You have the following data: The (natural) logs of aggregate annual US electrici

Question

You have the following data: The (natural) logs of aggregate annual US electricity sales, of average electricity price,

1. Under the Tools / Data Analysis menu, choose the "Regression" option to fit the following partial-adjustment model, while requesting the residuals:LNKWHt = 0 + 1*LNKWH(t-1) + 2*LNPEt + 3*LNGNPt.

2. Use the regression results to calculate the partial adjustment coefficient, , as (1-1); also calculate the long run price elasticity 2 as 2/, and the long run income elasticity 3 as 3/.

3. Answer all of the following:

A. The dependent variable is technically quantity transacted, but is the sign of 2 more consistent with an elasticity of demand, or an elasticity of supply?

B. Based on the calculated value of 3, is it correct to categorize electricity (over the 1952-84 period) as a "luxury" good? Why or why not?

C. Calculate the correlation between the actual and fitted LNKWH values. Is (as expected) the square of this correlation identical to the value reported in the regression results for R-square?

YEAR LNKWH LNKWH (t-1) LNPE LNGNP 1951 5.80 #N/A 1.14 6.36 1952 5.87 5.80 1.13 6.40 1953 5.98 5.87 1.10 6.44 1954 6.05 5.98 1.09 6.42 1955 6.21 6.05 1.01 6.49 1956 6.30 6.21 0.96 6.51 1957 6.36 6.30 0.94 6.53 1958 6.38 6.36 0.95 6.52 1959 6.47 6.38 0.92 6.58 1960 6.54 6.47 0.97 6.60 1961 6.58 6.54 0.97 6.63 1962 6.66 6.58 0.94 6.68 1963 6.73 6.66 0.90 6.72 1964 6.80 6.73 0.87 6.78 1965 6.86 6.80 0.83 6.83 1966 6.94 6.86 0.77 6.89 1967 7.00 6.94 0.74 6.92 1968 7.09 7.00 0.68 6.96 1969 7.18 7.09 0.63 6.99 1970 7.24 7.18 0.60 6.99 1971 7.29 7.24 0.61 7.02 1972 7.37 7.29 0.62 7.08 1973 7.45 7.37 0.62 7.13 1974 7.44 7.45 0.77 7.13 1975 7.47 7.44 0.84 7.12 1976 7.53 7.47 0.85 7.17 1977 7.57 7.53 0.89 7.22 1978 7.61 7.57 0.90 7.27 1979 7.64 7.61 0.89 7.30 1980 7.65 7.64 0.97 7.30 1981 7.67 7.65 1.03 7.31 1982 7.64 7.67 1.09 7.30 1983 7.67 7.64 1.07 7.34 1984 7.73 7.67 1.07 7.40

Explanation / Answer

1) Please find the summary statistic:

SUMMARY OUTPUT Regression Statistics Multiple R 0.999084 R Square 0.998169 Adjusted R Square 0.997985 Standard Error 0.027101 Observations 34 ANOVA df SS MS F Significance F Regression 3 12.00837 4.00279 5450.092 3.92E-41 Residual 30 0.022033 0.000734 Total 33 12.0304 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.56916 0.348318 -1.63402 0.112708 -1.28052 0.142203 -1.28052 0.142203 LNKWH (t-1) 0.791347 0.061231 12.92406 8.55E-14 0.666298 0.916397 0.666298 0.916397 LNPE -0.14169 0.0358 -3.95799 0.000429 -0.21481 -0.06858 -0.21481 -0.06858 LNGNP 0.318283 0.112421 2.831168 0.008202 0.088688 0.547877 0.088688 0.547877

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