# Instead of the slope of a line multiple regression

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Instead of the slope of a line, multiple regression coefficients represent the individual contribution of
the independent variables to the prediction of the dependent variable. Parameters or partial changes in the dependent variable are measured for a change in just one of the independent variables. A positive coefficient indicates a positive relationship. A negative coefficientindicates a negative relationship. A coefficient of 0 indicates no relationship between that independent variable and the prediction of the dependent variable.ANOVA is a statistical procedure used to test theories regarding the influence of explanatory variables in multiple regression. The null hypothesis is the multiple regression coefficients are equalto zero. The alternative is there is at least one explanatory variable with a nonzero coefficient. In other words, at least one explanatory variable predicts the criterion variable. R-Square is the proportion of the variance in the criterion variable accounted for in the testing. An adjusted R-Square takes into account the variance and sample size. Beta values are also included in ANOVA. The beta values measure how strongly each predictor variable affects the response variable. For example, a beta value of 3 represents a change of three standard deviations in the response variable for a change of one standard deviation in the predictor variable.Interactive Examples11Given the first observation of (10, 5, 6, 2, 9), the criterion has a value of 92Betavalues measure how strongly each predictor affects the criterion variable.3A positive coefficient indicates a positiverelationship.4ANOVA uses a null that the value of the multiple regression coefficients is 0.5ANOVAis a statistical procedure used to test multiple regression.3The alternative hypothesis for ANOVA is that at least oneexplanatory value is nonzero or predicts the dependent variable.6A coefficient of 0indicates no relationship.
7In multiple regression, multiple regressionCoefficients replace the slope.8In multiple regression, each observed value will contain more than one predictor value.5Given the third observation of (5, 1, 4.5, 6, 9.1), there are 4explanatory values.4The formulas for multiple regression are typically complex.5In simple regression, a two-dimensional line predicts the response values.8Simplelinear regression cannot be used with more than two predictors.SummaryMultiple regression allows more than one factor in a correlation study. It is often the case that multiple factors are associated with a certain response variable. Simple regression only considers one independent variable. Multiple regression considers two or more independent variables and is usually too complex to perform without the use of a computer.Applications In Health Care and Criminal Justice IntroductionCorrelation and regression are abundant in the health care field. A correlation in medical research may not always result in definite causes, but each step counts. The same can be said for the criminal justice field.
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