The mathematical Marriage Predictor

回归方程的英文范文Regression EquationIntroduction:In statistics, regression analysis is a widely used method for modeling the relationship between a dependent variable and one or more independent variables. The regression equation is a mathematical expression that represents this relationship. It allows us to estimate the value of the dependent variable based on the values of the independent variables.Y=β0+β1X1+β2X2+...+βnXn+εWhere:- X1, X2, ..., Xn represent the independent variables, also known as the predictor variables or explanatory variables.- β0, β1, β2, ..., βn represent the regression coefficients, which quantify the impact of each independent variable on the dependent variable.- ε represents the error term, which accounts for unexplained variability in the dependent variable.Estimating Regression Coefficients:The OLS method calculates the regression coefficients in such a way that the predicted values generated by the regression equation are as close as possible to the observed values. Thisensures that the model captures the relationship between the variables accurately.Interpreting Regression Coefficients:The regression coefficients indicate the change in the dependent variable for a unit change in the corresponding independent variable, assuming all other independent variables remain constant.For example, β1 represents the change in Y for a one-unit increase in X1, holding X2, X3, ..., Xn constant. If β1 is positive, it suggests that Y tends to increase as X1 increases. Conversely, if β1 is n egative, it indicates that Y tends to decrease as X1 increases.The coefficient β0 represents the intercept of the regression line with the Y-axis, i.e., the estimated value of Y when all independent variables are set to zero. However, interpreting β0 may not always be meaningful, depending on the context of the analysis.Model Fit and Significance:In addition to estimating the regression coefficients, it is essential to assess the overall fit and significance of the regression model. This helps determine whether the model adequately captures the relationship between the variables.The goodness-of-fit measures, such as R-squared and adjusted R-squared, quantify the proportion of variance in the dependent variable explained by the independent variables. A higher R-squared indicates a better fit.Hypothesis tests, such as the F-test and t-tests, assess the statistical significance of the regression coefficients. If the p-values associated with these tests are below a predetermined significance level (e.g., 0.05), we can conclude that the coefficients are significantly different from zero, suggesting a relationship between the variables.Conclusion:In summary, the regression equation provides a concise representation of the relationship between a dependent variable and one or more independent variables. It allows us to estimate the value of the dependent variable based on the values of the independent variables.Understanding the regression coefficients and assessing the model fit and significance are crucial for interpreting the results correctly. Proper analysis and interpretation of the regression equation can help researchers and practitioners gain insights into the relationship between variables and make informed decisions based on the findings.。

婚姻的本质英语作文Marriage is a complex and multi-faceted institution that holds great significance in human society.At its core, marriage is about building a life together with a partner, sharing dreams, goals, and experiences. It is a union based on love, trust, and commitment.One of the essential aspects of marriage is companionship. Having a life partner to share the joys and challenges of life provides a sense of stability and support.Marriage also involves shared responsibilities, whether it's raising a family, managing finances, or supporting each other through different stages of life.Another important element of marriage is emotional connection. It means being able to understand, empathize, and support your partner on an emotional level.Communication plays a crucial role in a successful marriage. Open and honest communication helps build a strong foundation of trust and understanding.Marriage goes beyond the couple; it often involves extended family and community. It creates a network of support and connection.However, marriage isn't always easy. It comes with its own set of challenges and requires constant effort and dedication from both partners.Understanding the essence of marriage is crucial for building and maintaining a healthy and fulfilling relationship.Would you like to present this composition in a particular style, such as a summary, polished text, Zhihu-style, or a specific type of social media copy? Let me know your choice, and I'll create accordingly.。

英文回答：A nomogram is a visual representation of a statistical model that aids in the prediction of specific events. It is widely utilized in fields such as medicine, biology, and epidemiology for forecasting oues such as disease risk, mortality, and other clinical endpoints. This toolprises a set of variables or predictors, each apanied by a corresponding line that signifies its impact on the overall prediction. By aggregating the contributions of each variable, a cumulative point value is derived, which can then be transformed into a predicted probability. This facilitates the easyprehension and interpretation of the predictive model, rendering it an invaluable resource for both researchers and clinicians.名词图（英語：Nomogram）是帮助预测特定事件的统计模型的视觉表现。

它被广泛用于医学，生物学，流行病学等领域，用于预测疾病风险，逝去率，以及其他临床终点。

这个工具预示着一组变量或预测器，每个变量或预测器都有对应的线条，表示其对总体预测的影响。

双语阅读：数学公式助你找到真爱以下是小编整理的英语文章：数学公式助你找到真爱，希望能对大家的英语学习有帮助。

Mathematics is probably not a subject that many people find sexy, but it could hold the key to finding true love.数学对于许多人来说可能并不性感，但是它却是帮你找到真爱的关键。

Mathematicians have developed a series of theories that can help people find the perfect partner.数学家们推理出一系列定理来帮助人们找到完美的另一半。

