Problem:
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 QˆX), 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?