Consider a firm subject to quarter-to-quarter variation in its sales. Suppose th

Question

Consider a firm subject to quarter-to-quarter variation in its sales. Suppose that the following equation was estimated using quarterly data for the period 2006-2013 (the time variable goes from 1 to 32). The variables D1, D2 and D3 are , respectively, dummy variables for the first , second, and third quarters (e.g., D is equal to 1 in the first quarter and 0 otherwise). Q1= a+bt+c1D1 +c2 D2 + c3 D3

The results of the estimation are presented here:

Dependent Variable: QT R-SQUARE F-RATIO P-VALUE ON F

OBSERVATION: 32 0.9817 361.133 0.0001

PARAMETER STANDARD

VARIABLE ESTIMATE ERROR T-RATIO P-VALUE

INTERCEPT 51.234 7.16 7.15 0.0001

T 31.127 0.524 5.97 0.0001

D1 -11.716 2.717 -4.31 0.0002

D2 -.1.424 0.636 -2.24 0.0985

D3 -17.367 2.112 -8.22 0.0001

A. At the 5 percent level of significance perform t- and F-tests to check for statistical significance of the coefficients and the equation. Discuss also the significance for the coefficients and equation in terms of p-values.

B. Calculate the intercept in each of the four quarters. What do these values imply?

C. Use this estimated equation to forecast sales in the four quarters of 2014.

Explanation / Answer

a) p-value for t-cofficients of all the parameters are almost zero except for D2 where it is 0.0985. So except D2 all other cofficients are statistically different from zero at 0.05 significance level. D2 is not statistically different from zero.

regarding p-value for f-test it is also very less i.e. almost zero . so this says that at 0.05 significance level the model considered is overall statistically significant

b)for D1 intercept = 51.234-11.716 = 39.518

D2 = 51.234-1.424 = 49.81

D3 = 51.234-17.367 = 33.867

D4 = 51.234

intercept means when the value of t is zero the value of Q1 will be the intercept value calculated for the respective quarter.

c)for quarter 1

Q1 = 39.518+31.127*33 = 1066.709

for quarter 2

Q2 = 49.81+31.127*34 = 1108.128

for quarter 3

Q1 = 33.867+31.127*35 = 1123.312

for quarter4

Q1 = 51.234+31.127*36 = 1171.806

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