Q1) Investor is considering 3 kinds of investments: a high-risk venture into oil leases with potential return of 15%, a medium-risk investment in stocks with a 9% return, and relatively safe bond investment with 5% return.  He has $50,000 to invest.  Since the risk, he will limit his investment in oil leases and stocks to 30% and his investment in oil leases and bonds to 50%.  How much must he invest in each to maximize his return, assuming investment returns are as expected?

i) Maximum = $1650 with Stock = $10,000, Bonds = $15,000

ii) Maximum = $3650 with Oil = $15,000, Stock = $10,000, Bonds = $25,000

iii) Maximum = $2750 with Oil = $15,000, Bonds = $10,000

iv) Maximum = $2750 with Oil = $15,000, Stock = $10,000, Bonds = $25,000

Q2) Tuddenham and Snyder got following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped):   Average height at 6 ≈ 3 feet 10 inches,  SD ≈1.7 inches. Average height at 18 ≈ 5 feet 10 inches, SD ≈ 2.5 inches, r≈0.80

i) Determine r.m.s. error for regression prediction of height at 18 from height at 6.

ii) Determine the r.m.s. error for regression prediction of height at 6 from height at 18. r.m.s. mean root means square.

Q3) Determine regression equation for forecasting final score from midterm score, based on following information:  average midterm score = 70, SD=10  Average  final score = 55, SD=20 r=0.60