3. For the following data set, the dependent variable {response) is the first variable. Choose the independent variables {predictors) as you judge appropriate. Use a spreadsheet or a statistical package (e.g., SPSS or SYSTAT or MIN1TAB) to perform the necessary regression calculations and to obtain the required graphs.

Question

Consumer Prices, Capacity Utilization, and Money Supply (n = 41, k = 4)
Year ChgCPI CapUtil ChgM1 ChgM2 ChgM3
1960 0.7 80.1 0.5 4.9 5.2
1961 1.3 77.3 3.2 7.4 8.1
1962 1.6 81.4 1.8 8.1 8.9
1963 1.0 83.5 3.7 8.4 9.3
1964 1.9 85.6 4.6 8.0 9.0
1965 3.5 89.5 4.7 8.1 9.0
1966 3.0 91.1 2.5 4.6 4.8
1967 4.7 87.2 6.6 9.3 10.4
1968 6.2 87.1 7.7 8.0 8.8
1969 5.6 86.6 3.3 3.7 1.4
1970 3.3 79.4 5.1 6.5 9.9
1971 3.4 77.9 6.5 13.4 14.6
1972 8.7 83.4 9.2 13.0 14.2
1973 12.3 87.7 5.5 6.6 11.2
1974 6.9 83.4 4.3 5.4 8.6
1975 4.9 72.9 4.7 12.7 9.4
1976 6.7 78.2 6.7 13.4 11.9
1977 9.0 82.6 8.0 10.3 12.2
1978 13.3 85.2 8.0 7.5 11.8
1979 12.5 85.3 6.9 7.9 10.0
1980 8.9 79.5 7.0 8.6 10.3
1981 3.8 78.3 6.9 9.7 13.0
1982 3.8 71.8 8.7 8.8 9.1
1983 3.9 74.4 9.8 11.3 9.6
1984 3.8 79.8 5.8 8.6 10.9
1985 1.1 78.8 12.3 8.0 7.3
1986 4.4 78.7 16.9 9.5 9.1
1987 4.4 81.3 3.5 3.6 5.4
1988 4.6 83.8 4.9 5.8 6.6
1989 6.1 83.6 0.8 5.5 3.8
1990 3.1 81.4 4.0 3.8 1.9
1991 2.9 77.9 8.7 3.0 1.3
1992 2.7 79.4 14.3 1.6 0.3
1993 2.7 80.4 10.3 1.5 1.5
1994 2.5 82.5 1.8 0.4 1.9
1995 3.3 82.6 -2.1 4.1 6.1
1996 1.7 81.6 -4.1 4.8 7.5
1997 1.6 82.7 -0.7 5.7 9.2
1998 2.7 81.4 2.2 8.8 11.0
1999 3.4 80.6 2.5 6.1 8.3
2000 1.6 80.7 -3.3 6.1 8.9

Variable Names: ChgCPI = percent change in the Consumer Price Index (CPI) over previous year, CapUtil = percent utilization of manufacturing capacity in current year, ChgM1 = percent change in currency and demand deposits (M1) over previous year, ChgM2 = percent change in small time deposits and other near-money (M2) over previous year, ChgM3 = percent change in large time deposits, Eurodollars, and other institutional balances (M3) over previous year

Write a concise report answer¬ing following questions 1 through 10. Label sec¬tions of your report to correspond to the questions. Insert tables and graphs in your report as appropri¬ate.

1. Is this cross-sectional data or time-series data? What is the unit of observation?

2. Are the X and Y data well-conditioned? If not, make any transformations that may be necessary and explain.
3. State your a priori hypotheses about the sign (+ or —) of each predictor and your reasoning about cause and effect. Would the intercept have meaning in this problem? Explain.
4. Perform the regression and write the estimated regression equation (round off to 3 or 4 significant digits for clarity). Do the coefficient signs agree with your a priori expectations?
5. Does the 95 percent confidence interval for each predictor coefficient include zero? What conclusion can you draw?
6. Do a two-tailed ‘t’ test for zero slope for each predictor coefficient at a = .05.
7. (a) Which p-values indicate predictor significance at α=0.05? (b) Do the p-values support the conclusions you reached from the ‘t’ tests? (c) Do you prefer the ‘t’ test or the p-value approach? Why?
8. Based on the R2 and ANOVA table for your model, how would you describe the fit?
9. Use the standard error to construct an approximate prediction interval for Y. Based on the width of this prediction interval, would you say the predictions are good enough to have practical value?
10. (a) Generate a correlation matrix for your predictors. Round the results to three decimal places,
(b) Based on the correlation matrix, is collinearity a problem? Explain.

Source: Applied Statistics in Business and Economics, Tata Mc-Graw Hill,

*****