Math 403 Mathematics and Technology Homework 4 1. Solve the following system of equations: 5x + 4y − 2z + 5.7 t − w = .5 12 x − 2y − 5t = −7 x − 2y + πz − 6t = 2 − 9 = −8 y w 2x − 5z + 3 7t +12w = 9.8 2. Find by (a) polynomial regression and (b) matrices (giving the matrices used) the equation of the polynomial of least degree that goes through the four points: (-2, 7) (1, 8) (2, -3) (5, 6) 3. Using Super Bowl number as independent variable and ticket price as dependent variable, perform several (at least three) regressions of different types on the data. Which of these is the best model? What does this model predict the ticket price will be for Super Bowl XXXXII (42)? Super Bowl Ticket Prices Year Cost Venue City 1967 $6-12 Memorial Coliseum Los Angeles 1968 $12 Orange Bowl Miami 1969 $12 Orange Bowl Miami 1970 $15 Tulane Stadium New Orleans 1971 $15 Orange Bowl Miami 1972 $15 Tulane Stadium New Orleans 1973 $15 Memorial Coliseum Los Angeles 1974 $15 Rice Stadium Houston 1975 $20 Tulane Stadium New Orleans 1976 $20 Orange Bowl Miami 1977 $20 Rose Bowl Pasadena, Calif. 1978 $30 Superdome New Orleans 1979 $30 Orange Bowl Miami 1980 $30 Rose Bowl Pasadena, Calif. 1981 $40 Superdome New Orleans 1982 $40 Silverdome Pontiac, Mich. 1983 $40 Rose Bowl Pasadena, Calif. 1984 $60 Tampa Stadium Tampa, Fla. 1985 $60 Stanford Stadium Palo Alto, Calif. 1986 $75 Superdome New Orleans 1987 $75 Rose Bowl Pasadena, Calif. 1988 $100 Jack Murphy Stadium San Diego 1989 $100 Joe Robbie Stadium Miami 1990 $125 Superdome New Orleans 1991 $150 Tampa Stadium Tampa, Fla. 1992 $150 Metrodome Minneapolis 1993 $175 Rose Bowl Pasadena, Calif. 1994 $175 Georgia Dome Atlanta 1995 $200 Joe Robbie Stadium Miami 1996 $200 Sun Devil Stadium Tempe, Ariz. 1997 $275 Superdome New Orleans 1998 $275 Qualcomm Stadium San Diego 1999 $325 Pro Player Stadium Miami 2000 $325 Georgia Dome Atlanta 2001 $325 Raymond James Stadium Tampa, Fla. 2002 $400 Superdome New Orleans 2003 $400 Qualcomm Stadium San Diego 2004 $500 Reliant Stadium Houston 2005 $500 ALLTEL Stadium Jacksonville, Fla. 2006 $600 Ford Field Detroit http://www.mysportsbook.com/news/sports_betting/153597.html .