Question

A forecaster used the regression equation Qt = a + bt + C1D1 + c2D2 + c3D3 and quarterly sales data for 19981-20161V (t = 1, ...,72) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1, D2, and D3 are dummy variables for quarters I, II, and III. DEPENDENT VARIABLE: QT R-SQUARE P-VALUE ON F OBSERVATIONS: 72 0.8798 122.547 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 36 12.54 2.87 0.0055 2.5 0.860 2.91 D1 12.0 3.26 3.68 0.0005 D2 30.0 10.68 2.81 0.0066 D3 45.0 18.45 2.44 0.0174 In any given year, quarterly sales tend to vary as follows: T 0.0049 A) QIV > QIII > QII > QI B) QIII > QII QI > QIV C) QI > QII > III > QIV D) QII > QIII > QIV>QI E) QI > QII > QIV > Q11

Answer 1

Answer option B)

c1 = 12, C2 = 30, C3 = 45, a = 36

for Quarter IV) D1= D2= D3 = 0

Sales Q4 = a +bt = 36+bt

Quarter 1 sales, D1 = 0

Sales = a +bt+ c1 = (a+c1)+ bt

Q1= 48+bt

Q2 = (a+C2)+bt= 66+bt

Q3= (a+C3)+bt = 81 + bt

for any given time,

QIV< QI < QII< QIII