# regression results

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 Preview

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 ...

#### 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).