PowerPoint Presentation

The Goal of MLRTypes of research questions answered through MLR analysis:How accurately can something be predicted with a set of IVs? (ex. predicting incoming students GPA)What is the relationship between a certain IV and the DV, while simultaneously controlling for confounding variables? (ex. relationship between TV broadcasting and game attendance while controlling for day of week, time of day, ticket price, teams won-loss records, etc)1234

Entering IVs into the MLR ModelStandard regressionFull model approach=all IVs used in model at same timeSome researchers will simply end the analysis at this point, others will examine assumptions, outliers, multicollinearity and create reduced models until they identify a single best model to predict the DVThis is the process we will use in this class, although testing assumptions is beyond our scope here12

Entering IVs into the MLR ModelSequential or Hierarchical regressionThe researcher determines an order to entering variables into the regression equation, usually based on some sort of theoretical or logical rationaleThe researcher then makes judgments as to the unique contributions of each IV in determining which to include & which to delete from the modelNot radically different than the previous process of reducing the full model, just a slightly different process sequential is sometimes thought to be prone to researcher bias in its subjectivity1

Entering IVs into the MLR ModelStatistical (often called Stepwise) regressionIVs are entered into the regression equation one at a time and is assessed in terms of what it adds to the equation at that point of entry and for how it impacts multicollinearity & assumptionsForward regression=IV with highest correlation to DV added first, then the second-highest, etcBackward regression=All variables entered, then one with lowest correlation to DV taken away, then the second-lowest, etcStepwise regression =A combination of alternating forward and backward regression procedures The use of stepwise regression is highly controversial in statistics1

Work with small # of predictorsWhy?Parsimony (a principle of good science)Small # predictors improves n/k ratioGreater # predictors, higher chance of shared variance among themLarge number of predictors can be replaced with smaller number of constructs -principal components see your next stats class(factor analysis)1

MLR ExampleLets go through this process in an exampleRQ: What is the relationship between television broadcasting, both national and local, and game attendance in mens college basketball (while controlling for potentially confounding variables)?Lets establish = .05 a priori1

MLR ExampleGraph the data to look for outliers

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Can also use an influential point estimator in SPSS (such as cooks distance (see later)MLR ExampleExamine the correlation matrix to see which variables are correlating with the DV and for multicollinearity among IVsNote: the entire correlation matrix would not fit here as it is 21x21 variablesVery little multicollinearityno pairwise correlations above r=.45 and few even above r=.3VariableAttendanceNATBROAD.436*LOCBROAD.343*MON-.035TUES.020WED.041THURS-.081*FRI-.099*SAT.064*SUN.024TIME-.088*HOMEWIN.455*VISWIN.302*RPI0203-.442*RPI0304-.388*CONFGAME.030CONFRPI.712*HISTORY.790*UNIVTYPE-.097*ENROLL.384*POPUL-.050INCOME.0541

MLR ExampleFind the R2 and Std. Error #s from the Model SummaryWhat can we learn here?

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MLR ExampleThe ANOVA box performs an F-test to accept/reject the null hypothesis that none of the IVs is purposeful in predicting the DV

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The coefficients box provides data on each of the IVs while all are in the model at the same timeessentially provides an examination of each IVs unique contribution to predicting the DV while controlling for all of the other IVs3. The unstandardized beta coefficients represent the y-intercept and slopes of the regression equationthese can be used as we did with SLR to predict the DV knowing the value of the IVs

MLR Example2. The p-value (Sig.) tells us whether each IV is a significant predictor of the DV (compare each to alpha level)4. The standardized beta coefficient allows us to compare the strength of each IV in predicting the DV1.

MLR Example

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MLR ExampleThe coefficients box (continued)Which variables correlate significantly with game attendance while controlling for other variables?Which variables are the strongest predictors of game attendance?How much does attendance increase or decrease if a game is broadcast on national television? on local television?1234

MLR ExampleAm I satisfied with this model, or should I examine another model by reducing via IV elimination?No data reduction was used with this study because of the research question being addressed (use of most of the IVs merely for control purposes)Ignoring that, what reduced models might we want to examine if we were so inclined?1

Other Prediction StatisticsCanonical correlation can be used to predict the value of two or more DVs with two or more IVsEx. Using HS GPA & SAT to predict undergrad GPA and graduation rate1

Other Prediction StatisticsDiscriminant analysis can be used to predict classification into categories of the DV with two or more IVsEx. Using IVs like age, education, hours worked per week, and income to predict ones life perspective (dull, routine, or exciting)Logistic regression can be used to predict classification into a dichotomous DV with two or more IVsEx. Using variables to predict steroid user or non-user

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