1. Data Given
Year CPI WPI Year CPI WPI
1960 29.8 31.7 1980 86.3 93.8
1961 30.0 31.6 1981 94.0 98.8
1962 30.4 31.6 1982 97.6 100.5
1963 30.9 31.6 1983 101.3 102.3
1964 31.2 31.7 1984 105.3 103.5
1965 31.8 32.8 1985 109.3 103.6
1966 32.9 33.3 1986 110.5 99.70
1967 33.9 33.7 1987 115.4 104.2
1968 35.5 34.6 1988 120.5 109.0
1969 37.7 36.3 1989 126.1 113.0
1970 39.8 37.1 1990 133.8 118.7
1971 41.1 38.6 1991 137.9 115.9
1972 42.5 41.1 1992 141.9 117.6
1973 46.2 47.4 1993 145.8 118.6
1974 51.9 57.3 1994 149.7 121.9
1975 55.5 59.7 1995 153.5 125.7
1976 58.2 62.5 1996 158.6 128.8
1977 62.1 66.2 1997 161.3 126.7
1978 67.7 72.7 1998 163.9 122.7
1979 76.7 83.4 1999 168.3 128.0

2. Regression on the given data
The SAS System
The REG Procedure
Model: MODEL1
Dependent Variable: CPI CPI
Number of Observations Read 40
Number of Observations Used 40
Analysis of Variance
Source DF Sum of Mean F Value Pr > F
Squares Square
Model 1 86235 86235 882.01 <.0001
Error 38 3715.30916 97.77129
Corrected Total 39 89951
Root MSE 9.88794 R-Square 0.9587
Dependent Mean 86.17000 Adj R-Sq 0.9576
CoeffVar 11.47492
Parameter Estimates
Variable Label DF Parameter Standard t Value Pr > |t| Variance
Estimate Error Inflation
Intercept Intercept 1 -13.77536 3.71075 -3.71 0.0007 0
WPI WPI 1 1.26999 0.04276 29.70 <.0001 1.00000

3. The SAS System
The REG Procedure
Model: MODEL1
Dependent Variable: CPI CPI

4. ***From the above we see that the data has auto correlation. To Remove the
Auto correlation we use the method of first difference

5. New Data Set:
First Difference method
Year CPI WPI CPID WPID Year CPI WPI CPID WPID
1960 29.8 31.7 1980 86.3 93.8 -9.6 -10.4
1961 30 31.6 -0.2 0.1 1981 94 98.8 -7.7 -5
1962 30.4 31.6 -0.4 0 1982 97.6 100.5 -3.6 -1.7
1963 30.9 31.6 -0.5 0 1983 101.3 102.3 -3.7 -1.8
1964 31.2 31.7 -0.3 -0.1 1984 105.3 103.5 -4 -1.2
1965 31.8 32.8 -0.6 -1.1 1985 109.3 103.6 -4 -0.1
1966 32.9 33.3 -1.1 -0.5 1986 110.5 99.7 -1.2 3.9
1967 33.9 33.7 -1 -0.4 1987 115.4 104.2 -4.9 -4.5
1968 35.5 34.6 -1.6 -0.9 1988 120.5 109 -5.1 -4.8
1969 37.7 36.3 -2.2 -1.7 1989 126.1 113 -5.6 -4
1970 39.8 37.1 -2.1 -0.8 1990 133.8 118.7 -7.7 -5.7
1971 41.1 38.6 -1.3 -1.5 1991 137.9 115.9 -4.1 2.8
1972 42.5 41.1 -1.4 -2.5 1992 141.9 117.6 -4 -1.7
1973 46.2 47.4 -3.7 -6.3 1993 145.8 118.6 -3.9 -1
1974 51.9 57.3 -5.7 -9.9 1994 149.7 121.9 -3.9 -3.3
1975 55.5 59.7 -3.6 -2.4 1995 153.5 125.7 -3.8 -3.8
1976 58.2 62.5 -2.7 -2.8 1996 158.6 128.8 -5.1 -3.1
1977 62.1 66.2 -3.9 -3.7 1997 161.3 126.7 -2.7 2.1
1978 67.7 72.7 -5.6 -6.5 1998 163.9 122.7 -2.6 4
1979 76.7 83.4 -9 -10.7 1999 168.3 128 -4.4 -5.3
Plotting the Data to check volatility:
6
4
2
0
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
-2
CPI
-4
WPI
-6
-8
-10
-12

6. *** WPI is More Volatile observed from the graph contradicting to normal notion. May be because
CPI in US is managed
Running the linear regression on the new Data Set after removing the Auto –Correlation
The SAS System
The REG Procedure
Model: MODEL1
Dependent Variable: CPID CPID
Number of Observations Read 38
Number of Observations Used 38
Analysis of Variance
Source DF Sum of Mean F Value Pr > F
Squares Square
Model 1 73.11367 73.11367 20.99 <.0001
Error 36 125.37712 3.48270
Corrected Total 37 198.49079
Root MSE 1.86620 R-Square 0.3683
Dependent Mean -3.63947 Adj R-Sq 0.3508
CoeffVar -51.27661
Parameter Estimates
Variable Label DF Parameter Standard t Value Pr > |t| Variance
Estimate Error Inflation
Intercept Intercept 1 -2.65555 0.37117 -7.15 <.0001 0
WPID WPID 1 0.41087 0.08967 4.58 <.0001 1.00000

7. The SAS System
The REG Procedure
Model: MODEL1
Dependent Variable: CPID CPID

8. Residual Plot is Decent
Residuals are random in plot
R-Square can be improved by removing the outliers seen in graph 3
Quantile graph seem to be good.

9. Conclusion:
Our interpretation is that WPI does feed in CPI but always there would be a lag.
Thus because of this R-square value is comparatively low. Hence, we believe a
time series analysis will be a apt technique to analyse the given data set.