Exam 7: Demand Estimation and Forecasting

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Refer to the following: The following linear demand specification is estimated for Conlan Enterprises, a price-setting firm: Q=a+bP+cM+dPRQ = a + b P + c M + d P _ { R } where Q is the quantity demanded of the product Conlan Enterprises sells, P is the price of that product, M is income, and PRP _ { R } is the price of a related product. The results of the estimation are presented below: DEPENDENT VARIABLE: Q R-SQUARE F-RATIO P-VALUEONF OBSERVATIONS: 32 0.7984 36.14 0.0001 VARIABLE PARAMETER STANDARD ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 846.30 76.70 11.03 0.0001 P -8.60 2.60 -3.31 0.0026 M 0.0184 0.0048 3.83 0.0007 PR -4.3075 1.230 -3.50 0.0016 For the next 2 questions suppose income remains at $10,000 but the price of the related good increases to $60 and Conlan decides to raise the price of its product to $50. -What is the new own price elasticity of demand?

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Refer to the following: The manufacturer of Beanie Baby dolls used quarterly price data for 2005I - 2013IV (t = 1, ..., 36) and the regression equation Pt=a+bt+c1D1t+c2D2t+c3D3tP _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t } to forecast doll prices in the year 2014. PtP _ { t } is the quarterly price of dolls, and D1t,D2tD 1 _ { t } , D 2 _ { t } and D3tD 3 _ { t } are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 36 0.9078 76.34 0.0001 VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTERCEPT 24.0 6.20 3.87 0.0005 T 0.800 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.00 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 -What is the estimated intercept of the trend line in the 4th quarter?

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Refer to the following: The following linear demand specification is estimated for Conlan Enterprises, a price-setting firm: Q=a+bP+cM+dPRQ = a + b P + c M + d P _ { R } where Q is the quantity demanded of the product Conlan Enterprises sells, P is the price of that product, M is income, and PRP _ { R } is the price of a related product. The results of the estimation are presented below: DEPENDENT VARIABLE: Q R-SQUARE F-RATIO P-VALUEONF OBSERVATIONS: 32 0.7984 36.14 0.0001 VARIABLE PARAMETER STANDARD ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 846.30 76.70 11.03 0.0001 P -8.60 2.60 -3.31 0.0026 M 0.0184 0.0048 3.83 0.0007 PR -4.3075 1.230 -3.50 0.0016 Assume that the income is $10,000, the price of the related good is $40, and Conlan chooses to set the price of this product at $30. -At the prices and income given above, what is the price elasticity of demand?

(Multiple Choice)
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Refer to the following: 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 } and quarterly sales data for 1996I-2013IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2D _ { 1 } , D _ { 2 } and D3D _ { 3 } are dummy variables for quarters I, II, and III. DEPENDENTVARIAELE: aT R-SQUARE F-RATIO P-VALUE ON F OESERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIAELE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 -The estimated QUARTERLY increase in sales is ______ units, and the estimated ANNUAL increase in sales is ______ units.

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Problems in forecasting include:

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Refer to the following: 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 } and quarterly sales data for 1996I-2013IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2D _ { 1 } , D _ { 2 } and D3D _ { 3 } are dummy variables for quarters I, II, and III. DEPENDENTVARIAELE: aT R-SQUARE F-RATIO P-VALUE ON F OESERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIAELE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 -At the 5 percent level of significance, is there a statistically significant trend in sales?

(Multiple Choice)
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Refer to the following: 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 } and quarterly sales data for 1996I-2013IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2D _ { 1 } , D _ { 2 } and D3D _ { 3 } are dummy variables for quarters I, II, and III. DEPENDENTVARIAELE: aT R-SQUARE F-RATIO P-VALUE ON F OESERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIAELE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 -Using the estimation results given above, the predicted level of sales in 2014I is _______ units.

(Multiple Choice)
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Refer to the following: 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 } and quarterly sales data for 1996I-2013IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2D _ { 1 } , D _ { 2 } and D3D _ { 3 } are dummy variables for quarters I, II, and III. DEPENDENTVARIAELE: aT R-SQUARE F-RATIO P-VALUE ON F OESERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIAELE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 -In any given year, quarterly sales tend to vary as follows:

(Multiple Choice)
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Refer to the following: The manufacturer of Beanie Baby dolls used quarterly price data for 2005I - 2013IV (t = 1, ..., 36) and the regression equation Pt=a+bt+c1D1t+c2D2t+c3D3tP _ { t } = a + b t + c _ { 1 } D 1 _ { t } + c _ { 2 } D 2 _ { t } + c _ { 3 } D 3 _ { t } to forecast doll prices in the year 2014. PtP _ { t } is the quarterly price of dolls, and D1t,D2tD 1 _ { t } , D 2 _ { t } and D3tD 3 _ { t } are dummy variables for quarters I, II, and III, respectively. DEPENDENT VARIABLE: PT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 36 0.9078 76.34 0.0001 VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTERCEPT 24.0 6.20 3.87 0.0005 T 0.800 0.240 3.33 0.0022 D1 -8.0 2.60 -3.08 0.0043 D2 -6.00 1.80 -3.33 0.0022 D3 -4.0 0.60 -6.67 0.0001 -At the 2 percent level of statistical significance, is there a statistically significant trend in the price of dolls?

