Question

Situation: The Ipod Touch has been out for two years now and a lot of data has been collected.

Relevant Relationship:

There is a functional relationship between Price of an IPod Touch,pp and Weekly Demand,ss.

Below is a table of data that have been collected

Price,pp,($)	Weekly Demand,ss,(1,000s)
150	211
170	201
190	193
210	189
230	184
250	173

A.. Find the linear model that best fits this data using regression and enter the model below

(for entry round the linear parameter value to nearest 0.01 and constant parameter to nearest 1)

s=T(p)=s=T(p)=    

B. The squared correlation coefficient r2r2 was Select an answer below above  0.95

(note: values less than 0.95 MAY mean the model is not appropriate for making predictions)

Now answer these two questions using the UNROUNDED model parameters

C. What does the model predict will be the weekly demand if the price of an ipod touch is $177 ?  (nearest 100)

D. According to the model at what should the price be set in order to have a weekly demand of 193,900 ipod Touches? $ (nearest $1)

Note: In the "real" world Apple sold about 20 million Ipod Touch's from Sept. 2007-Sept. 2009 Answer

Answer 1

	Price(X)	Demand(Y)	(Y-Y bar)2	(X-Xbar)2	(X-Xbar)(Y-Ybar)	Y_hat	(Y_hat-Ybar)2	(Y-Y_hat)2
	150	211	=(C2-$C$9)^2	=(B2-$B$9)^2	=(C2-$C$9)*(B2-$B$9)	=$B$11+$B$10*B2	=(G2-$C$9)^2	=(C2-G2)^2
	170	201	=(C3-$C$9)^2	=(B3-$B$9)^2	=(C3-$C$9)*(B3-$B$9)	=$B$11+$B$10*B3	=(G3-$C$9)^2	=(C3-G3)^2
	190	193	=(C4-$C$9)^2	=(B4-$B$9)^2	=(C4-$C$9)*(B4-$B$9)	=$B$11+$B$10*B4	=(G4-$C$9)^2	=(C4-G4)^2
	210	189	=(C5-$C$9)^2	=(B5-$B$9)^2	=(C5-$C$9)*(B5-$B$9)	=$B$11+$B$10*B5	=(G5-$C$9)^2	=(C5-G5)^2
	230	184	=(C6-$C$9)^2	=(B6-$B$9)^2	=(C6-$C$9)*(B6-$B$9)	=$B$11+$B$10*B6	=(G6-$C$9)^2	=(C6-G6)^2
	250	173	=(C7-$C$9)^2	=(B7-$B$9)^2	=(C7-$C$9)*(B7-$B$9)	=$B$11+$B$10*B7	=(G7-$C$9)^2	=(C7-G7)^2
Total	=SUM(B2:B7)	=SUM(C2:C7)	=SUM(D2:D7)	=SUM(E2:E7)	=SUM(F2:F7)	=SUM(G2:G7)	=SUM(H2:H7)	=SUM(I2:I7)
Mean	=B8/6	=C8/6
Beta1	=F8/E8
Beta0	=C9-B10*B9
SSR	=H8
SST	=D8
R2	=B12/B13

	Price(X)	Demand(Y)	(Y-Y bar)2	(X-Xbar)2	(X-Xbar)(Y-Ybar)	Y_hat	(Y_hat-Ybar)2	(Y-Y_hat)2
	150	211	367.3611	2500	-958.333	209.3333	306.25	2.777778
	170	201	84.02778	900	-275	202.3333	110.25	1.777778
	190	193	1.361111	100	-11.6667	195.3333	12.25	5.444444
	210	189	8.027778	100	-28.3333	188.3333	12.25	0.444444
	230	184	61.36111	900	-235	181.3333	110.25	7.111111
	250	173	354.6944	2500	-941.667	174.3333	306.25	1.777778
Total	1200	1151	876.8333	7000	-2450	1151	857.5	19.33333
Mean	200	191.8333
Beta1	-0.35
Beta0	261.8333
SSR	857.5
SST	876.8333
R2	0.977951

a) The fitted linear model

demand = 261.8333 - 0.35 price

b)

c) demand =261.8333 - 0.35 (177) = 199.8833

d) The price to be set 190 theoretically.

By the fitted model it should be, 194.0952

193.9 = 261.8333 - 0.35 (price)

therefore, price = 194.0952