# Criminal Justice: Explain The Least Squares Regression Line

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Homework Unit Five Statistics for Criminal Justice -1 CCJ 5704 By Edward M. Hobbs March 24, 2012 1.Explain the least-squares regression line. If a scatter plot shows a linear relationship between two quantitative variables, least-squares regression is a method for finding a line that summarizes the relationship between the two variables, at least within the domain of the explanatory variable, x.The…show more content…
It is a mathematical model for the data. 2. It is the line that makes the sum of the squares of the residuals as small as possible. 3. The point x-y is on the line, where x is the mean of the x values, and y is the mean of the y values. 4. Its form is y(hat) = a + bx. (Note that b is slope and a is the y-intercept.) 5. b = r(sy/sx). (On the regression line, a change of one standard deviation in x corresponds to a change of standard deviation y. 6. a = y - bx. 7. The slope b is the approximate change in y when x increases by 1. 2. How do you use the regression line for prediction? To make a prediction when you have population data, take average of group; group averages very often form line, also to make a prediction when you have a sample, take all group averages and draw a line of best fit; use line to predict. Regression models are often constructed based on certain conditions that must be verified for the model to fit the data well, and to be able to predict accurately. Regression analysis procedures have as their primary purpose the development of an equation that can be used for predicting values on some Dependent Variable, Y, given Independent Variables, X, for all members of a