Answer the attached questions.
Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted X, is regarded as the predictor, explanatory, or independent variable. The other variable, denoted Y, is regarded as the response, outcome, or dependent variable. Suppose that we are given n-i.i.d observations { (x;, y;)}"_, from the assumed simple linear regression model Y = BIX + Bo + . Answer the following questions on simple linear regression. 5-a. Denote 1 and Bo as the point estimators of B, and Bo, respectively, that are obtained through the least squares method. Show, step by step, that the two point estimators are unbiased. Derive the least squares estimator of of and determine whether it is unbiased or not. Show your work step by step. 5-b. Calculate _'_1(yi - Bix; - Bo) (Bix, + Bo). Determine whether the point (X, Y) is on the line Y = 1X + Bo. Explain your reasoning mathematically. 5-c. Using the maximum likelihood estimation (MLE) technique, derive a point estimator for the coefficient B1 and the intercept Bo, respectively. Determine whether the point estimators that you obtained via MLE are unbiased or not. Justify your conclusion mathematically. 5-d. Calculate the variance of the four estimators from Questions 5-a and 5-c, respectively. Show your work step by step. 5-e. Suppose that we are using the simple linear regression model Y = B1 X + Bo + 1 while the true model is Y = 1X1 + B2X2 + Bo + 82 where Bo, B1, and B2 are constants. We assume that the distributions of &, and e2 are both N(0,02), i.e., normal distribution with variance o?. We further assume that the two noise variables are uncorrelated. Find the least squares estimator of B, in this case and determine whether the point estimator that you obtain is biased or not. If it is biased, calculate the bias.vi payments accounts, still PLEsuit IsOnly foreign currency traded with the Canadian dollar. 7. For each of the following situations, outline the effect on the price of the Canadian dollar in terms of US dollars and draw a demand and supply graph that illustrates the changes that occur in the foreign exchange market for the Canadian dollar. . A contractionary monetary policy initiated by the Bank of Canada raises Canadian interest rates. b. Canada's real output rises at a time when real output in the United States is falling. c. Americans (but not Canadians) find Canada a more attractive place to make financial investments. d. Given Canada's aging population, more Canadian "snowbirds" travel to the United States each winter. e. Due to a credit crisis that affects US financial institutions more than it does Canadian ones, Canada's attractiveness as a destination for direct and portfolio investment increases. f. The Bank of Canada initiates an expansionary monetary policy that reduces Canadian interest rates.DATE NAME 1. What are the main purposes of a legal system? (that is, what benefits does a legal system give to a nation?] 2. Name and describe the two most common types of legal systems in the world today. 3. What are the main sources of law in the U.S. common law system? 4. What is the difference between procedural law and substantive law? 5. What is federalism? 6. How do past decisions issued by judges make the law more predictable? 7. What are the three branches of the federal government, and how do they exercise the powers given to them in the U.S. constitution? B. Subject matter jurisdiction is the power to issue orders affecting the rights of a plaintiff and defendant. True or false? 9. Federal question jurisdiction is one of the types of jurisdiction exercised by federal courts. True or false? 10. The Tenth Circuit Court of appeals exercises which of the following types of jurisdiction? (Circle the correct answer) a. Appellate jurisdiction b. Original jurisdiction c. Special court jurisdiction d. Personal jurisdiction 11. A party who begins a lawsuit by filing a is called a plaintiff. 12. The party who files an indictment in a criminal court is called the 13. Describe two ethical duties of an attorney who represents a party in a lawsuit. 14. After all the evidence is presented in a trial, what is the job of the jury? 15. A person who has an actual stake in the outcome of litigation is said to have 16. A court may exercise filed. Jurisdiction over a party who has minimum contacts with the state in which a case is 17. A court may permit the filing of a class action if (Circle all that apply)
