Starting with the data fro Problem 6 and the data on the price of a related comm
ID: 1167551 • Letter: S
Question
Starting with the data fro 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 for a commodity (which we now relable (Q x), on the price of the commodity (which we now relable (Qx), on the price of the commodity (which we now lable Px), consumer income (which we now label Y), and price of the rleated commodity (Pz), and we obtgained the following results.
Qx=121.86-9.50Px+ 0.04Y - 2.21P
(-5.12) (2.18) (-0.68)
R2=0.9633 F=167.33 D-W=2.38
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
(b) Evaluate the regression results. 1.P15(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 order 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) What type of commodity is Z? Can you be sure? Are X and Z complements or substitutes?
Explanation / Answer
(1) Regression Interpretation
(a) Qx = 121.86 - 9.50Px + 0.04Y - 2.21Pz
If Px = Y = Pz = 0, then Qx = 121.86. This is autonomous demand, or the maximum quantity demanded by consumers if the good is sold for free.
The goods own price is inversely related to its demand, following the law of demand. If Y & Pz are both kept constant, for every 1% change in goods own price, its demand will change by 9.5% in the opposite direction.
Income coefficient is 0.04, implying that as income changes by 1%, demand changes by 0.04% in the same direction, which indicates the good is normal.
As the price of related good changes by 1%, demand changes by 2.21% in the opposite direction. This signifies that X & Z are complements.
(b) R2 value is 0.9633, implying that 96.33% of the variability is explained by the explanatory variables, which is very high, indicating a goodness of fit.
(c) Judging by the absolute t-values, only the coefficients of own price and income are significant and these variables do affect Qx. But t-value for related good price is less than 2, so is insignificant and cannot explain the model.
(d) X is a normal good, and Z is a complementary good, as explained in previous section.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.