These include tips such as not trying to hide the less attractive parts of your appearance in your online dating profile pictures and looking for people who had fewer colds as a child.这些定理小贴士包括：不要试图在自己在线约会的简历上掩盖自己的外在不足;寻找儿时很少感冒的对象。

They have also proposed mathematical approaches to finding the perfect wife or husband - by not choosing to settle down until after the age of 22 years old.他们同时用数学方法建议大家，要寻找完美的老公或老婆，请不要在22岁前稳定下来。

Dr Hannah Fry, a lecturer at University College London and author of a new book on The Mathematics of Love, outlined the theories at the Oxford Literary Festival.Hannah Fry博士，来自伦敦学院大学的学者，同时也是这本名为《爱情数学》的新书作者，在牛津文化节上罗列了一系列的定理。

数学家发明求婚公式算出最Fiancee Formula 求婚公式佳求婚时间Worried your boyfriend is never going to propose? Then buy him a calculator. Mathematicians have come up with a 'fiancee formula' that allows men to work out the perfect time to pop the question.All he needs is the age he would first consider marrying and hiscut-off point- an d the equation does the rest.Maths professor Anthony Dooley said: 'Applying maths to matters of the heart is al ways dangerous. In life you are dealing with emotions and have to think much har der.'But if you want to work out the right moment to start getting serious, this gives you a mathematical framework.'The formula is based on a statistical technique known as optimal stopping - or the best time to do something.Writing in the third person, he said: 'As for the author, he can tell you that, looki ng back and doing some calculations, he did follow the marriage solution, albeit by accident, and it has worked out perfectly.'The formula was devised with men in mind but could equally apply to women, incl uding those uncertain about whether to accept a proposal. It could also help nervo us men calculate when to avoid the ultimate commitment.But those who find they have passed the optimal age for proposing should not pa nic - simply pop the question to the next good prospect who comes along. Professor Dooley, of New South Wales University in Sydney, added: 'Probability isn' t the most romantic basis for a marriage but while the formula won't fit everyone it does seem to fit a lot of couples, whether through accident or design.'担心男友不向你求婚？给他买个计算器吧！日前，数学家研究出一个“求婚公式”，让男士们可以计算出求婚的最佳时间。

Almost 50 years ago, psychiatrists Richard Rahe and Thomas Holmes developed an inventory of the most distressing human experiences that we could have. Number one on the list? Death of a spouse. Number two, divorce. Three, marital separation. Now, generally, but not always, for those three to occur, we need what comes in number seven on the list, which is marriage.差不多五十年前，精神病学家理查德·赖特和托马斯·赫姆斯列出了一份清单，包含了我们所能拥有的最痛苦的人类经历。

排名第一的是配偶的去世。

第二：离婚。

第三：婚内分居。

通常是这样，但并非总是如此，要让这三件事情发生，我们需要先实现名单上的第七条，也就是婚姻。

Fourth on the list is imprisonment in an institution. Now, some say number seven has been counted twice.名单上的第四条是在监狱里被监禁。

有人会说第七条已经算了两次。

（译者注：将婚姻比做囚牢）I don't believe that.对此我并不认同。

When the life stress inventory was built, back then, a long-term relationship pretty much equated to a marriage. Not so now. So for the purposes of this talk, I'm going to be including de facto relationships, common-law marriages and same-sex marriages, or same-sex relationships soon to become marriages. And I can say from my work with same-sex couples, the principles I'm about to talk about are no different. They're the same across all relationships.在这份生活压力清单诞生的那个年代，一个长期的关系几乎等同于婚姻。

