# 微积分作业代写calclulus代考| Method of least squares

my-assignmentexpert™ 微积分calculus作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的微积分calculus作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于economics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此微积分calculus作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在经济学作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的微积分calculus代写服务。我们的专家在微积分calculus学 代写方面经验极为丰富，各种微积分calculus相关的作业也就用不着 说。

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分作业代写calclulus代考|Method of least squares

In the year 1801 the world of astronomy was excited by the discovery of a new minor planet, Ceres, whose (rough) position in the night sky had been
3.D Least squares
147
noted a few times before it vanished from view. The young Carl Friedrich Gauss $[19,20]$ used a method – one he had worked out while still a student – to plot the orbit of the planet, and he was able to tell astronomers where in the sky to search for it. That method is the subject of this section.

In the first example that follows, we imagine the planet’s orbit in the night sky to be a straight line which has to be fitted in some optimal fashion to a set of discrete pairs of observations which are subject to errors. In the second example, the method is applied to discrete observations on a supposed planetary orbit. In the third example, the method is extended to continuous domains.

The field of statistics deals with “observations” (measurements) on variables that are known to be subject to random errors. When we observe two or more variables at once, it is often appropriate to ask what is the relationship between these two variables. This question is the basis of the study known as “regression analysis”, which is outside the scope of this book. But the core of regression analysis is an application of the differential calculus called the method of least squares, invented independently by Gauss.

## 微积分作业代写calclulus代考|Fitting a straight line to observations

Suppose we believe that a variable $y$ is in some way dependent on a variable $x$ by the relation $y=k x+b$. In situations such as this it is implicitly assumed that the independent variable is delerministic, that is, given, and not subject to error, while the dependent variable is subject to observation or measurement errors.

To find the dependency relationship, we select a sequence of values $\left{x_{1}, x_{2}, \ldots, x_{n}\right}$ of the independent variable, and measure the corresponding values $\left{y_{1}, y_{2}, \ldots, y_{n}\right}$ of the dependent variable.
$\mathrm{~ B e ̣ c a ̊ i ล ิ e ̂ ~ ถ ้ ง อ ิ}$
148
Applications
them, the observations won’t necessarily lie exactly on the straight line, but may fall above or below the line, as in Figure $3.10$ above.

## 微积分作业代写calclulus代考|Method of least squares

1801 年，天文学界因发现了一颗新的小行星谷神星而兴奋不已，谷神星在夜空中的（粗略）位置是
3.D 最小二乘
147

## 微积分作业代写calclulus代考|Fitting a straight line to observations

̣ลิถ้งอิ 乙和̣C一种̊一世l不和̂ r这d一种不
148