A forecaster used the following regression equation Q1 = a + bt + c1D1 + c2 D2 +

Question

A forecaster used the following regression equation Q1 = a + bt + c1D1 + c2 D2 + c3D3

and quarterly sales data during 1999//to 2007/V(t=1,....,35) for an appliance manufacturer to obtain the estimation results shown below. Q is quarterly sales, and D1, D2, and D3 are seasonal dummy variables for quarters I, II, and III.

DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ON F

OBSERVATIONS: 35 0.9219 88.54 0.0001

PARAMETER STANDARD

VARIABLE ESTIMATE ERROR T-RATIO P-VALUE

INTERCEPT 21.0 6.2 3.39 0.0019

T 0.90 0.24 3.75 0.0007

D1 -8.0 2.60 -3.33 0.0043

D2 -6.0 1.80 -3.33 0.0022

D3 -4.0 0.60 -6.67 0.0001

a. Do the statistical estimates indicate a trend in sales? If so, what is the trend in units per quarter. Explain.

b. What are the estimated intercepts for each of the four quarters? Explain.

c. What level of sales are forecasted sales for the 1st, 2nd, 3rd, and 4th quarters of 2008? Explain.

Explanation / Answer

a. Do the statistical estimates indicate a trend in sales? If so, what is the trend in units per quarter. Explain.

p-value of t is 0.0007 < 0.05

hence it is significant

unit of b is sales per time

b. What are the estimated intercepts for each of the four quarters? Explain.

for

Q1 - intercept = 21 -8 = 13

Q2 - intercept = 21 -6 = 15

Q3 - intercept = 21 -4 = 17

Q4 - intercept = 21 = 21

c. What level of sales are forecasted sales for the 1st, 2nd, 3rd, and 4th quarters of 2008? Explain

y^ = 21 +0.9 *t -8 *D1 -6 *D2 -4 *D3

for 2008 Q1 , D 1 = 1 ,D2 = 0 , D3 = 0 , t = 37

y^ = 21 + 0.9 * 37 -8 = 46.3

Q2 , D 1 = 0 ,D2 = 1 , D3 = 0 , t = 38

y^ = 21 + 0.9 * 38-6 = 49.2

Q3 , D 1 = 0 ,D2 = 0 , D3 = 1 , t = 39

y^ = 21 + 0.9 * 39 -4 = 52.1

Q4 , D 1 = 0 ,D2 = 0 , D3 = 0 , t = 40

y^ = 21 + 0.9 * 40 = 57

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