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,p and Weekly Demand,s. Below is a table of data that have been collected Price,p.($) Weekly Demand, s, (1,000s) 150 210 170 208 190 199 210 187 230 183 250 168 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) 8= T(p) = B. The squared correlation coefficient 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 using the UNROUNDED model parameters C. What does the model predict will be the weekly demand if the price of an ipod touch is $183 ? (nearest 100)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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### Situation Analysis for iPod Touch Demand

The iPod Touch has been on the market for two years, and substantial data has been collected regarding its performance. This analysis seeks to understand the functional relationship between the price of an iPod Touch and its weekly demand.

### Relevant Relationship

There is a functional relationship between the Price of an iPod Touch, \( p \), and Weekly Demand, \( s \). The table below summarizes the collected data:

| Price, \( p \) (\$) | Weekly Demand, \( s \) (1,000s) |
|---------------------|--------------------------------|
| 150                 | 210                            |
| 170                 | 208                            |
| 190                 | 199                            |
| 210                 | 187                            |
| 230                 | 183                            |
| 250                 | 168                            |

### Tasks and Analysis
#### A. Linear Model Determination
Find the linear model that best fits this data using regression and enter the model below. For entry, round the linear parameter value to the nearest 0.01 and the constant parameter to the nearest 1.

\[ s = T(p) = \]

#### B. Correlation Coefficient
The squared correlation coefficient was 0.95. (Note: Values less than 0.95 may indicate that the model is not appropriate for making predictions).

#### C. Weekly Demand Prediction
Using the unrounded model parameters, what does the model predict will be the weekly demand if the price of an iPod Touch is \$183? 

\[ \text{(nearest 100)} \]

#### D. Price Setting for a Target Demand
According to the model, at what price should the iPod Touch be set to achieve a weekly demand of 186,100 units?

\[ \text{\$ (nearest \$1)} \]

### Real-World Context
Note: In the "real" world, Apple sold about 20 million iPod Touch units from Sept. 2007 - Sept. 2009.
Transcribed Image Text:### Situation Analysis for iPod Touch Demand The iPod Touch has been on the market for two years, and substantial data has been collected regarding its performance. This analysis seeks to understand the functional relationship between the price of an iPod Touch and its weekly demand. ### Relevant Relationship There is a functional relationship between the Price of an iPod Touch, \( p \), and Weekly Demand, \( s \). The table below summarizes the collected data: | Price, \( p \) (\$) | Weekly Demand, \( s \) (1,000s) | |---------------------|--------------------------------| | 150 | 210 | | 170 | 208 | | 190 | 199 | | 210 | 187 | | 230 | 183 | | 250 | 168 | ### Tasks and Analysis #### A. Linear Model Determination Find the linear model that best fits this data using regression and enter the model below. For entry, round the linear parameter value to the nearest 0.01 and the constant parameter to the nearest 1. \[ s = T(p) = \] #### B. Correlation Coefficient The squared correlation coefficient was 0.95. (Note: Values less than 0.95 may indicate that the model is not appropriate for making predictions). #### C. Weekly Demand Prediction Using the unrounded model parameters, what does the model predict will be the weekly demand if the price of an iPod Touch is \$183? \[ \text{(nearest 100)} \] #### D. Price Setting for a Target Demand According to the model, at what price should the iPod Touch be set to achieve a weekly demand of 186,100 units? \[ \text{\$ (nearest \$1)} \] ### Real-World Context Note: In the "real" world, Apple sold about 20 million iPod Touch units from Sept. 2007 - Sept. 2009.
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