The following linear demand specification is estimated for Conlan Enterprises, a

Question

The following linear demand specification is estimated for Conlan Enterprises, a price-setting firm:

Q = a + bP + cM + dPR

Where Q is the quantity demanded of the product Conlan Enterprises sells, P is the price of that product, M is income, and PR is the price of a related product. The results of the estimation are presented below:

DEPENDENT VARIABLE:     Q           R-SQUARE              F-RATIO                 P-VALUE ON F
OBSERVATIONS:    32                         0.7984                     36.14                            0.0001

VARIABLE                       PARAMETER       STANDARD
                                          ESTIMATE           ERROR                T-RATIO             P-VALUE

INTERCEPT                       846.30                 76.70                      11.03                   0.0001
P                                          -8.60                   2.60                         -3.31                   0.0026
M                                        0.0184                0.0048                       3.83                    0.0007
PR                                     -4.3075                1.230                        -3.50                    0.0016
  
  

a. Evaluate all estimated coefficients based on their t-statistics. Be specific.
b. What is the critical value of F-statistic at the 1% level of significance? Based on this
     statistics, what can you conclude about the results of this regression?
c. Assuming that the income is $10,000, the price of the related good is $40, and Conlan chooses to set the price of this product at $30, determine the following:

Explanation / Answer

1. Ho: B0=0

degree of freedom is 28, so t value at 1% significance level is 2.763, and -2.763. SO all the coefficient are individually significant. with their coefficient value as given below

2. F(3,28) = 4.568 since our model F stat is 36.14 which is greater than critical value. so our model is overall significant. we cannot reject any variable from the model.

3.

The quantity of product Conlan expect to sell = 434.4. Putting the values of variable in the equation.

The own-price elasticity of demand = P*dQ/Q*dP = 30*-(8.6/434.6) = -.593

The income elasticity of demand = I*dQ/Q*dI = (1000/434.6)*.0184 = .042

VARIABLE   ESTIMATE STANDARD ERROR PARAMETER T-RATIO P-VALUE INTERCEPT 846.3 76.7 11.03 0.0001 P -8.6 2.6 -3.31 0.0026 M 0.0184 0.0048 3.83 0.0007 PR -4.3075 1.23 -3.5 0.0016

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