Regal Theatre puts on community theatre productions each season. After several years of gathering data, they noted some trends between the length of the plays they produced and the number of tickets they sold for Friday evening shows. They created the model shown below Hrs played ticket sold 1 119 1.5 139 1.75 145 2 149 2.25 150 2.5 149 3 139 4 89 a) What does the ordered pair (3,139) represent in the context of this situation? b) Determine the function's average rate of change over each of the following intervals. Make sure to describe how to interpret the meaning of the average rate of change in each case. i) 1≤x≤2.25 ii) 2.5≤x≤4 c) Does the function have positive concavity or negative concavity (or a combination of the two)? What does this tell you about the situation?
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.
Regal Theatre puts on community theatre productions each season. After several years of gathering data, they noted some trends between the length of the plays they produced and the number of tickets they sold for Friday evening shows. They created the model shown below
Hrs played ticket sold
1 119
1.5 139
1.75 145
2 149
2.25 150
2.5 149
3 139
4 89
a) What does the ordered pair (3,139) represent in the context of this situation?
b) Determine the function's average rate of change over each of the following intervals. Make sure to describe how to interpret the meaning of the average rate of change in each case.
i) 1≤x≤2.25
ii) 2.5≤x≤4
c) Does the function have positive concavity or negative concavity (or a combination of the two)? What does this tell you about the situation?
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