(Multiple Choice)
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Refer to the following: A consulting firm estimates the following quarterly sales forecasting model: Qt=a+bt+cDQ _ { t } = a + b t + c D The equation is estimated using quarterly data from 2003I-2013III (t = 1,..., 43). The variable D is a dummy variable for the second quarter where: D = 1 in the second quarter, and 0 otherwise. The results of the estimation are: DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ONF OBSERVATIONS: 43 0.8644 127.5 0.0001 VARIABLE PARAMETER STANDARD ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 22.5 9.32 2.41 0.0201 T 1.86 0.55 3.38 0.0016 D 2.0 0.71 2.82 0.0075 -Using the estimated trend line, what is the predicted level of sales in 2013IV ?

(Multiple Choice)
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Refer to the following: The estimated demand for a good is Q^=255P+0.32M+12PR\hat { Q } = 25 - 5 P + 0.32 M + 12 P _ { R } where Q is the quantity demanded of the good, P is the price of the good, M is income, and PRP _ { R } is the price of related good R. -If the price of the good falls by $4, the quantity demanded will ________ by ________ units.

(Multiple Choice)
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Refer to the following: A consulting firm estimates the following quarterly sales forecasting model: Qt=a+bt+cDQ _ { t } = a + b t + c D The equation is estimated using quarterly data from 2003I-2013III (t = 1,..., 43). The variable D is a dummy variable for the second quarter where: D = 1 in the second quarter, and 0 otherwise. The results of the estimation are: DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ONF OBSERVATIONS: 43 0.8644 127.5 0.0001 VARIABLE PARAMETER STANDARD ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 22.5 9.32 2.41 0.0201 T 1.86 0.55 3.38 0.0016 D 2.0 0.71 2.82 0.0075 -What is the estimated intercept of the trend line in the second quarter?

(Multiple Choice)
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A representative sample

(Multiple Choice)
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Refer to the following: 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 } and quarterly sales data for 1996I-2013IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2D _ { 1 } , D _ { 2 } and D3D _ { 3 } are dummy variables for quarters I, II, and III. DEPENDENTVARIAELE: aT R-SQUARE F-RATIO P-VALUE ON F OESERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIAELE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 -Using the estimation results given above, the predicted level of sales in 2014II is _______ units.

(Multiple Choice)
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At the 1 percent level of significance, the number of degrees of freedom for a t-test is _____, and the critical value of the t-statistic is ________. Only parameter estimate(s) ________ is (are) NOT statistically significant at the 1 percent level of significance.

(Multiple Choice)
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Refer to the following: 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 } and quarterly sales data for 1996I-2013IV (t = 1, ..., 64) for an appliance manufacturer to obtain the results shown below. Q is quarterly sales, and D1,D2D _ { 1 } , D _ { 2 } and D3D _ { 3 } are dummy variables for quarters I, II, and III. DEPENDENTVARIAELE: aT R-SQUARE F-RATIO P-VALUE ON F OESERVATIONS: 64 0.8768 107.982 0.0001 PARAMETER STANDARD VARIAELE ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 30.0 12.8 2.34 0.0224 T 1.5 0.70 2.14 0.0362 D1 10.0 3.0 3.33 0.0015 D2 25.0 7.2 3.47 0.0010 D3 40.0 15.8 2.53 0.0140 -At the 5 percent level of significance, is there a statistically significant trend in sales?

(Multiple Choice)
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The estimated cross-price elasticity of demand for cement relative to the price of asphalt is

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If tax revenue per capita (M) increases 5%, the estimated quantity of cement demanded will

(Multiple Choice)
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Refer to the following: A consulting firm estimates the following quarterly sales forecasting model: Qt=a+bt+cDQ _ { t } = a + b t + c D The equation is estimated using quarterly data from 2003I-2013III (t = 1,..., 43). The variable D is a dummy variable for the second quarter where: D = 1 in the second quarter, and 0 otherwise. The results of the estimation are: DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ONF OBSERVATIONS: 43 0.8644 127.5 0.0001 VARIABLE PARAMETER STANDARD ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 22.5 9.32 2.41 0.0201 T 1.86 0.55 3.38 0.0016 D 2.0 0.71 2.82 0.0075 -At the 1 percent level of significance, is there a statistically significant trend in sales?

(Multiple Choice)
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Refer to the following: A consulting firm estimates the following quarterly sales forecasting model: Qt=a+bt+cDQ _ { t } = a + b t + c D The equation is estimated using quarterly data from 2003I-2013III (t = 1,..., 43). The variable D is a dummy variable for the second quarter where: D = 1 in the second quarter, and 0 otherwise. The results of the estimation are: DEPENDENT VARIABLE: QT R-SQUARE F-RATIO P-VALUE ONF OBSERVATIONS: 43 0.8644 127.5 0.0001 VARIABLE PARAMETER STANDARD ESTIMATE ERROR T-RATIO P-VALUE INTERCEPT 22.5 9.32 2.41 0.0201 T 1.86 0.55 3.38 0.0016 D 2.0 0.71 2.82 0.0075 -Using the estimated trend line, what is the predicted level of sales in 2014I ?

(Multiple Choice)
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