The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information. City Police Number of Crimes City Police Number of Crimes Oxford 25 20 Holgate 2
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 city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.
| City | Police | Number of Crimes | City | Police | Number of Crimes | ||||||||||||||
| Oxford | 25 | 20 | Holgate | 26 | 9 | ||||||||||||||
| Starksville | 26 | 16 | Carey | 21 | 21 | ||||||||||||||
| Danville | 32 | 9 | Whistler | 20 | 24 | ||||||||||||||
| Athens | 35 | 11 | Woodville | 28 | 10 | ||||||||||||||
Click here for the Excel Data File
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Determine the regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
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Estimate the number of crimes for a city with 27 police officers. (Round your answer to the nearest whole number.)
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Interpret the regression equation.
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