A fast food restaurant chain whose menu featureshamburgers and chicken sandwidchs is about to add a fish sandwichto its menu.There was a considerable debate among the executives about the likely demand and what the appropriate price should be. A recently hired economics graduate observed that the demand curve would reveal great deal about the relationship between price and demand. She convinced the executives to conduct an experimenta random sample of 20 restaurants was drawn. The restaurants were almost identical in terms of sales and in the demographics of the surrounding area. At each reastaurant , the fish sandwich was sold at a different price. the number of sandwiches sold over a 7 day period and the price were recorded.
A. Compare the linear, quadratic, and cubic models to determine the best model. Justify your selection statistically.
B. What is the residual for the 1st observation (sales = 377, price = 1.50) based on your best model.
C. Are there any large leverage points? Justify.
D. With 95% confidence, find the interval of weekly sales if the price is $2 for a particular restaurant.
Data
Sales Price
377 1.50
364 1.59
326 1.70
339 1.75
341 1.79
318 1.89
308 1.95
305 1.99
293 2.10
294 2.19
281 2.25
290 2.29
276 2.39
274 2.50
273 2.59
268 2.69
270 2.75
269 2.79
265 2.89
268 2.99