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Regression Analysis with SPSS . Robert A. Yaffee, Ph.D. Statistics, Mapping and Social Science Group Academic Computing Services Information Technology Services New York University Office: 75 Third Ave Level C3 Tel: 212.998.3402 E-mail: yaffee@nyu.edu February 04. Outline .

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## Regression Analysis with SPSS

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**Regression Analysiswith SPSS**Robert A. Yaffee, Ph.D. Statistics, Mapping and Social Science Group Academic Computing Services Information Technology Services New York University Office: 75 Third Ave Level C3 Tel: 212.998.3402 E-mail: yaffee@nyu.edu February 04**Outline**• Conceptualization • Schematic Diagrams of Linear Regression processes • Using SPSS, we plot and test relationships for linearity • Nonlinear relationships are transformed to linear ones • General Linear Model • Derivation of Sums of Squares and ANOVADerivation of intercept and regression coefficients • The Prediction Interval and its derivation • Model Assumptions • Explanation • Testing • Assessment • Alternatives when assumptions are unfulfilled**Conceptualization of Regression Analysis**• Hypothesis testing • Path Analytical Decomposition of effects**Hypothesis Testing**• For example: hypothesis 1 : X is statistically significantly related to Y. • The relationship is positive (as X increases, Y increases) or negative (as X decreases, Y increases). • The magnitude of the relationship is small, medium, or large. If the magnitude is small, then a unit change in x is associated with a small change in Y.**Regression AnalysisHave a clear notion of what you can and**cannot do with regression analysis • Conceptualization • A Path Model of a Regression Analysis**In a path analysis, Yi is endogenous. It is the outcome of**several paths. Direct effects on Y3: C,E, F Indirect effects on Y3: BF, BDF Total Effects= Direct + Indirect effects**Interaction coefficient: C**X1 and X2 must be in model for interaction to be properly specified.**A Precursor to Modeling with Regression**• Data Exploration: Run a scatterplot matrix and search for linear relationships with the dependent variable.**A Matrix of Scatterplots will appear**Search for distinct linear relationships**Decomposition of the sum of squares**• Total SS = model SS + error SS and if we divide by df • This yields the Variance Decomposition: We have the total variance= model variance + error variance**F test for significance and R2 for magnitude of effect**• R2 = Model var/total var • F test for model significance • = Model Var/Error Var**The Multiple Regression Equation**• We proceed to the derivation of its components: • The intercept: a • The regression parameters, b1 and b2**If we recall that the formula for the correlation**coefficient can be expressed as follows:**Extending the bivariate case**To the Multiple linear regression case**It is also easy to extend the bivariate intercept**to the multivariate case as follows.**Significance Tests for the Regression Coefficients**• We find the significance of the parameter estimates by using the F or t test. • The R2 is the proportion of variance explained.**Significance tests**• If we are using a type II sum of squares, we are dealing with the ballantine. DV Variance explained = a + b**Significance tests**T tests for statistical significance**Significance tests**Standard Error of intercept Standard error of regression coefficient**Programming Protocol**After invoking SPSS, procede to File, Open, Data**Select a Data Set (we choose employee.sav) and click on open****To inspect the variable formats, click on variable view on**the lower left**Because gender is a string variable, we need to recode**gender into a numeric format**We autorecode gender by clicking on transform and then**autorecode**We select gender and move it into the variable box on the**right**Click on ok and the numeric variable sex is created**It has values 1 for female and 2 for male and those values labels are inserted.**Entering independent variables**• These variables are entered in blocks. First the potentially confounding covariates that have to entered. • We enter time on job, beginning salary, and previous experience.**We now enter the hypotheses we wish to test**• We are testing for minority or sex differences in salary after controlling for the time on job, previous experience, and beginning salary. • We enter minority and numeric gender (sex)**We select the following statistics from the dialog box and**click on continue

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