A forecaster used the regression equation $Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }$ and quarterly sales data for 2004I-2021IV (t = 1,...,64)for an appliance manufacturer to obtain the results shown below.Q is quarterly sales,and $D _ { 1 } , D _ { 2 }$ and $D _ { 3 }$ are dummy variables for quarters I,II,and III. The estimated QUARTERLY increase in sales is ______ units,and the estimated ANNUAL increase in sales is ______ units.
A)1.5; 6
B)1.4; 4
C)30; 4
D)1.5; 40
E)none of the above

Question

A forecaster used the regression equation $Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }$ and quarterly sales data for 2004I-2021IV (t = 1,...,64)for an appliance manufacturer to obtain the results shown below.Q is quarterly sales,and $D _ { 1 } , D _ { 2 }$ and $D _ { 3 }$ are dummy variables for quarters I,II,and III.  The estimated QUARTERLY increase in sales is ______ units,and the estimated ANNUAL increase in sales is ______ units.
A)1.5; 6 
B)1.4; 4 
C)30; 4 
D)1.5; 40 
E)none of the above

Quizplus · Accepted Answer

The estimated quarterly increase in sales is the coefficient of t: b = 1.5
The estimated annual increase in sales is 4 times the estimated quarterly increase: 4b = 6. Therefore, the answer is (A) 1.5; 6.

A Forecaster Used the Regression Equation Qt=a+bt+c1D1+c2D2+c3D3Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }Qt​=a+bt+c1​D1​+c2​D2​+c3​D3​

A Forecaster Used the Regression Equation $Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }$