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 a commodity (which we now reliable (Q x), on the price of the commodity (which we now reliable (Qx), on the price of the commodity (which we now live Px), consumer income (which we now label Y), and price of the related commodity (Pz), and we obtained 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
The year 1986 1987 1988 1989 1990
Pz($) 14 15 15 16 17
The year 1991 1992 1993 1994 1995
Pz($) 18 17 18 19 20
The year 1996 1997 1998 1999 2000
Pz($) 20 19 21 21 22
The year 2001 2002 2003 2004 2005
Pz($) 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 $1, the quantity demanded (Qx) will decrease by 9.50 units.
(c) What type of commodity is Z? Can you be sure? Are X and Z complements or substitutes?
Starting with the data fro Problem 6 and the data on the price of a related commodity for the years 1986 to 2005 given below, we estimated the regression for the quantity demanded a commodity (which we now reliable (Q x), on the price of the commodity (which we now reliable (Qx), on the price of the commodity (which we now live Px), consumer income (which we now label Y), and price of the related commodity (Pz), and we obtained the following results.
Qx=121.86-9.50Px+ 0.04Y - 2.21P
(-5.12) (2.18) (-0.68)
R2=0.9633 F=167.33 D-W=2.38
The year 1986 1987 1988 1989 1990
Pz($) 14 15 15 16 17
The year 1991 1992 1993 1994 1995
Pz($) 18 17 18 19 20
The year 1996 1997 1998 1999 2000
Pz($) 20 19 21 21 22
The 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?
