Table 10.15 shows data on two variables for the UK from the Central Statistical Office for the period 1970 to 2003.

Cars New registrations of cars shown in thousands as a monthly average.

Income Real household disposable income, per head at 2001 prices.

(a) What type of causal relationship might you expect between these two variables?

(b) Draw a scatter diagram for this data and comment on any relationship observed.

(c) For the period 1970
–
89 estimate a regression model for this data. Estimate a second equation for the entire period. Estimate a third for the period 1991 to 2003.

(d) Evaluate the regression models statistically.

(e) Evaluate the regression equations in terms of their likely reliability for forecasting.

(f ) Using the equations, forecast Cars for 2006. Assess the reliability of your forecasts. Comment on the likely factors causing inaccuracies in your forecasts.

EXERCISES 393 New registration of cars and per capita income: UK Income Cars 1970 5205 91.4 1971 5241 108.5 1972 5658 138.6 1973 6000 137.3 1974 5951 102.8 1975 6011 98.6 1976 5989 106.5 1977 5870 109.4 1978 6301 131.6 1979 6666 142.1 1980 6767 126.6 1981 6730 124.5 1982 6714 132.1 1983 6849 150.5 1984 7093 146.6 1985 7316 153.5 1986 7602 156.9 Income Cars 1987 7865 168 1988 8276 184.2 1989 8640 192.1 1990 8917 167.1 1991 9066 133.3 1992 9298 133.3 1993 9536 148 1994 9657 158.9 1995 9859 161.5 1996 10 078 168.2 1997 10 461 179.7 1998 10 474 188.4 1999 10 786 186.8 2000 11 427 194.8 2001 11 900 214.8 2002 12 042 223.5 2003 12 262 220.5 Data available in file T1015.

Table 10.15