Starting with the data for problem 6 and the data on the price of a related comm

Question

Starting with the data for problem 6 and the data on the price of a related commodity for the years 1986 to 2005 given below, we estimated the regression for the quantity demanded of a commodity (which we now relabel QX), on the price of the commodity (which we now label PX), consumer income (which we now label Y), and the price of the related commodity (PZ), and we obtained the following results. (If you can, run this regression yourself; you should get results identical or very similar to those given below.) Year 1986 1987 1988 1989 1990 PZ ($) 14 15 15 16 17 Year 1991 1992 1993 1994 1995 PZ ($) 18 17 18 19 20 Year 1996 1997 1998 1999 2000 PZ ($) 20 19 21 21 22 Year 2001 2002 2003 2004 2005 PZ ($) 23 23 24 25 25 QX = 121.86 9.50PX + 0.04Y 2.21PZ (-5.12) (2.18) (-0.68) R2 = 0.9633 F = 167.33 D W = 2.38 (b) is to evaluate the above regression results in terms of the signs of the coefficients, the statistical significance of the coefficients, and the explanatory power of the regression (R2). The number in parentheses below the estimated slope coefficients refer to the estimated t values. The rule of thumb for testing the significance of the coefficients is if the absolute t value is greater than 2, the coefficient is significant, which means the coefficient is significantly different from 0. For example, the absolute t value for Px is 5.12, which is greater than 2; therefore, the coefficient of Px, (-9.50) is significant. In other words, Px does affect Qx. If the price of the commodity X increases by $1, the quantity demanded (Qx) will decrease by 9.50 units. (c) Are X and Z complements or substitutes?

Explanation / Answer

y=-9.470x1+0.029x2+114.074
where x_1 represents the independent variable 'price'
x_2 represents the independent variable 'consumer^' s income^'
and,y represents the dependent variable 'quantity demanded^'
Let us test the significance for the slope parameters of the independent variables.
The null hypothesis,H_0 states that there is no significant correlation, or the correlation coefficient ?=0.
Decision Rule:
Reject H_0 if the p-value < 0.05 (significance level,alpha)

Independent Variables p- value Null Hypothesis Decision Conclusion
x_1 0.00007 ?_1=0 Reject H_0 x_1 has a significant contribution in the regression model
x_2 0.0003 ?_1=0 Reject H_0 x_2 has a significant contribution in the regression model

The unadjusted and the adjusted coefficients of determination are given as 0.984 and 0.964 respectively.

The null hypothesis,H_0 states that there is no significant correlation, or the correlation coefficient ?=0.
Significance Level, ? = 0.05

Decision Rule:
Reject H_0 if the Significance F( p-value) < 0.05 (significance level,alpha)

From the ANOVA table, we find that the Significance F=1.856

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