Restaurant business. A data set containing the rankings of restaurant businesses in 2020 was created by the

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Restaurant business. A data set containing the rankings of restaurant businesses in 2020 was created by the Restaurant Business magazine. Four different restaurant types (Bakery Café, BBQ, Burger and Italian/Pizza) were retrieved from it, along with their yearly sales (in $ million) and year-over-year (YOY) number of units (in %). The data are shown in the following table. Restaurant Sales ($ million) YOY (%) Bakery Café 348 -3.8 Bakery Café 289 -5.6 Bakery Café 252 3.3 Bakery Café 192 0.0 Bakery Café 174 0.0 Bakery Café 162 -0.5 Bakery Café 152 8.0 Bakery Café 148 -2.8 BBQ 349 -6.4 BBQ 329 -11.1 BBQ 191 -6.9 BBQ 170 1.4 BBQ 168 -3.2 BBQ 136 21.6 BBQ 129 3.7 Burger 343 -10.7 Burger 290 8.6 Burger 275 -3.7 Burger 265 -3.4 Burger 227 -6.5 Burger 185 -11.5 Burger 179 1.1 Burger 159 0.7 Burger 138 7.7 Burger 126 7.1 Italian/Pizza 417 1.9 Italian/Pizza 275 1.9 Italian/Pizza 218 -3.4 Italian/Pizza 217 -1.7 Italian/Pizza 196 -14.1 Italian/Pizza 189 -1.3 Italian/Pizza 173 1.4 Italian/Pizza 164 3.1 Italian/Pizza 153 1.5 Italian/Pizza 150 0.0 Source: Based on information from Restaurant Business Online, www .restaurantbusinessonline.com, on January 30, 2021.

a. Propose a complete second-order model for the sales of a restaurant as a function of type of restaurant and YOY units.

b. Give the equation of the curve relating sales to YOY units for Italian/Pizza restaurants.

c. Repeat part b for sale of BBQ restaurants.

d. Which b’s in the model, part

a, allow for differences among the mean sales for the four different types of restaurants?

e. Fit the model, part

a, to the data using an available statistical software package. Is the model statistically useful for predicting sale? Test using a = .10.

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