Lab 10 Instructions: Each group can work together on this lab; however, each member of the group will submit their answers online for auto grading. Each member will have two chances to submit their answers so if you work in a group this will benefit all group members. Each member will get the score they submit. Each individuals highest scores will count toward their grade. Orange Juice: How much should a convenience store charge for a half-gallon of orange juice? This chain collected data on the sales of orange juice at 50 randomly selected locations. The stores were in similar neigh- borhoods and had comparable levels of business. The stores sold the orange juice at different prices. The prices ranged between $1.25 and $4.25. Use JMP to fit a linear model, a log-log model and a quadratic model for these data. NOTE: For numerical answers, if the answer should be extrapolation put in 88 as your answer. Model 1: Fit an estimated simple linear regression model with price as the explanatory variable and sales as the response. Open Fit Model. Put Sales into the Y box under Pick Role Variables and put Price into the Add button under Construct Model Effects. Change Emphasis to Minimal Report and Run. 1. (Model 1) Based on Model 1 what is the predicted sales for a store selling orange juice for $2.25? 2. (Model 1) In Model 1 what is the predicted sales for half gallon carton of orange juice when the price is set of $5? . 3. (Model 1) Based on Model 1: percent of the variability in the sales of half gallon cartons of orange juice is explained by the linear relationship between sales and price of orange juice. 4. (Model 1) Based on Model 1: We expect approximately percent of the sales of half gallon cartons orange juice will be within 60.33 units of the predicted sales of half gallon cartons orange juice. 5. (Model 1) In the linear model which assumptions are violated? 6. (Model 1) Based on Model 1: For every 10 cent increase in the price of orange juice, we predict the sales of half gallon cartons of orange juice to decrease by . Model 2: Fit an estimated log-log model with ln(price) as the explanatory variable and ln(sales) as the response. Open Fit Model. Put ln(Sales) into the Y box under Pick Role Variables and put ln(Price) into the Add button under Construct Model Effects. Change Emphasis to Minimal Report and Run. 7. (Model 2) In Model 2 what is the predicted sales for half gallon cartons of orange juice if the price is set at $2.25? 8. (Model 2) In Model 2 what is the predicted sales for half gallon carton of orange juice when the price is set of $5? . 9. (Model 2) In Model 2 for every 10% increase in the price of orange juice the predicted median sales for half gallon cartons of orange juice will decrease by percent. (Be careful about your response here since the answer is already a decrease). 10. (Model 2) In Model 2 for every 2% increase in the price of orange juice the predicted median sales for half gallon cartons of orange juice will decrease by percent. 11. (Model 2) In the Log-Log model which assumptions are violated?

Model 3: Fit an estimated quadratic model with price as the explanatory variable and sales as the response. Open Fit Model. Put Sales into the Y box under Pick Role Variables and put Price into the Add button under Construct Model Effects. Highlight Price click on Macros and Select Polynomial to Degree. Click on the red arrow next to Model Specification and uncheck the default of Center Polynomials. Change Emphasis to Minimal Report and Run. 12. (Model 3) In Model 3 perform a hypothesis test to determine if there is a concave upward relationship between the sales and the price of orange juice. What is the p-value for this test. (Think carefully about your answer here.) 13. (Model 3) In Model 3 what is the predicted sales for half gallon carton of orange juice when the price is set of $2.25? . 14. (Model 3) In Model 3 what is the predicted sales for half gallon carton of orange juice when the price is set of $5? . 15. (Model 3) In the quadratic model which assumptions are violate? 16. Based on your answers to 5, 11 and 15 which model does the best job of meeting all the assumptions?

here is the JMP Data.

Sales	Price	In(Sales)	In(Price)
43	1.5	3.7612	0.405465
12	3.9	2.484907	1.360977
15	3.8	2.70805	1.335001
27	1.9	3.295837	0.641854
8	4.2	2.079442	1.435085
12	4.1	2.484907	1.410987
27	2.7	3.295837	0.993252
17	2.2	2.833213	0.788457
61	1.9	4.110874	0.641854
20	3.7	2.995732	1.308333
95	1.3	4.553877	0.262364
33	1.6	3.496508	0.470004
19	3	2.944439	1.098612
15	3.8	2.70805	1.335001
43	1.5	3.7612	0.405465
11	3.1	2.397895	1.131402
20	3.5	2.995732	1.252763
36	2.9	3.583519	1.064711
7	4.1	1.94591	1.410987
9	3.3	2.197225	1.193922
21	2.9	3.044522	1.064711
25	2.8	3.218876	1.029619
29	2.6	3.367296	0.955511
18	2.3	2.890372	0.832909
6	4.1	1.791759	1.410987
7	4.2	1.94591	1.435085
15	3.4	2.70805	1.223775
23	1.7	3.135494	0.530628
51	1.6	3.931826	0.470004
93	1.7	4.532599	0.530628
51	1.5	3.931826	0.405465
14	4.2	2.639057	1.435085
41	1.7	3.713572	0.530628
8	3.9	2.079442	1.360977
114	1.5	4.736198	0.405465
35	3	3.555348	1.098612
18	2.5	2.890372	0.916291
9	3.8	2.197225	1.335001
46	2.3	3.828641	0.832909
17	2.5	2.833213	0.916291
43	1.8	3.7612	0.587787
63	1.3	4.143135	0.262364
8	4.1	2.079442	1.410987
34	2.1	3.526361	0.741937
145	1.4	4.976734	0.336472
18	2.9	2.890372	1.064711
40	2.2	3.688879	0.788457
17	3.3	2.833213	1.193922
17	3.7	2.833213	1.308333
12	4.2	2.484907	1.435085
	2.25		0.81093