The Excel le (prices.xls) contains data on three variables, gas price (Y ), natu
ID: 3317254 • Letter: T
Question
The Excel le (prices.xls) contains data on three variables, gas price (Y ), natural gas (X), and electricity (Z) of a sample of 10 observations from 1996 to 2005.
(a) Find the least-squares regression equation of Y on X and Z with the aid of Stata. [Hint: the regression equation is Y = 0 + 1X + 2Z + .]
(b) Find the coefficient of determination, R2, with the aid of the computer software. What does the number in R2 imply?
(c) Find the value of the F-test. What does the F-test say about the overall signicance of this model?
(d) Test the null hypothesis at the 0.05 signicance level that the regression coefficient of the population regression B1, is 0.0 versus the alternative hypothesis that the regression
coefficient exceeds 0.0.
(e) Test the null hypothesis at the 0.05 signicance level that the regression coefficient of the population regression, B2, is 0.0 versus the alternative hypothesis that the regression
coefficient exceeds 0.0.
(f) Based on the estimated equation bY = b0 + b1X + b2Z, determine the estimated value of Y from the given values of X and Z.
(g) Estimate the gas price at the natural gas of 9 and the electricity of 8.
(h) Calculate the VIF for each independent variable. Is there any multi-collinearity problemin this regression? Please explain.
Year Gas Price Natural Gas Electricity 1,996 1.27 6.34 8.36 1,997 1.24 6.94 8.43 1,998 1.07 6.82 8.26 1,999 1.18 6.69 8.16 2,000 1.52 7.76 8.24 2,001 1.46 9.63 8.63 2,002 1.39 7.89 8.46 2,003 1.60 9.63 8.7 2,004 1.90 10.75 8.97 2,005 2.31 12.81 9.1Explanation / Answer
Regression Analysis: Gas Price versus Natural Gas, Electricity
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 2 1.12033 0.560165 30.80 0.000
Natural Gas 1 0.10725 0.107248 5.90 0.046
Electricity 1 0.00094 0.000938 0.05 0.827
Error 7 0.12731 0.018187
Total 9 1.24764
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.134860 89.80% 86.88% 75.86%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -0.63 3.11 -0.20 0.845
Natural Gas 0.1532 0.0631 2.43 0.046 8.82
Electricity 0.096 0.423 0.23 0.827 8.82
a)
Regression Equation
Gas Price = -0.63 + 0.1532 Natural Gas + 0.096 Electricity
b)
R2 = 89.80% this implies adequacy of the fitted regression model is good.
C)
F = 30.80 with p- value 0.00 this implies Model is significant with respect to parameters.
d)
Ho : B1 = 0 Vs Ha : B1 >0
P- value = 0.046 < 0.05 then we reject Ho.
e)
Ho : B2 = 0 Vs Ha : B2 >0
P- value = 0.827 > 0.05 then we do not reject Ho.
g)
at natural gas of 9 and electricity 8 gas prize is,
Gas Price = -0.63 + 0.1532 Natural Gas + 0.096 Electricity
Gas Price = -0.63 + 0.1532 * 9 + 0.096 * 8
Gas Price = 1.52
h)
Natural Gas having VIF 8.82 > 1 and Electricity having VIF 8.82 > 1 therefore there is problem of multi-collinearity presnt in the regression analysis.
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