This paper presents statistics on major factors that affects the property crime rates in the U.S.
The property crime rates of 45.7% occurs more in urban areas. About 16.8% of the crimes were committed by high school dropouts and only 0.4% of the crimes that occurs were related to the population density. The type of property crimes that happens includes larceny-theft, home burglary, home invasion, grand theft auto, forgery, and arson. These types of crimes may be caused by factors such as high school dropouts, the population density per square mile, and people living in urban areas. The paper will focus on the crimes against properties such as larceny-theft, home ...view middle of the document...
The intercept of the slope of the line is b₀.
* Dependent variable:
* Y = the percentage of property crimes that occur in the U.S.
* Independent variables: It summarizes the central tendency of the data provided.
* x₁ = the percentage of Dropouts in the U.S.
* x₂ = the percentage of the population Density in the U.S.
* x₃ = the percentage of residents living in an Urban area in the U.S.
* The standard error, also referred to as s, is the idea of the scattered of the actual points around the regression line.
* The adjusted multiple coefficient of determination, also referred to as Adjusted R².
* Inferences to test the hypothesis and confidence intervals, the overall F-test, and the prediction of the dependent variable
* Investigate the multicollinearity by examining if there are correlations among the independent variables that are so high that they may be used as a separate independent variable.
* The p-value is basically the area under the left or right tail of a normal curve. I have tested the p-value for each independent variable and compared the value to alpha 0.10. These following p-values (see Exhibit attached) are x₁ p-value = .0005, x₂ p-value = .0006, and x₃ p-value = 2.30E-10. After identifying the p-values from the regression output, I was able to formulate a multiple regression equation of ŷ = -1052.5531 + 57.7544x₁ -1.9318x₂ + 67.8889x₃ from the model. This equation will help explain the relationships between the independent variables of Dropout (x₁), Density (x₂), Urban (x₃) and the dependent variable of Crimes.
* According to the output, the standard error, s, is the point estimate of the standard deviation of the square root of s². The regression analysis shows that s is equal to 745.822. This gives me a rough idea of the actual points that are scattered around the regression line. The less standard error, the more precise the true value is.
* The adjusted multiple coefficient of determination, also referred to as R², is equal to 0.633. The adjusted R² helps avoid overestimating the independent variables. This means that 63.3% of the variability of Crimes can be best explained by the values of x₁, x₂, and x₃.
* According to the scattered plots for each independent variables, when property crimes goes up, the number of dropouts and the number of residents living in urban areas goes up. As for the population density, the slope of the line has a slight increase.
Inferences about the Regression Coefficient
* As stated above for the p-value, I was able to perform a hypothesis test for the regression coefficients of β₁, β₂, β₃. The coefficients of β₁, β₂, β₃ are the same as x₁, x₂, and x₃. This was examined by looking at the individual p-values to verify if these coefficients will be used in the model for explanation.
* The overall F-test of the relationship between the property crimes...