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# You decide to estimate the following quarterly sales forecasting model for new boat sales in your local county: Qt = a + bt + cD The equation is...

2. The marketing manager of a large supermarket chain wants to determine how sales of the soft drinks are affected by shelf space and product placement. The soft drinks were placed either at the front or back of the aisle. Data collected from a random sample of 20 equal-sized stores is summarized below.

a. Write out the multiple regression equation.
b. Estimate the regression coefficients using ordinary least squares and interpret them.
c. Predict the weekly sales for a store with 10 feet of shelf space situated at the back of the aisle.
d. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model.

Sales Space Place
1.6 5 0
2.2 5 1
1.4 5 0
1.9 10 0
2.4 10 0
2.6 10 1
2.3 15 0
2.7 15 0
2.8 15 1
2.6 20 0
2.9 20 0
3.1 20 1
1.9 10 0
2.4 10 0
2.6 10 1
2.3 15 0
2.7 15 0
1.4 5 0
1.9 10 0
2.4 10 0

Place = 1 indicates front of aisle
Place = 0 indicates back of aisle
Space = feet of shelf space
Sales given in 1000/week

1.You decide to estimate the following quarterly sales forecasting model for new boat sales in your local county: Qt = a + bt + cD The equation is estimated using quarterly data on new boat sales in the county from the 3rd quarter of 2001 to the 4th quarter of 2007 ( t = 1,…,26). The variable D is a dummy variable for the second quarter, which is the “season” for selling new boats: D = 1 in the second quarter, and 0 otherwise. The results of the estimation are: DEPENDENT VARIALBE: QT R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 26 0.5216 12.54 0.0002 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P- VALUE INTERCEPT 241.3 65.36 3.69 0.0012 T 47.52 13.55 3.51 0.0019 D 34.66 10.33 3.36 0.0027 a. Do the statistical estimates indicate a trend in sales? If so, what is the trend in units per quarter? b. Do the statistical estimates indicate a seasonal effect on 2nd quarter sales? If so, what is the seasonal effect in units per quarter? c. What are the forecasted sales for the 1st quarter of 2008? d. What are the forecasted sales for the 2nd quarter of 2008? e. What are the forecasted sales for the 3rd quarter of 2008? f. What are the forecasted sales for the 4th quarter of 2008? 2. The marketing manager of a large supermarket chain wants to determine how sales of the soft drinks are affected by shelf space and product placement. The soft drinks were placed either at the front or back of the aisle. Data collected from a random sample of 20 equal-sized stores is summarized below. a. Write out the multiple regression equation. b. Estimate the regression coefficients using ordinary least squares and interpret them. c. Predict the weekly sales for a store with 10 feet of shelf space situated at the back of the aisle. d. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model. Sales Space Place 1.6 5 0 2.2 5 1 1.4 5 0 Place = 1 indicates front of aisle 1.9 10 0 Place = 0 indicates back of aisle 2.4 10 0
2.6 10 1 Space = feet of shelf space 2.3 15 0 2.7 15 0 Sales given in 1000/week 2.8 15 1 2.6 20 0 2.9 20 0 3.1 20 1 1.9 10 0 2.4 10 0 2.6 10 1 2.3 15 0 2.7 15 0 1.4 5 0 1.9 10 0 2.4 10 0

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