寻找最佳伴侣——数学原理下的稳定最优配对方式1我们大概都经历过这种情况, 你对班上几位女生(或者男生) 有意思, 但是不知道他们是否对你有意. 让情况更复杂的是, 你对这些女孩子们的兴趣不是平等的. 如果可能, 你希望能够跟你首选的姑娘约会, 不行的话, 你希望能够约到排名第二的, 并以此类推. 使情况进一步复杂的是, 不光你对姑娘们感兴趣, 班上的其他男生也对姑娘们感兴趣, 但是你也不知道他们心中的排名.如果你是一位善意的班主任, 希望帮孩子们解决这个配对的难题, 你应该怎么做呢? (提示: 一些数学算法的知识会对你有用.) 2配对自古就是人们热衷, 但又没有好的办法解决的难题. 随之应运而生的有月老, 红娘, 婚姻介绍所, 以及现在的婚恋网站, 电视相亲等. 这个难题凸显在婚恋市场, 但是不局限于此, 国外大学申请, 找工作等等众多的人类行为中都能遇到它.这个难题甚至自成一个学术领域, 在经济学上隶属于market design (市场设计) 的研究, 因为市场就是要把最合适的买家和卖家配对. 2012年获得诺贝尔经济学奖的美国经济学家 Alvin Roth 就专门研究这个领域[1]. 他不仅仅在学术研究上有建树, 更是把学术研究的成果付诸于实际应用. 他曾经改造了美国纽约市初中升高中的申请系统[2], 一年中, 使得没有被分配到学校的初中毕业生的数量下降了90%. 他所使用的, 就是 deferred acceptance algorithm (推迟接受算法). 这个算法是怎么工作的呢?3我们还是以开篇的那个例子来说明. 传统的做法(被称为immediate acceptance, 即”立即接受法”), 是大家都去追自己最心仪的女生. 而这个女生面对几位追求者, 要立刻做个决定. 被拒绝的男生们调整一下心情, 再去追求心中的 No. 2. 以此类推. (当然, 这模型是非常简化了的.)这样做法有一个严重的问题: 当你被你的No. 1 拒绝后, 再去追求你的 No. 2 的时候, 你心中的No.2 可能已经在第一轮中选择了其他人. 但坑爹的是, 有可能你正是你心中No.2 心中的No.1, 但是她并不知道. 所以她在第一轮中, 因为没有被你追求, 而屈就他人. 比及你在第一轮中表白失败, 再去找你的No.2 时, 已然晚矣.形容的有点混乱哈. 我从新描述一下. 假设班上三男(分别是A, B, C), 三女 (分别是x, y, z), 见下图:图一: 班上三男三女他们心中对异性的排名见图二.图二: 各位男女生对异性的排名第一轮中, 男生们向心中的No. 1女示好, 即A, B 两男向心中最喜欢的x女示好, 而C男向y女示好.图三: 第一轮中, 各自向心中的 No. 1 示爱如果采用immediate acceptance, 此轮之后的结果是, x-A, y-C 两对结成情侣. 注意, y 女虽然心中首选是B男, 但是由于B男在此轮中正在追逐x女, 无奈下y女屈就于唯一来献殷勤的C男. 比及第二轮开始时, 唯一还 available 的就是z女了.图四: 传统配对方法的结果 (拆散多少天造地设的情侣)最后的结果是 x-A, y-C, z-B 三对恋人. 注意: y女和B男两人都更愿意离开自己的现任伴侣而彼此在一起. 这种不稳定的状态就是很多文学影视作品的来源哈. 在数学上, 这也恰恰被称为是”不稳定”(unstable)的组合. 顾名思义, 我们希望能够有种算法, 给我们的结果是所有配对都是稳定的.4作为班主任的你, 这时候就会想到(如果你学习了比如Gale 和Shapley 这篇刊登于1962年1月美国数学月刊的经典论文的话[3]), 你就会想到这是一个呼唤你采用 deferred acceptance algorithm 的课题. 你会让同学们这么做:每个男生在第一轮中向自己心中的No. 1 示爱. 但是各位姑娘们不用立即决定(所以该方法名称中有”deferred”一词), 而是先hold 住了. 在第二轮中, 每个男生再向心中的 No. 2 示爱. 从第二轮开始, 每位姑娘们只保留自己到现在为止所收获的最心仪的男生(但是不用答应他, 只hold在心理), 而拒绝其他所有人. 而被拒绝的男生(也就是现在尚没有人hold着你的男生) 则继续在下一轮中向心中排名的下一个姑娘表白. 以此类推, 一轮轮继续下去, 直到所有想示爱的男生都示完为止. 此时, 每个手中有 offer 的姑娘, 可以选择接受.以上就是deferred acceptance algorithm 的做法. 大家算一下, 就会发现, 在我们这个简单的例子中, 最后的结果是 x-A, y-B, z-C 三组恋人终成眷侣. 而这是一个 stable 的结果. 所有6人中, 你不可能找到一男一女符合以下条件: 他们都更愿意抛弃已有的伴侣而与彼此在一起.图五: 运用'推迟接受'算法得到的理想结果5Deferred acceptance algorithm 能够从数学上证明是一定会产生 stable 配对的算法. 这使它成为一个重要的工具, 因为这类的配对问题在现实生活中太常见了. 申请过美国大学的同学们都知道, 美国大学的申请和录取, 也是一个寻求最佳配对的问题. 不同的是, 婚恋中的配对是一对一, 而大学的录取是一对多(可以用一个类似deferred acceptance algorithm 的算法解决).配对问题在医疗中也有应用. Roth 的一大贡献就是在美国建立了肾脏移植交换所 (kidney exchange). 他的算法使原来没有机会得到肾脏移植手术的病人能够有机会接受手术[4].数学是个越学越觉得神奇的东西. 治病救人, 成人之美.最后，给大家3道思考题，从易到难分别是：1）deferred acceptance algorithm 是一定会结束的吗？换句话说，是否这个过程会无止境的进行下去？2）如果所有配对都是稳定组合，我们把这结果叫做稳定结果。