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) 150 209 170 205 190 200 210 192 230 177 250 175 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)= B. The squared correlation coefficient r2 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 parameters C. What does the model predict will be the weekly demand if the price of an ipod touch is $172 ? (nearest 100) D. According to the model at what should the price be set in order to have a weekly demand of 264,100 ipod Touches? $ (nearest $1)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Situation: The Ipod Touch has been out for two years now and a lot of data has been collected.
Relevant Relationship:
There is a
Below is a table of data that have been collected
| Price,p |
|---|
| ,($) | Weekly Demand,s |
|---|
| ,(1,000s) | |
|---|---|
| 150 | 209 |
| 170 | 205 |
| 190 | 200 |
| 210 | 192 |
| 230 | 177 |
| 250 | 175 |
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)=
B. The squared
(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 $172 ? (nearest 100)
D. According to the model at what should the price be set in order to have a weekly demand of 264,100 ipod Touches? $ (nearest $1)
Note: In the "real" world Apple sold about 20 million Ipod Touch's from Sept. 2007-Sept. 2009 Answer
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