ECONOMETRICS PROBLEM (a ) The multiple regression result for gasoline demand (GD

Question

ECONOMETRICS PROBLEM

(a) The multiple regression result for gasoline demand (GD in Thousand Barrels/Day) is presented under equation 1 below. The explanatory variables are the price of gasoline (GP in  Dollar per Barrel); the price of diesel (DP in  Dollar per Barrel) and income (Y in  Dollar Million). You are required to interpret the result with particular reference
to the economic meaning of the sign and size of the coefficients, the p-value, the Adjusted R-squared, the Durbin-Watson statistic, and the F-statistic including the diagnostic tests.

GDt = 15.819 4.073GPt+ 1.037DPt+ 3.305Yt
         (0.041)    (0.034)     (0.029       (0.017

R2 = 0.77; ADJUSTED R2 = 0.75; F-STAT= 40.53 (0.014); DW = 1.90

Note: The chosen level of statistical significance is 5% and figures in the parentheses denote the p values

Ramsey RESET- F(1, 35)=12.964(0.046); JB=23.756(0.026);
ARCH-F(1, 34)=5.380(0.217); Breusch-Pagan LM = 3.004(0.429)

(b) The above has been re-specified by taking the natural log of both sides of the model. The result is presented below. Interpret the result with particular reference to the same requirements in (a)LnGDt= 3.862 0.759LnGPt+ 0.407LnDPt+ 0.230LnYt
             (0.012) (0.011)           (0.001)            (0.031)
R2= 0.79; Adjusted-R2 = 0.77; F Stat = 44.67 (0.001); DW = 1.91

Note: The chosen level of statistical significance is 5% and figures in the parentheses denote the p values

Ramsey RESET- F(1, 35)=2.369(0.392); JB=13.067(0.148);

ARCH-F(1, 34)=6.027(0.484); Breusch-Pagan LM = 2.611(0.139)

Explanation / Answer

(a) In this model, we finds that the slope of the regression line is –4.073 when the gasoline demand is effect by price of gasoline and other variable zero. This says that price of gasoline is expected to decrease by 4.073 Dollar per Barrel on average per 1 Thousand Barrels/Day increase in gasoline demand.

Similarly, when the gasoline demand is effect by price of diesel or income, we say that price of diesel or income is expected to increase 1.037 or 3.305 Dollar per Barrel on average per 1 Thousand Barrels/Day increase in gasoline demand.

All the explanatory variable, the p-value is less than 0.05, which says that there is a significant effect between these variables that is we reject the null hypothesis. We conclude that the coefficient is not equal to zero because changes in the predictor's value are related to changes in the response variable.

the value of adjusted R-squared is 0.75 indicates that the model explains 75% the variability of the response variables around its mean.

The Durbin-Watson d = 1.90, which is between the two critical values of 1.5 < d < 2.5 and therefore we can assume that there is no first order linear auto-correlation in our multiple linear regression data.

F-statistic says that the null hypothesis that there is no linear relationship between the variables (R²=0). Here the F-test is highly significant, thus we can assume that there is a linear relationship between the variables in our model.

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