Multiple Regression – Basic RelationshipsPurpose of multiple regressionTypes of multiple regressionStandard multiple regressionHierarchical multiple regressionStepwise multiple regressionProblem 1 - standard multiple regressionDissecting problem 1 - 1Dissecting problem 1 - 2Request a standard multiple regressionSpecify the variables and selection methodSpecify the statistics output optionsRequest the regression outputLEVEL OF MEASUREMENTSAMPLE SIZEOVERALL RELATIONSHIP BETWEEN INDEPENDENT AND DEPENDENT VARIABLES - 1OVERALL RELATIONSHIP BETWEEN INDEPENDENT AND DEPENDENT VARIABLES - 2RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 1RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 2RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 3RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 4RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 5RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 6RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 7RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 8Answer to problem 1Problem 2 – hierarchical regressionDissecting problem 2 - 1Dissecting problem 2 - 2Request a hierarchical multiple regressionSpecify independent variables to control forAdd the other independent variablesSlide 33Slide 34Slide 35Slide 36OVERALL RELATIONSHIP BETWEEN INDEPENDENT AND DEPENDENT VARIABLESREDUCTION IN ERROR IN PREDICTING DEPENDENT VARIABLE - 1REDUCTION IN ERROR IN PREDICTING DEPENDENT VARIABLE - 2RELATIONSHIP OF ADDED INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 1RELATIONSHIP OF ADDED INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 2RELATIONSHIP OF ADDED INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 3RELATIONSHIP OF ADDED INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 4RELATIONSHIP OF ADDED INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 5RELATIONSHIP OF ADDED INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 6Answer to problem 2Problem 3 – Stepwise RegressionDissecting problem 3 - 1Dissecting problem 3 - 2Dissecting problem 3 - 3Request a stepwise multiple regressionSpecify variables and method for selecting variablesOpen statistics options dialog boxSlide 54Slide 55Slide 56Slide 57RELATIONSHIP BETWEEN BEST PREDICTORS AND THE DEPENDENT VARIABLE - 1RELATIONSHIP BETWEEN BEST PREDICTORS AND THE DEPENDENT VARIABLE - 2RELATIONSHIP BETWEEN BEST PREDICTORS AND THE DEPENDENT VARIABLE - 3RELATIONSHIP BETWEEN BEST PREDICTORS AND THE DEPENDENT VARIABLE - 4Answer to problem 3Standard multiple regression - 1Standard multiple regression - 2Standard multiple regression - 3Hierarchical regression - 1Hierarchical regression - 2Hierarchical regression - 3Stepwise regression - 1Stepwise regression - 2Stepwise regression - 3Stepwise regression - 4SW388R7Data Analysis & Computers IISlide 1Multiple Regression – Basic RelationshipsPurpose of multiple regressionDifferent types of multiple regressionStandard multiple regressionHierarchical multiple regressionStepwise multiple regressionSteps in solving regression problemsSW388R7Data Analysis & Computers IISlide 2Purpose of multiple regressionThe purpose of multiple regression is to analyze the relationship between metric or dichotomous independent variables and a metric dependent variable.If there is a relationship, using the information in the independent variables will improve our accuracy in predicting values for the dependent variable.SW388R7Data Analysis & Computers IISlide 3Types of multiple regressionThere are three types of multiple regression, each of which is designed to answer a different question:Standard multiple regression is used to evaluate the relationships between a set of independent variables and a dependent variable.Hierarchical, or sequential, regression is used to examine the relationships between a set of independent variables and a dependent variable, after controlling for the effects of some other independent variables on the dependent variable.Stepwise, or statistical, regression is used to identify the subset of independent variables that has the strongest relationship to a dependent variable.SW388R7Data Analysis & Computers IISlide 4Standard multiple regressionIn standard multiple regression, all of the independent variables are entered into the regression equation at the same timeMultiple R and R² measure the strength of the relationship between the set of independent variables and the dependent variable. An F test is used to determine if the relationship can be generalized to the population represented by the sample.A t-test is used to evaluate the individual relationship between each independent variable and the dependent variable.SW388R7Data Analysis & Computers IISlide 5Hierarchical multiple regressionIn hierarchical multiple regression, the independent variables are entered in two stages.In the first stage, the independent variables that we want to control for are entered into the regression. In the second stage, the independent variables whose relationship we want to examine after the controls are entered.A statistical test of the change in R² from the first stage is used to evaluate the importance of the variables entered in the second stage.SW388R7Data Analysis & Computers IISlide 6Stepwise multiple regressionStepwise regression is designed to find the most parsimonious set of predictors that are most effective in predicting the dependent variable.Variables are added to the regression equation one at a time, using the statistical criterion of maximizing the R² of the included variables.When none of the possible addition can make a statistically significant improvement in R², the analysis stops.SW388R7Data Analysis & Computers IISlide 7Problem 1 - standard multiple regressionIn the dataset GSS2000.sav, is the following statement true, false, or an incorrect application of a statistic? Assume that there is no problem with missing data, violation of assumptions, or outliers, and that the split sample validation will confirm the generalizability of the results. Use a level of significance of 0.05. The variables "strength of affiliation" [reliten] and "frequency of prayer" [pray] have a strong relationship to the variable "frequency of attendance at religious services" [attend].Survey respondents who were less strongly affiliated with their religion attended religious services less