The average admission prices P for movie theaters from 2001 through 2008 can be approximated by the model P = 0.0103t2 + 0.119t + 5.55, 1 ≤ t ≤ 8 where t represents the year, with t = 1 corresponding to 2001.† (a) Use the model to complete the table to determine when the average admission price reached or surpassed $6.50. (Round your answer to two decimal places.) t P 1 $ 2 $ 3 $ 4 $ 5 $ 6 $ 7 $ 8 $ The average admission price reached or surpassed $6.50 sometime in 2002.The average admission price reached or surpassed $6.50 sometime in 2003. The average admission price reached or surpassed $6.50 sometime in 2004.The average admission price reached or surpassed $6.50 sometime in 2005.The average admission price reached or surpassed $6.50 sometime in 2006. (b) Verify your result from part (a) algebraically. (Round your answer to two decimal places.) t = yrs (c) Use the model to predict the average admission price for movie theaters in 2012. (Round your answer to two decimal places.) $ Is this prediction reasonable? How does this value compare with the admission price where you live?
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.
The average admission prices P for movie theaters from 2001 through 2008 can be approximated by the model
where t represents the year, with t = 1 corresponding to 2001.†
| t | P |
|---|---|
| 1 | $ |
| 2 | $ |
| 3 | $ |
| 4 | $ |
| 5 | $ |
| 6 | $ |
| 7 | $ |
| 8 | $ |
(b) Verify your result from part (a) algebraically. (Round your answer to two decimal places.)
t = yrs
(c) Use the model to predict the average admission price for movie theaters in 2012. (Round your answer to two decimal places.)
$
Is this prediction reasonable? How does this value compare with the admission price where you live?
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