Explain the following 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.9. How price changes impact the labor market Consider the labor market for the fast-food industry, which consists mainly of high school and college students, Assume that all fast food restaurants are profit maximizing. The following calculator shows the market demand curve (blue curve) and market supply curve (orange curve) for student workers, who are responsible for making cheeseburgers. At any time in this problem, you can click the Reset to Initial Values button to return the elements in the calculator to their original positions, You wil not be graded on any changes to the calculator; it's just here to help you answer the following questions. Tool tip: You can directly change the values in the boxes with the white background by clicking in the box and typing. The graph and any related values will change accordingly. Graph Input Tool (?) LABOR MARKET CALCULATOR I Wage rate Labor demanded Labor supplied Price of a WAGE RATE cheeseburger QUANTITY OF LABOR (Thousands of worken) when the price of a cheeseburger is $4, the equilibrium wage in the fay food labor market is per hour. Suppose that the demand for cheeseburgers increases enough is that the price of a cheeseburger ries to fa. Ordinary, this would result in a new siplibrium employment level and wage in the labor market for young people who work in fast food reviauranis. However, restaurants claim they can only afford to pay the initial ppalibrium maps, In this labor market, if the price of cheeseburgers incenses, but restaurants continue to pay the equiileum wage that prevailed before the marease in demand for cheeseburgers, there will be a laborHW 1 (1) - Word (Product Activation Failed) SERT DESIGN PAGE LAYOUT REFERENCES MAILINGS REVIEW VIEW 1. Towards the end of the 20th century, the U.S. government wanted to save money by closing a small portion of its domestic military installations. While many people agreed that saving money was a desirable goal, people in areas potentially affected by a closing soon reacted negatively. Congress finally selected a panel whose task was to develop a list of installations to close, with the legislation specifying that Congress could not alter the list. Since the goal was to save money, why was this problem so hard to solve? 2. Your car gets 29 miles per gallon (mpg) at 60 miles per hour (mph) and 25 mpg a 70 mph. At what speed should you make a 525-mile trip: a. If gas costs $3 per gallon and your time is worth $18 per hour b. If gas costs $4 per gallon and your time is worth $12 per hour c. If gas costs $5 per gallon and your time is worth $9 per hour 3. A firm is planning to manufacture a new product. As the selling price is increased, the quantity that can be sold decreases. Numerically the sales department estimates: P =$475-0.250 Where P = selling price per unit and Q = quantity sold On the other hand, management estimates that the average unit cost of manufacturing and selling the product will decrease as the quantity sold increases, They estimate C = $480 + $22,500 Where C = cost to produce and sell Q per year The firm's management wishes to maximize profit. What quantity should be sold? How much profit will be made? ENGLISH (CANADA)Topic 6 The following is an accounts receivable aging schedule for Caulfield Lid on 30 June 2019. Customer Total Number of days past due 1-30 31-60 61-90 Over 90 Bela 18,000 11,000 7,000 Tom 22,000 22,000 Jason 35,000 15,000 12,000 8,000 Lee 41,000 41,000 Estimated percentage uncollectable 5% 10% 25% 50% At 30 June 2019, the unadjusted balance in allowance for doubtful debts is a credit of $8,000. At 31 March 2020, a debtor named Alan declared bankrupt and unable to pay $500 owing to Caulfield Lid. At 15 May 2020, a cheque for $500 is received from Alan whose account was written-off as uncollectable on 31 March. At 30 June 2020, the unadjusted balance in allowance for doubtful debts is a debit of $500 and the ageing schedule indicates that total estimated bad debts will be $25,000. Required: a) Show the general journal entry to record the adjusting entry at balance day 30 June 2019. b) Show the general journal entry record the events and transactions related to Alan in 2020. c) Show the general journal entry to record the adjusting entry at balance day 30 June 2020
