Question 1 (25 Marks) Consider the simple (two-variable) linear regression model for which the population regression equation can be written in conventional notation as: Y1 = Bo + BiXi + ui where Y, and X, are observable variables, Bo and B, are unknown (constant) regression coefficients, and u; is an unobservable random error. The Ordinary Least Squares (OLS) sample regression equation corresponding to regression equation above is P = Bot Bix,+ 0 where Bo is OLS estimator of the intercept coefficient Bo , , is OLS estimator of the slope coefficient B1, 0, is the OLS residual for the i-th sample observation and N is the number of observations in the sample. (a) Show that the OLS slope coefficient estimator , is a linear function of Y, sample values. Stating explicitly all required assumptions, prove that the OLS slope coefficient estimator , is an unbiased estimator of the slope coefficient , . (10) (b) Derive an expression for the variance of , . (10) (c) Now consider the following quadratic form Y1 = Bo + B , X, + B2 X, + 1 (i) What problems might be created if the equation, Y = Bo + B,X, + up , in the first model is estimated rather than the second equation, Y, = P, + B, X, + B,X2, + u,? (5) (ii) Derive an expression which includes S, and B2 from the equation, Y, = P. + B,X, + B2X", + up that captures that impact of x on y. (5)DFB, Inc. expects earnings next year of $5.00 per share, and it plans to pay a $3.00 dividend to shareholders (assume that is one year from now). DFB will retain $2.00 per share of its earnings to reinvest in new projects that have an expected return of 15.0%% per year. Suppose DFB will maintain the same dividend payout rate, retention rate, and return on new investments in the future and will not change its number of outstanding shares. Assume next dividend is due in one year. a. What growth rate of earnings would you forecast for DFB? b. If OFB's equity cost of capital is 12.0%, what price would you estimate for DFB stock? c. Suppose Instead that DFB paid a dividend of $4.00 per share at the end of this year and retained only $1.00 per share in earnings. That is, it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the future, what stock price would you estimate for the firm now? Should DFB raise its dividend? a. What growth rate of earnings would you forecast for DFB? DFB's growth rate of eamings is |%. (Round to one decimal place.) b. If DFB's equity cost of capital is 12.0%, what price would you estimate for DFB stock? If OFB's equity cost of capital is 12.0%, then DFB's stock price will be $. (Round to the nearest cent) c. Suppose instead that DFB paid a dividend of $4.00 per share at the end of this year and retained only $1.00 per share in earnings. That is, it chose to pay a higher dividend instead of reinvesting in as many new projects. If DFB maintains this higher payout rate in the future, what stock price would you estimate for the firm now? If DFB paid a dividend of $4.00 per share next year and retained only $1.00 per share in earnings, then OFB's stock price would be $ . (Round to the nearest cent.) Should DFB raise its dividend? (Select the best choice below.) O A. Yes, DFB should raise dividends because, according to the dividend-discount model, doing so will always improve the share price. Q B. No. DFB should not raise dividends because the projects are positive NPV. O C. Yes, DFB should raise dividends because the return on now investments is lower than the cost of capital. D. No, DFB should not raise dividends because companies should always reinvest as much as possible, Click to select your answer(s).Pick any three of the topics above and write a concise yet through response about each topic. Include how learning this information has broadened your understanding of CTE, how it has changed your thoughts about teaching or working in the CTE area, how it will change our classroom approach with your students and fellow CTE teachers (don't forget the Vocational Director and staff), include any other educational ponderings you encountered. Respond to all three topics in the same document The total of all three topics combined should be between 1000 to 1200 words. Topics 1. Name and describe the first five planning decisions every CTE teacher should make when planning a program or daily lessons. 2. Compare and contrast the different types of supervision and give an example of when each one has a place in your curriculum and setting. 3. Justify why including effort as part of your grading system is an important aspect of attribution retraining. 4. Describe a situation in which you use "wait time" to improve communication in your interactions with students in your CTE setting. 5. Identify two educational resources regarding safety in the classroom, lab or CTE setting that can provide training materials and/or curriculum content to assist you in educating students about safety practices. Describe each resource in detail. 6. Explain why continuing education and professional development for faculty in health and safety practices is essential for both the instructor and students of a CTE program. 7. Describe the four key components to an effective preventive maintenance program and describe one application in your current CTE program. 8. Justify the need for a Safety Checklist Program in any CTE setting 9. Justify why the philosophy of fact-finding is more important and effective in practice than faultfinding after an incident has occurred. 10. Describe the overall role of health and safety (prevention and response) in relationship to effective teaching and learning.calculating her debt payments-to-income ratio with and without the college loan. (Remember the 20 percent rule.) (LO5.3) 6. Joshua borrowed $500 for one year and paid $50 in interest. The bank charged him a $5 service charge. What is the finance charge on this loan? (LOS.4) 7. In problem 5, Joshua borrowed $500 on January 1, 2017, and paid it all back at once on December 31, 2017. What was the APR? (LO5.4) 8. If Joshua paid the $500 in 12 equal monthly payments in problem 5. what is the APR? (LO5.4) 9. Sidney took a $200 cash advance by using checks linked to her credit card account. The bank charges a 2 percent cash advance fee on the amount borrowed and offers no grace period on cash advances. Sidney paid the balance in full when the bill arrived. What was the cash advance fee? What was the interest for one month at an 18 percent APR? What was the total amount she paid? What if she had made the purchase with her credit card and paid off her bill in full promptly? (L05.4) 10. Brooke lacks cash to pay for a $600 washing machine. She could buy it from the store on credit by making 12 monthly payments of $52.74 each. The total cost would then be $632.88. Instead, Brooke decides to deposit $50 a month in the bank until she has saved enough money to pay cash for the washing machine. One year later, she has saved $642-$600 in deposits plus interest. When she goes back to the store, she finds that the washing machine now costs $660. Its price has gone up 10 percent-the current rate of inflation. Was postponing her purchase a good trade-off for Brooke? (L05.4) 11. What are the interest cost and the total amount due on a six-month loan of $1,500 at 13.2 percent simple annual interest? (L05.4) 12. After visiting several automobile dealerships, Richard selects the car he wants. He likes its $10,000 price, but financing through the dealer is no bargain. He has $2,000 cash for a down payment, so he needs an $8,ooo loan. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $8,ooo for a period of four years at an add-on interest rate of 11 percent. (LOS.4) a. What is the total interest on Richard's loan? b. What is the total cost of the car? TE E Focus + 100% Book Pro DN DD