Below are data for U.S. DPI and PCE on two major components of consumer spending

Question

Below are data for U.S. DPI and PCE on two major components of consumer spending, motor vehicles and parts and housing and utilities. One is a durable good and the other is comprised of housing and other services and non-durables, such as natural gas purchases. Using scatter diagrams and trendlines, generate graphs showing the relationship of each of the consumption categories to DPI and find the equation of the graph and the R squared. Use your results to answer the questions to the right. Questions: c) B. Find the equation that shows the relationship between housing and utilities expenditures (PCE) and DPI (insert a linear trendline and show the equation on the scatterplot). d) What are the R squares for the equations? Which one is better? Can you provide an economic rationale to explain the difference? e) Use the equations to calculate estimated values for both types of expenditures for 2011 and 2012. How well did the equations predict values for 2011 and 2012? Data f) If DPI increases at a rate of 2.2% in 2013 and then at a rate of 2.6% in 2014, what are the predicted values for consumer spending on motor vehicles and parts? On housing and utilities? Year DPI Motor Vehicles and Parts Answers: 1964. 462 26 a) 1965. 498 30 b) 1966. 537 30 c) 1967. 575 30 d) 1968. 625 35 e) 1969. 674 37 f) 1970. 736 35 Motor Vehicles and Parts 1971. 801 43 2013 12,194 1972. 869 49 2014 12,511 1973. 978 54 Housing and Utilities 1974. 1,072 48 2013 12,194 1975. 1,187 53 2014 12,511 1976. 1,302 68 1977. 1,435 80 1978. 1,607 89 1979. 1,791 90 1980. 2,003 84 1981. 2,237 93 1982. 2,413 100 1983. 2,600 123 1984. 2,892 147 1985. 3,079 170 1986. 3,259 188 1987. 3,435 188 1988. 3,726 202 1989. 3,991 208 1990. 4,254 205 1991. 4,445 186 1992. 4,737 205 1993. 4,922 225 1994. 5,184 250 1995. 5,457 256 1996. 5,760 274 1997. 6,075 293 1998. 6,499 320 1999. 6,803 351 2000. 7,327 363 2001. 7,649 383 2002. 8,010 401 2003. 8,378 401 2004. 8,889 404 2005. 9,277 408 2006. 9,916 395 2007. 10,424 400 2008. 11,025 339 2009. 10,722 316 2010. 11,127 343 2011. 11,549 374 2012 p. 11,931 407 Year DPI Housing and Utilities 1964. 462 72 1965. 498 77 1966. 537 81 1967. 575 86 1968. 625 93 1969. 674 101 1970. 736 109 1971. 801 120 1972. 869 131 1973. 978 144 1974. 1,072 159 1975. 1,187 177 1976. 1,302 195 1977. 1,435 218 1978. 1,607 244 1979. 1,791 273 1980. 2,003 312 1981. 2,237 352 1982. 2,413 387 1983. 2,600 421 1984. 2,892 458 1985. 3,079 501 1986. 3,259 536 1987. 3,435 572 1988. 3,726 615 1989. 3,991 656 1990. 4,254 696 1991. 4,445 736 1992. 4,737 771 1993. 4,922 815 1994. 5,184 867 1995. 5,457 914 1996. 5,760 961 1997. 6,075 1,010 1998. 6,499 1,065 1999. 6,803 1,125 2000. 7,327 1,199 2001. 7,649 1,288 2002. 8,010 1,335 2003. 8,378 1,394 2004. 8,889 1,462 2005. 9,277 1,583 2006. 9,916 1,686 2007. 10,424 1,756 2008. 11,025 1,831 2009. 10,722 1,872 2010. 11,127 1,892 2011. 