Question

Show the work please

1. Suppose you collected data from 1986 to 2005 to estimate the following demand function:

Q_X = b₀ + b₁ P_X + b₂ P_R + b₃ M

Assume R is a substitute and X is a normal good. The estimation results are reported below:

Dependent Variable: QX
Method: Least Squares
Date: 07/23/06   Time: 11:10
Sample: 1 20
Included observations: 20
Variable	Coefficient	Std. Error	t-Statistic	P-Value
C	19.777074	1.784179	11.0846	0.0000
PX	-13.79169	2.303381	-5.987587	0.0000
PR	5.069939	0.844016	6.006920	0.0000
M	0.257197	0.080063	3.212410	0.0054
R-squared	0.872386	F-statistic		36.45966
Adjusted R-squared	0.848459	P-Value for F-statistic		0.0000

           

            a. Conduct t tests to see if the coefficients are statistically significant at the 5% level of significance. Disregard the intercept. Use the p-values. A simple yes or no is not enough. Explain

           

            b. Conduct an F- test to see if the equation, as a whole, is statistically significant at the 5%. Use the p-value. A simple yes or no is not enough. Explain.

                       

Answer 1

a.The t statistics square measure already provided within the output. The t-test tests the alternate hypothesis that the constant of the variable is zero (or the variable is statistically significant).

For Px, p-value for the t-test = zero. At significance level of fifty, 0 < 0.05. so p-value < significance level. thus PX is statistically vital. this can be expected because the value of a standard sensible can have an effect on the demand of the great. If value will increase, individuals wouldn't be ready to purchase the maximum amount of the great s they were shopping for before. it's negatively associated with amount demanded of the traditional sensible.

For PR, p-value for the t-test = zero. At significance level of fifty, 0 < 0.05. so p-value < significance level. thus PR is statistically vital. this can be expected because the value of a complement will increase (decreases), the individuals would be shopping for less (more) of the complement and additional (less) of the traditional sensible. it's completely associated with the quanitity demanded of the traditional sensible.

For M, p-value for the t-test = zero. At significance level of fifty, 0.0054 < 0.05. so p-value < significance level. thus M is statistically vital.

b.The F datum is goven up to thirty six.45966.

The F check tests that the equation as an entire is statistically vital. p-value = zero. SInce p-value of zero < significance level of zero.05, we tend to conclude that the model is important.

c. R sq. is zero.872386. this can be on the point of one. It means the model could be a excellent work. 87.24% of variation within the quantitiy demanded is explained by the freelance variables.

-------------------------------

-------------------------------