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.
| Year |
DPI |
Motor Vehicles and Parts |
| 1964 |
462,3 |
25,8 |
| 1965 |
497,8 |
29,6 |
| 1966 |
537,4 |
29,9 |
| 1967 |
575,1 |
29,6 |
| 1968 |
624,7 |
35,4 |
| 1969 |
673,8 |
37,4 |
| 1970 |
735,5 |
34,5 |
| 1971 |
801,4 |
43,2 |
| 1972 |
869,0 |
49,4 |
| 1973 |
978,1 |
54,4 |
| 1974 |
1 071,7 |
48,2 |
| 1975 |
1 187,3 |
52,6 |
| 1976 |
1 302,3 |
68,2 |
| 1977 |
1 435,0 |
79,8 |
| 1978 |
1 607,3 |
89,2 |
| 1979 |
1 790,9 |
90,2 |
| 1980 |
2 002,7 |
84,4 |
| 1981 |
2 237,1 |
93,0 |
| 1982 |
2 412,7 |
100,0 |
| 1983 |
2 599,8 |
122,9 |
| 1984 |
2 891,5 |
147,2 |
| 1985 |
3 079,3 |
170,1 |
| 1986 |
3 258,8 |
187,5 |
| 1987 |
3 435,3 |
188,2 |
| 1988 |
3 726,3 |
202,2 |
| 1989 |
3 991,4 |
207,8 |
| 1990 |
4 254,0 |
205,1 |
| 1991 |
4 444,9 |
185,7 |
| 1992. |
4 736,7 |
204,8 |
| 1993 |
4 921,6 |
224,7 |
| 1994 |
5 184,3 |
249,8 |
| 1995 |
5 457,0 |
255,7 |
| 1996 |
5 759,6 |
273,5 |
| 1997 |
6 074,6 |
293,1 |
| 1998 |
6 498,9 |
320,2 |
| 1999 |
6 803,3 |
350,7 |
| 2000 |
7 327,2 |
363,2 |
| 2001 |
7 648,5 |
383,3 |
| 2002 |
8 009,7 |
401,3 |
| 2003 |
8 377,8 |
401,0 |
| 2004 |
8 889,4 |
403,9 |
| 2005 |
9 277,3 |
408,2 |
| 2006 |
9 915,7 |
394,8 |
| 2007 |
10 423,6 |
399,9 |
| 2008 |
11 024,5 |
339,3 |
| 2009 |
10 722,4 |
316,0 |
| 2010 |
11 127,1 |
342,7 |
| 2011 |
11 549,3 |
373,6 |
| 2012 p. |
11 931,2 |
407,0 |
|
|
|
| Year |
DPI |
Housing and Utilities |
| 1964 |
462,3 |
72,1 |
| 1965 |
497,8 |
76,6 |
| 1966 |
537,4 |
81,2 |
| 1967 |
575,1 |
86,3 |
| 1968 |
624,7 |
92,7 |
| 1969 |
673,8 |
101,0 |
| 1970 |
735,5 |
109,4 |
| 1971 |
801,4 |
120,0 |
| 1972 |
869,0 |
131,2 |
| 1973 |
978,1 |
143,5 |
| 1974 |
1 071,7 |
158,6 |
| 1975 |
1 187,3 |
176,5 |
| 1976 |
1 302,3 |
194,7 |
| 1977 |
1 435,0 |
217,8 |
| 1978 |
1 607,3 |
244,3 |
| 1979 |
1 790,9 |
273,4 |
| 1980 |
2 002,7 |
311,8 |
| 1981 |
2 237,1 |
352,0 |
| 1982 |
2 412,7 |
387,0 |
| 1983 |
2 599,8 |
421,2 |
| 1984 |
2 891,5 |
458,3 |
| 1985 |
3 079,3 |
500,7 |
| 1986 |
3 258,8 |
535,7 |
| 1987 |
3 435,3 |
571,8 |
| 1988 |
3 726,3 |
614,5 |
| 1989 |
3 991,4 |
655,6 |
| 1990 |
4 254,0 |
696,4 |
| 1991 |
4 444,9 |
735,5 |
| 1992. |
4 736,7 |
771,2 |
| 1993 |
4 921,6 |
814,5 |
| 1994 |
5 184,3 |
866,5 |
| 1995 |
5 457,0 |
913,8 |
| 1996 |
5 759,6 |
961,2 |
| 1997 |
6 074,6 |
1 009,9 |
| 1998 |
6 498,9 |
1 065,2 |
| 1999 |
6 803,3 |
1 125,0 |
| 2000 |
7 327,2 |
1 198,6 |
| 2001 |
7 648,5 |
1 287,7 |
| 2002 |
8 009,7 |
1 334,8 |
| 2003 |
8 377,8 |
1 393,9 |
| 2004 |
8 889,4 |
1 462,4 |
| 2005 |
9 277,3 |
1 582,6 |
| 2006 |
9 915,7 |
1 686,2 |
| 2007 |
10 423,6 |
1 756,2 |
| 2008 |
11 024,5 |
1 831,0 |
| 2009 |
10 722,4 |
1 871,6 |
| 2010 |
11 127,1 |
1 891,9 |
| 2011 |
11 549,3 |
1 929,9 |
| 2012 p. |
11 931,2 |
1 965,9 |
Questions:
a) Plot the data using a scatterplot.
b) Find the equation that shows the relationship between motor vehicles and parts expenditure (PCE) and DPI (insert a linear trendline and show the equation on the scatterplot).
c) 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?
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?