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Starting with the data on the price of a related commodity for years 1986 to 2005 listed below, we have estimated the regression for the quantity demanded of a commodity (which we now label Q ̂X), 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.
Year Pz($) 1986
14 1987
15 1988
15 1989
16 1990
17
Year Pz($) 1991
18 1992
17 1993
18 1994
19 1995
20
Year Pz($) 1996
20 1997
19 1998
21 1999
21 2000
22
Year Pz($) 2001
23 2002
23 2003
24 2004
25 2005
25
Q ̂x = 121.86 - 9.50Px + 0.04Y - 2.21Pz
(5.12) (2.18) (-0.68)
R2 = 0.9633 F = 167.33 D - W = 2.38
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 zero. 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) X and Z are complementary or substitutes?
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Solution Summary
Evaluate the regression results in terms of the signs of the coefficients, the statistical significance of the coefficients and the explanatory power of the regression (R2).
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The estimated regression equation is given as:
= 0.9633 F = 167.33
Where = quantity demanded of the commodity X
= Price of the commodity X
Y = consumer income
= Price of the commodity Z
It is given that the regression equation is estimated by using a sample of size n = 20. Hence the given regression results can be interpreted as follows:
1. The explanatory power of the model can be measured by using the R2 value. R2 = 0.9633 implies that the explanatory power of the model is 96.33%. This means 96.33% variations in the quantity demanded can be explained by the variations in the explanatory variables used in the model.
2. The F value ...
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