Provide step by step solutions to the attached questions. Draw graphs where necessary.

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.A restaurant faces very high demand for its signature mousse desserts in the evening but is less busy during the day. Its manager estimates that inverse demand functions are pe = 30 - Qe in the evening and pd = 16 -Qd during the day, where e and d denote evening and daytime. The marginal cost of producing its dessert evening, MCe, is $8. The marginal cost of producing its dessert daytime, MCd, is $4. There is no fixed cost of producing dessert. Create a spreadsheet with the column headings Qe, Pe, TRe, MRe, TCe, MCe, ne, Qd, Pd, TRd, MRd, TCd, MCd, and nd. (note: ne is profit evening and nd indicates profit daytime) a. What are the optimal prices for the dessert that the restaurant should charge during the evening hours? b. What is the optimal quantity for the dessert that the restaurant should produce during the evening hours? c. What is the total cost of producing the optimal quantity for the dessert during the evening hours? d. What is the maximum profit for the dessert that the restaurant should produce during the evening hours? e. What are the optimal prices for the dessert that the restaurant should charge during the daytime hours? f. What is the optimal quantity for the dessert that the restaurant should produce during the daytime hours? I g. What is the total cost of producing the optimal quantity for the dessert during the daytime hours? h. What is the maximum profit for the dessert that the restaurant should produce during the daytime hours?Homework for Chapter 10: Problem # 1 in the text (Chapter 10) NOTE: PLEASE USE THE ATTACHED EXCEL FILE TITLED "Homework for Chapter 10_Excel" TO SOLVE THE FOLLOWING PROBLEM. You are considering the following bonds to include in your portfolio: Bond 1 Bond 2 Bond 3 Price $900.00 $1,100.00 $1,000.00 Face Value $1,000.00 $1,000.00 $1,000.00 Coupon Rate 7.00% 10.00% 9.00% Frequency 2 4 Maturity (Years) 15 20 30 Required Return 9.00% 8.00% 9.00% a) Determine the highest price you would be willing to pay for each of these bonds using the PV function. Also find whether the bond is undervalued, overvalued, or fairly valued (25 points). b) Determine the yield to maturity on these bonds using the RATE function assuming that you purchase them at the given price. Also calculate the current yield of each bond (25 points). c) Determine the yield to call of each bond using the RATE function if the time to first call and the call premium are the following (25 points): Bond A Bond B Bond C Call Premium % 3.00% 4.00% 5.00% Years to first call 5 4 3 d) Assume the following settlement dates for each bond: Bond 1 Bond 2 Bond 3 Settlement Date 1/1/2018 6/1/2018 9/1/2018 Use the PRICE and YIELD functions to recalculate your answers on parts (a), (b), and (c) (25 points)