There is a functional relationshup between Price of an IPod Touch,g and Weekly D

Question

There is a functional relationshup between Price of an IPod Touch,g and Weekly Demand,s Below is a table of data that have been collected Price,p,(S) | Weekly Demand,s,a,000s) 216 206 196 187 176 173 150 170 190 210 230 250 A. Find the linear model that bestfits this data using regression and enter the model below (for entry round the inear parameter value to nearest 001 and constant parameter to nearest 1) Preiew B. The squared correlation coeficient 2 was Select an answer 0.95 (note values less than 0 95 MAY mean the model is not appropriate for making predictions) Now answer these two questions usng the UNROUNDED model parameters C What does the model predict will be the weekdy denand if the pnce of an pod touch is $194 7 (nearest 100) D Acrding to the modea rice be et n rder to hare a wey dend of 186,500 pod Touches? (nearest 81) Mote In the real world Apple sold sbout 20 milion inod Touch's rom Sapt 2007-Sept 2003 Answer

Explanation / Answer

## By using R-software

> Price=c(150,170,190,210,230,250)
> Price
[1] 150 170 190 210 230 250
> Demand=c(216,206,196,187,176,173)
> Demand
[1] 216 206 196 187 176 173
> fit=lm(Demand~Price)
> fit

Call:
lm(formula = Demand ~ Price)

Coefficients:
(Intercept) Price  
282.0476 -0.4486  

A) The linear regression model is:

Demand= 282.05 - 0.45*Price

B) > r=cor(Price,Demand)
> rsq=r*r
> rsq
[1] 0.99 ## Squared Correlation coefficient

C) Weekly demand when price id $ 194 is

Demand= 282.05 - 0.45*194

= 194.75

Hence weekly demand is =194,750

D) Price when weekly demad is 186500

Demand= 282.05 - 0.45*Price

Price= -(186.5 -282.05)/0.45

= $212

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