平方和), we are referring to a specific operation that involves squaring each residue and then summing these squared values. This operation can be applied in various contexts, such as modular arithmetic, where residues are the remainders left after division by a certain modulus. Understanding the square sum of residues (残余的平方和) not only deepens our grasp of mathematical principles but also opens up pathways to solving complex problems. To illustrate this concept, let’s consider a simple example. Suppose we are working with the modulus 5. The residues when dividing integers by 5 are 0, 1, 2, 3, and 4. If we were to compute the square sum of residues (残余的平方和), we would square each of these residues: - 0² = 0 - 1² = 1 - 2² = 4 - 3² = 9 - 4² = 16 Next, we sum these squared values: 0 + 1 + 4 + 9 + 16 = 30. Thus, the square sum of residues (残余的平方和) for the modulus 5 is 30. This seemingly simple calculation has profound implications in various fields such as cryptography, coding theory, and statistical analysis. In cryptography, for instance, the properties of residues and their squares are utilized to create secure encryption algorithms. The unpredictability of the square sum of residues (残余的平方和) can be harnessed to ensure that even if some information is intercepted, it remains incomprehensible without the proper decryption key. Moreover, in statistical analysis, the square sum of residues (残余的平方和) can be used in regression analysis to measure how well a model fits a set of data points. By calculating the squared differences between observed and predicted values, analysts can assess the accuracy of their models. A lower square sum of residues (残余的平方和) indicates a better fit, allowing researchers to make more reliable predictions based on their data. In conclusion, the square sum of residues (残余的平方和) is not just a mathematical curiosity; it is a powerful tool with wide-ranging applications. Whether in theoretical mathematics or practical applications like cryptography and statistics, understanding how to compute and utilize the square sum of residues (残余的平方和) can provide valuable insights and enhance problem-solving capabilities. As we continue to explore the depths of mathematics, concepts like these remind us of the intricate connections between numbers and their real-world implications.