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values for parameters obtained from regression

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Use the following to answer a-e. Please show all work in as much detail as possible. Assume Q is the quantity demanded for medical care services. The linear industry demand function takes the form

Q = a +bp +cM +dPr

where:
P = the price of the medical care
M = median household income
Pr = the price of a related good

dependent variable: Q R-square F-ratio P-value on F
0.8118 28.75 0.0001

Observations: 24

Variable PARAMETER ESTIMATE std error T-Ratio P-value

INTERCEPT 68.38 12.665 5.41 0.0001
P -6.5 3.15 -2.06 0.0492
M 0.13926 0.0131 10.63 0.0001
PR -10.77 2.45 -4.4 0.0002

a. Is the sign of ^b (hat over b) as would be predicted theoretically? Why/
b. What does the sign of ^c(hat over c) imply about the good?
c. what does the sign of ^d imply about the relation between the medical good and the related good R?
d. Are the parameter estimates ^a, ^b, ^c, and ^d statistically significant at the 5% level of significance?
e. Using the values P = 225, M= 24,000, and Pr =60, calculate the estimates of
(1) the price elasticity of demand (^Ed)
(2) the income elasticity of demand (^Ey)
(3) the cross-price elasticity (^Ec)

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This posting explores values for parameters obtained from regression.

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The equation given in the question is

Q = a +bp +cM +dPr

where

P = the price of the medical care
M = median household income
Pr = the price of a related good

The table provides various values for parameters obtained from regression. Before addressing those it will be a good idea to determine what signs to expect from each parameter above (b, c, d), and why should that parameter have that particular sign. To begin with consider b, the parameter with the variable p that is the price of medical care. One would expect the quantity demanded to fall as price of care goes up, that is as p rises Q should fall, and that is possible if b is less than zero, that is b is negative. M is the median household income, an indicator of wealth. The wealthier people get the more they can pay for medical care, and hence one would expect that the parameter with M, c should be positive. Finally, assuming that there is a related good d is the parameter associated with the price of the related good. One point to note here is that the related good may be a substitute (that is something that can be used instead of healthcare, and I cannot think of a substitute here!), or a complement (that is something that is ...

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