Determine Whether the Statement Is True or False

question 73

Multiple Choice

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The least-squares line must pass through at least one data point.

• A) It is false. Example. Find the least-squares line for the data Solution. Here, we have n = 5 and The least-squares line for the data is given by linear equation Y = f(x) = mx + b Where the constants m and b satisfy the normal equations Then, we obtain the normal equations Solving them, we found m = 1, b = 0.4 Therefore, the required least-squares line is y = x + 0.4 The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.
• B) It is true Suppose that we are given two data points If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amounts d1, d2, respectively. The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares be made as small as possible. But it is possible only in case when least-squares line passes through at least one data point.

Understand the formation and basis of international law through customs, treaties, agreements, and organizations.

Grasp the legal considerations and implications of sovereign immunity in the context of international law.

Identify the principles of comity and the act of state doctrine and their application in international legal disputes.

Comprehend the mechanisms for resolving international business disputes, including arbitration and judicial decisions.

---

Definitions:

Demand Curve

An illustrative chart depicting how the cost of an item correlates with consumer demand for that item.

Perfectly Inelastic

A market scenario where demand or supply does not change in response to price changes.

Industry's Demand

The total demand for all the products or services provided by a specific sector of the economy.

Marginal Decision Rule

A principle used in economics and decision-making that recommends comparing the additional benefits of a decision or action to its additional costs.