Solve the following.
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.(b) Assume these firms behave like price takers, how much will they produce and what price will they charge? Draw the outcome on a graph. What is the individual firms producer surplus? What is the total producer surplus of the market? (3 marks) (c) Suppose the four firms join together to form a single firm monopoly. What price will the cartel charge and how much output does the cartel produce? What is producer surplus for the cartel? (Hint: the marginal cost curve for the cartel firm is the supply curve found in part (a) with MC replacing P in this equation and MR = 200 -Q). What happens to consumer surplus and total welfare? (4 marks) 4. Calculate the own price elasticity of demand in the following situations (a) A price rise from po = 2 to p1 = 5 causes quantity demand to fall from go = 30 to q1 = 15 (1 mark) (b) The demand curve is given by q = 1/p with the slope of the demand curve given by $ = -1/p2. What is the own price elasticity of demand at any point?(2 marks) (c) The demand curve is given by q = 4 - 2p with the slope of the demand curve given by dp = -2. What is the own price clasticity of demand at: (i) p = 4; and (ii) p = 10? (2 marks) 5. Suppose the cost of producing q cars and q2 trucks is 45000 +80q1 + 10092. Calculate the measure of economies of scope when (1 mark each): (a) q1 = 100 and q2 = 200 (b) q1 = 500 and q2 = 800 6. Answer the following questions True, False, or Uncertain. Give a brief explanation of your answer. 1 mark for correctly identifying T, F. or U. 4 marks for explanation. (a) If a single price monopoly is instituted in what was a competitive market, consumer surplus will decrease more than producers gain. (b) If a firm's marginal cost is less than the firm's marginal revenue then the firm should decrease output and increase price. (c) If price is less than average cost then a firm will shut down. (d) A monopolist does not make a shutdown decision in the short-run and an exit decision in the long run since only competitive firms make these decisions.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)a. There are common questions of law or fact b. Diversity jurisdiction is present c. Separate lawsuits for all plaintiffs would be impractical d. A lead plaintiff will adequately protect the interest of the class 18. During the discovery process in a civil case, a party may use which of the following? (Circle all that apply) a. A motion to suppress evidence based on an illegal search b. Requests for admission to another party c. Depositions for possible trial witnesses d. A motion to recuse the judge for bias 19. How may a deposition be used during a trial? 20. If the statute of limitations has expired, what type of motion should a defendant file? a. A motion for default judgment b. A motion for judgment notwithstanding the verdict C. A motion to dismiss d. A motion for summary judgment 21. The process used to select a jury is called a. Res judicata b. Voir dire c. Res ipsa loquitor d. Stare decisi 22. Cross examination is designed to permit a party to exercise which constitutional right? 23. The process used to collect a money judgment is called a. Sentencing b. Garnishment C. Execution d. Liquidation 24. A method of alternate dispute resolution (ADR) without using a third party neutral is known as 25. An ADR technique that encourages the parties to recognize their common interests is called 26. After hearing the evidence and arguments of the parties, an arbitrator issues 27. Which type of ADR most resembles a trial
