Violent crime rates in the United States are shown in the table for various years. Year Number of Violent Crimes per 100,00 people 1990 730 1995 685 2000 507 2005 469 2009 432 2016 386 (a) Find a linear model for f(a). Round all numbers to 3 decimal places.
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.
Violent crime rates in the United States are shown in the table for various years.
| Year | Number of Violent Crimes per 100,00 people |
| 1990 | 730 |
| 1995 | 685 |
| 2000 | 507 |
| 2005 | 469 |
| 2009 | 432 |
| 2016 | 386 |
(a) Find a linear model for f(a). Round all numbers to 3 decimal places.
Use regression to find the best fit linear equation for the given data.
The simple linear regression equation is given by :
,
Where Y is the dependent variable, X is the independent variable, a is the intercept (value of Y when x is zero) and b is the slope (measure of change in Y per unit change in X).
The formula to calculate slope and intercept are :
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