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. Using a 5 percent significance level,these estimation results indicate that sales in
A)the first quarter are greater than sales in any other quarter.
B)the second quarter are greater than sales in any other quarter.
C)the third quarter are greater than sales in any other quarter.
D)the fourth quarter are greater than sales in any other quarter.

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.  Using a 5 percent significance level,these estimation results indicate that sales in
A)the first quarter are greater than sales in any other quarter. 
B)the second quarter are greater than sales in any other quarter. 
C)the third quarter are greater than sales in any other quarter. 
D)the fourth quarter are greater than sales in any other quarter.

Quizplus · Accepted Answer

The coefficient of the dummy variable for the third quarter (D3) is positive and significant at the 5% level, which means that sales in the third quarter are higher than in the reference quarter (which is not specified in the question). None of the other dummy variables are significant, so we cannot conclude that sales in any other quarter are higher than in the reference quarter. Therefore, the answer is C, the third quarter has the highest sales.

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 $Q _ { t } = a + b t + c _ { 1 } D _ { 1 } + c _ { 2 } D _ { 2 } + c _ { 3 } D _ { 3 }$