11,549 1,930 2012 p. 11,931 1,966 Source: Economic Report of the President, 2013. Appendix B. Below are data for U.S. DPI and PCE on two major components of consumer spending, motor vehicles and parts and housing and utilities. One is a durable good and the other is comprised of housing and other services and non-durables, such as natural gas purchases. Using scatter diagrams and trendlines, generate graphs showing the relationship of each of the consumption categories to DPI and find the equation of the graph and the R squared. Use your results to answer the questions to the right. Questions: c) B. Find the equation that shows the relationship between housing and utilities expenditures (PCE) and DPI (insert a linear trendline and show the equation on the scatterplot). d) What are the R squares for the equations? Which one is better? Can you provide an economic rationale to explain the difference? e) Use the equations to calculate estimated values for both types of expenditures for 2011 and 2012. How well did the equations predict values for 2011 and 2012? Data f) If DPI increases at a rate of 2.2% in 2013 and then at a rate of 2.6% in 2014, what are the predicted values for consumer spending on motor vehicles and parts? On housing and utilities? Year DPI Motor Vehicles and Parts Answers: 1964. 462 26 a) 1965. 498 30 b) 1966. 537 30 c) 1967. 575 30 d) 1968. 625 35 e) 1969. 674 37 f) 1970. 736 35 Motor Vehicles and Parts 1971. 801 43 2013 12,194 1972. 869 49 2014 12,511 1973. 978 54 Housing and Utilities 1974. 1,072 48 2013 12,194 1975. 1,187 53 2014 12,511 1976. 1,302 68 1977. 1,435 80 1978. 1,607 89 1979. 1,791 90 1980. 2,003 84 1981. 2,237 93 1982. 2,413 100 1983. 2,600 123 1984. 2,892 147 1985. 3,079 170 1986. 3,259 188 1987. 3,435 188 1988. 3,726 202 1989. 3,991 208 1990. 4,254 205 1991. 4,445 186 1992. 4,737 205 1993. 4,922 225 1994. 5,184 250 1995. 5,457 256 1996. 5,760 274 1997. 6,075 293 1998. 6,499 320 1999. 6,803 351 2000. 7,327 363 2001. 7,649 383 2002. 8,010 401 2003. 8,378 401 2004. 8,889 404 2005. 9,277 408 2006. 9,916 395 2007. 10,424 400 2008. 11,025 339 2009. 10,722 316 2010. 11,127 343 2011. 11,549 374 2012 p. 11,931 407 Year DPI Housing and Utilities 1964. 462 72 1965. 498 77 1966. 537 81 1967. 575 86 1968. 625 93 1969. 674 101 1970. 736 109 1971. 801 120 1972. 869 131 1973. 978 144 1974. 1,072 159 1975. 1,187 177 1976. 1,302 195 1977. 1,435 218 1978. 1,607 244 1979. 1,791 273 1980. 2,003 312 1981. 2,237 352 1982. 2,413 387 1983. 2,600 421 1984. 2,892 458 1985. 3,079 501 1986. 3,259 536 1987. 3,435 572 1988. 3,726 615 1989. 3,991 656 1990. 4,254 696 1991. 4,445 736 1992. 4,737 771 1993. 4,922 815 1994. 5,184 867 1995. 5,457 914 1996. 5,760 961 1997. 6,075 1,010 1998. 6,499 1,065 1999. 6,803 1,125 2000. 7,327 1,199 2001. 7,649 1,288 2002. 8,010 1,335 2003. 8,378 1,394 2004. 8,889 1,462 2005. 9,277 1,583 2006. 9,916 1,686 2007. 10,424 1,756 2008. 11,025 1,831 2009. 10,722 1,872 2010. 11,127 1,892 2011. 11,549 1,930 2012 p. 11,931 1,966 Source: Economic Report of the President, 2013. Appendix B.

Explanation / Answer

c) PCE=0.1696*DPI -20.323 d) R2 = .9042 and 0.9993 e) estimated pCE on motor parts = 450.3818 and actual value is 373.6 so we overestimate the 2011 value estimated pCE on utilities = 1938.43828 and actual value is 1929.9 so we overestimate the 2011 value estimated pCE on motor parts = 464.1302 and actual value is 407 so we overestimate the 2012 value estimated pCE on utilities = 2003.20852 and actual value is 1965.9 so we overestimate the 2012 value f) Motor Vehicles and Parts estimated Dpi estimated PCE 2013 12193.6864 15191.52859 2014 12510.72225 15586.50833 Housing and Utilities 2013 12,193.68640 2,048

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