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Lecture

# Crim 320 week 13.docx

7 Pages
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Department
Criminology
Course Code
CRIM 320
Professor
Patrick Lussier

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Simple and Multiple Regression Simple regression  Is it possible to predict a certain outcome (Y) with only one predictor (X)? Simple regression  Research question: o Is age a good predictor of the total number of crimes committed in adulthood?  Research hypothesis: o H1: older offenders have had more opportunities to offend and, therefore, have committed more crimes in adulthood  Null hypothesis o H0: age is not related to the number of crimes committed by offenders in adulthood Simple regression  Equation: o Y= a + b(x) + e o Y=the predicted value for a given value of x (independent variable) o X=the predictor, the variable expected to predict the value of y (dependent variable) o A=intercept or the mean value of y when x=0 o B=regression coefficient or the weight given to X in order to predict the value of Y  The change in x associated with one-unit of change in Y o E=residuals  Represents the prediction error or the gap between the predicted value of Y and the actual value of Y The regression line uses Y to best fit the data at each value of x: the ordinary least squares regression… Residual variance: “gap” between regression line and each Y Regression variance/residual variance  how well the regression line “explains” all observations The bigger the slope, the stronger the relationship Multiple Regression Multiple Regression  Improve the prediction of y by using multiple (several) independent variables (Xi)  Looking for the combination of weights for the IV (Xi) to get predicted values of Y as close as possible from the actual values of YPurpose of multiple regression  How good is the prediction of the DV (Y) base don this set of predictors (Xi)?  Is there a significant relationship between the predictors (Xi) and the DV (Y)? o What are the predictors of the criminological phenomenon  Is it possible to improve our ability to predict the value of the DV (Y) by adding another IV (Xi)?  Is one set (block) of predictors better at predicting the value of the DV? Multiple regression  Equation: o Y=a + b1(x1) + b2(x2) + b3(x3) + b4(x4) + ……. + e Different types of regression  Standard multiple regression  Hierarchical (sequential) regression  Statistical (stepwise) regression Standard multiple regression  All the IVs are entered into the regression equation at once  Each IV evaluated in terms of what it adds to the prediction of the DV that is different from the variance explained by all the other IVs  Determine the unique contribution (weight) of each variable in the prediction of the dependent variable  The single best procedure to simply assess relationships among variables Hierarchical (sequential) regression  IVs are “entered” into the equation in an order specified by the researcher or a theory  Estimation of the variable’s (or group of variables) contribution over or above the contribution of variables (or group of variables) already in the equation  Based on theoretical ground, a certain variable (or set of variables) may be given priority as to the explained variance of the DV  Allow the researcher to control the advancement of the regression process Statistical (stepwise) regression  The order of entry of variables is based only on statistical criteria  Minor differences in these statistics can have profound effect on the apparent importance of an IV (e.g., which variable is entered first in the equation)  Typically used to develop a subset of IVs that is useful in predicting the DV, and to eliminate those IVs not providing additional predicting value to those IVs already in the equation  Model-building rather than model-testing procedure (exploratory purpose)  Least interesting of the three approaches General Considerations A rough guide to multiple regression  Selection of ID variables (intevcal/ratio, dichotomous) and DV (interval/ratio)  Descriptive analysis (univariate outliers, skewness)  Analysis of the correlation matrix  Selection of method (enter, block, stepwise)  Regression  Look for multicollinearity (level of tolerance)  Distribution of multivariate outliers  Analysis and interpretation Variables  Theory should guide the selection of variables  Linear relationship between IVs and DV  Only one dependent variable  DV data should be interval/ratio  IVs data should be interval/ratio/dichotomous Sample size  Standard regression and hierarchical regression, a minimum of 20 cases per variables used  Stepwise regression, a minimum of 40 variables per cases  More cases required when the effect size is small, the DV is nor normally distributed, or measurement error is high Multicollinearity  Regression will be best when each IV is strongly correlated with the DV but uncorrelated with other IVs  OLS regression inspects for unique variance accounted by each IV  If two IV share the same “variance,” nothing unique about those will be captured by the analysis o Inspection of tolerance level in SPSS output o Tolerance varies from 0-1.00 o Value close to 0 indicate a problem of multicollinearity o A problem when getting closer to .30 (or lower) SPSS examples The 2d:4d ratio  A proxy measure of prenatal exposure to testosterone  Low ratio linked to “masculinisation” of the brain  Research suggests that LOW ratio is predictive of emoti
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