estimated regression line

简明释义

估计回归线

英英释义

例句

1.The slope of the estimated regression line indicates how much the dependent variable changes with a one-unit change in the independent variable.

估计回归线的斜率表示自变量每改变一个单位，因变量变化的程度。

2.In our analysis, the estimated regression line helps predict future sales based on past trends.

在我们的分析中，估计回归线有助于根据过去的趋势预测未来的销售。

3.The estimated regression line can be used to assess the effectiveness of marketing strategies over time.

估计回归线可用于评估营销策略随时间的有效性。

4.The data points closely follow the estimated regression line, indicating a strong correlation between the variables.

数据点紧密跟随估计回归线，表明变量之间存在强相关性。

5.We plotted the estimated regression line on the scatter plot to visualize the relationship between height and weight.

我们在散点图上绘制了估计回归线，以可视化身高与体重之间的关系。

作文

In the field of statistics and data analysis, understanding relationships between variables is crucial. One of the essential tools used to analyze these relationships is the concept of an estimated regression line. This line represents the best fit through a set of data points on a graph, allowing researchers to make predictions and understand trends. The estimated regression line, or in Chinese, 估计回归线, is derived from a method called linear regression, which calculates the slope and intercept based on the given data. Linear regression assumes that there is a linear relationship between the independent variable (often denoted as X) and the dependent variable (denoted as Y). By plotting these variables on a Cartesian plane, the estimated regression line provides a visual representation of this relationship. For example, if we were to analyze the impact of study hours on exam scores, we would collect data on how many hours students studied and their corresponding scores. By applying linear regression, we can derive the estimated regression line that best fits our data points, helping us to predict exam scores based on study hours.The importance of the estimated regression line lies not only in its ability to provide predictions but also in its capacity to quantify the strength of the relationship between variables. The slope of the line indicates how much the dependent variable is expected to increase (or decrease) for each unit increase in the independent variable. In our study hours example, if the slope of the estimated regression line is positive, it suggests that more study hours lead to higher exam scores. Conversely, a negative slope would indicate an inverse relationship.Moreover, the estimated regression line can help identify outliers or anomalies in the data. Outliers are data points that deviate significantly from the trend established by the line. Recognizing these points is important as they can skew the results of the analysis, leading to inaccurate conclusions. By examining the estimated regression line and the distribution of data points around it, researchers can better understand the overall data set.In practical applications, the estimated regression line is widely used across various fields, including economics, psychology, and health sciences. For instance, economists may use it to model consumer behavior, while psychologists might apply it to understand the correlation between therapy duration and improvement in mental health. In public health, researchers could analyze the relationship between exercise frequency and overall well-being using the estimated regression line.In conclusion, the estimated regression line is a fundamental aspect of statistical analysis that aids in understanding the relationships between variables. It allows for predictions, quantifies relationships, and helps identify outliers, making it an invaluable tool in research. As we continue to collect and analyze data in various domains, mastering the concept of the estimated regression line will undoubtedly enhance our analytical capabilities and improve our decision-making processes.

在统计学和数据分析领域，理解变量之间的关系至关重要。用于分析这些关系的基本工具之一是“估计回归线”的概念。这条线表示通过一组数据点的最佳拟合，使研究人员能够进行预测并理解趋势。“估计回归线”源自一种称为线性回归的方法，该方法根据给定数据计算斜率和截距。线性回归假设自变量（通常用X表示）和因变量（用Y表示）之间存在线性关系。通过在笛卡尔平面上绘制这些变量，“估计回归线”提供了这种关系的可视化表示。例如，如果我们要分析学习时间对考试成绩的影响，我们将收集学生学习了多少小时及其对应的分数的数据。通过应用线性回归，我们可以得出最佳拟合我们数据点的“估计回归线”，这有助于我们根据学习时间预测考试成绩。“估计回归线”的重要性不仅在于它提供预测的能力，还在于它量化变量之间关系强度的能力。线的斜率表明自变量每增加一个单位，因变量预计会增加（或减少）多少。在我们的学习时间示例中，如果“估计回归线”的斜率是正的，这表明更多的学习时间会导致更高的考试成绩。相反，负斜率则表明存在反向关系。此外，“估计回归线”还可以帮助识别数据中的异常值或离群点。离群点是与线所建立的趋势显著偏离的数据点。识别这些点很重要，因为它们可能会扭曲分析结果，导致不准确的结论。通过检查“估计回归线”及其周围数据点的分布，研究人员可以更好地理解整个数据集。在实际应用中，“估计回归线”在经济学、心理学和健康科学等各个领域得到广泛使用。例如，经济学家可能会使用它来建模消费者行为，而心理学家可能会应用它来理解治疗时间与心理健康改善之间的相关性。在公共卫生领域，研究人员可以使用“估计回归线”分析运动频率与整体健康之间的关系。总之，“估计回归线”是统计分析的基本方面，有助于理解变量之间的关系。它允许进行预测，量化关系，并帮助识别离群点，使其成为研究中不可或缺的工具。随着我们继续在各个领域收集和分析数据，掌握“估计回归线”的概念无疑将增强我们的分析能力，提高我们的决策过程。