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Situation: The Ipod Touch has been out for many years now and a lot of data has been collected.Relevant Relationship:There is a functional relationship between Price of an IPod Touch,𝑝 and Weekly Demand,𝑠.Below is a table of data that have been collectedPrice,𝑝,($) Weekly Demand,𝑠,(1,000s)150 208170 199190 200210 184230 182250 176A. 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=  B. The squared correlation coefficient was 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 parametersC. What does the model predict will be the weekly demand if the price of an ipod touch is $246 ? (nearest 100)D. According to the model at what should the price be set in order to have a weekly demand of 179,800 ipod Touches? $ (nearest $1)

Question

Situation: The Ipod Touch has been out for many years now and a lot of data has been collected.Relevant Relationship:There is a functional relationship between Price of an IPod Touch,𝑝 and Weekly Demand,𝑠.Below is a table of data that have been collectedPrice,𝑝,()WeeklyDemand,𝑠,(1,000s)150208170199190200210184230182250176A.Findthelinearmodelthatbestfitsthisdatausingregressionandenterthemodelbelow(forentryroundthelinearparametervaluetonearest0.01andconstantparametertonearest1)𝑠= B.Thesquaredcorrelationcoefficientwas0.95(note:valueslessthan0.95MAYmeanthemodelisnotappropriateformakingpredictions)NowanswerthesetwoquestionsusingtheUNROUNDEDmodelparametersC.Whatdoesthemodelpredictwillbetheweeklydemandifthepriceofanipodtouchis) Weekly Demand,𝑠,(1,000s)150 208170 199190 200210 184230 182250 176A. 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=  B. The squared correlation coefficient was 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 parametersC. What does the model predict will be the weekly demand if the price of an ipod touch is 246 ? (nearest 100)D. According to the model at what should the price be set in order to have a weekly demand of 179,800 ipod Touches? (nearest (nearest 1)

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Solution

A. To find the linear model that best fits this data using regression, we need to use a statistical software or calculator to input the data and perform a linear regression analysis. The output will give us the slope and y-intercept of the best fit line, which will form our model in the form of 𝑠= mx + b, where m is the slope and b is the y-intercept.

B. The squared correlation coefficient of 0.95 indicates a very strong positive linear relationship between the price of an iPod Touch and the weekly demand. However, it's important to note that correlation does not imply causation, and other factors could be influencing this relationship.

C. To predict the weekly demand if the price of an iPod Touch is 246,wewouldsubstitute246, we would substitute 246 into our linear model for the price (x-value) and solve for the weekly demand (s-value).

D. To find the price that would result in a weekly demand of 179,800 iPod Touches, we would substitute 179.8 (since the demand is in 1,000s) into our linear model for the weekly demand (s-value) and solve for the price (x-value).

Please note that without the actual regression analysis, I can't provide the specific linear model or the exact numerical answers for parts C and D.

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