Multiple Linear Regression | My Assignment Tutor

MSc Methods TutorialMultiple Linear RegressionMultiple regression Examines the influence of several predictorvariables (IVs) on an outcome variable (DV) Calculates a model (regression equation) toestimate outcome scores from multiple predictors Determines which predictors make a significantcontribution to the outcome (after “controllingfor” other predictors in the model)Simple regression equation describes a straight line:aMultiple regression equation describes a “line” drawn through a “multidimensionalspace” but principle is the same – a (the constant) represents the value of Y when allX (predictor variables) are zero each predictor has its own slope value (b), which isthe change in Y when X changes by one unit,and all other predictors are held constant1 1 2 2 3 3ˆY a b x b x b x b x      k kExample 1: A researcher is interested in understanding thefactors that may influence levels of depression inthe general population. They hypothesise 3 factors (IVs) that are likely to beimportant: age, physical health & social support. Data are collected by survey – participants reportage, physical health, social support, and depression. Multiple regression analysis will determine whichfactors are significant predictors of depression inthe sample.First, run correlation analysis in SPSSFrom top menu, select: Analyze → Correlate → BivariateMove all the variables into the Variables box, then click OKCorrelations with depression:Age, r = -.253, p = .043Health, r = -.136, p = .283 (ns)Social Support, r = -.285, p = .023Run multiple regression in SPSSFrom top menu, select: Analyze → Regression → LinearRun linear regression in SPSSSelect the predictors (IV) and outcome (DV)Choose Forward as Method – SPSS then adds IVs into the model one at atime, starting with the best predictor (strongest correlation with DV),then next best, and so on. If adding the next IV will not significantlyincrease the proportion of variance in DV scores that can be explained bythe model, SPSS stops adding IVs.SPSS outputR Square = proportion of variance in DV explained by each modelAdjusted R square = an estimate of the variance explained in thepopulation for each model(N.B. adjusted R square is always smaller than R square)Footnotes tell you which predictors are included in eachmodel. Here there is no third model including “physicalhealth” as a predictor, because it does not significantlyimprove on the variance explained by Model 2.Sig. F Change:Does Model 1 explain a sig. amount of variance in the DV?Does Model 2 explain sig. more variance than Model 2?Models:In SPSS,Forwardmethodadds oneadditionalpredictor ineach model.Equation for Model 2:Y = constant + b1×1 + b2x2Depression = 7.379 + (-.101 x Social Support) + (-.034 x Age)Model 2 predictors:Social Support: β = -.287,p = .018;Age: β = -.256, p = .034Significance test for Model 2:F (2, 61) = 5.243, p = .008In breakout rooms – run the analysis &answer following questions (15 mins) What is R-squared change for each model? What is variance explained by each model? What is multiple regression equation for Model 2? Using the equation, predict the depression scorefor someone who is 70 years old and has a socialsupport score of 10.Back in main room Predicted depression score for a 70 yearold with SS score of 10: Depression = 7.379 + (-.101 x SS) + (-.034 x Age)= 7.379 – (.101 x 10) – (.034 x 70)= 7.379 – 1.01 – 2.38= 3.99Reporting the regression analysis:A multiple linear regression was carried out to determinewhether age, social support, and physical health weresignificant predictors of depression using Forward selection toconstruct the model. Social support and age were included assignificant predictors of depression in the final model, butphysical health was not. The final regression model accountedfor a significant proportion of the variance in depressionscores: R² = 14.7%, F (2, 61) = 5.243, p = .008. The regressionequation was: Depression = 7.379 – (.101 x Social Support) –(.034 x Age), indicating that Depression scores would beexpected to decrease by an average of about 0.1 for each unitincrease in Social Support, and to decrease by about 0.03 foreach 1 year increase in age.Any questions?5 minute breakMultiple Regression – Example 2 Basis for Report 2 Topic: Do individual differences inemotion regulation predictsatisfaction with life?Background – Emotion Regulation Research suggests individual differences in how people tryto control everyday emotions are important predictors ofemotional experience and well-being (e.g. Gross, 2013) It is claimed that – use of suppression to control emotion is associated withan increase in negative affective experiences, a decreasein positive affective experiences, and lower subjectivewell-being use of reappraisal to control emotion is associated witha decrease in negative affective experiences, an increasein positive affective experiences, and higher subjectivewell-beingA study: Aim was to examine these relationships in a sample of 234(117 F, 117 M) undergraduate university students aged between18 and 24 (mean age = 20.3, sd = 1.6). Participants completed two paper-and-pencil questionnaires – 10-item Emotion Regulation Questionnaire (ERQ; Gross &John, 2003) to measure individual differences in use ofsuppression and reappraisal for self-regulating emotions; 6-item Riverside Life Satisfaction Scale (RLSS; Margolis et al,2019) to measure general well-being. Hypotheses: (1) suppression use will negatively predict lifesatisfaction & (2) reappraisal use will positively predictlife satisfaction.Measures (materials) – Emotion Regulation – ERQ (Gross & John, 2003) Life Satisfaction – RLSS (Margolis et al, 2019)• All items were measured on 7-point Likert scales (1 = strongly disagree, 7 = strongly agree),scale scores were calculated as the sums of individual itemsData in SPSS: Analysis:1) Bivariate correlations betweenthe 3 measures2) Regression (using Forwardmethod) with Life Satisfactionas the DV and the two emotionregulation strategies (reappraisal& suppression) as IVs –In breakout rooms – run the analysis &answer following questions (15 mins) What proportion of the variance in Life Satisfactionin the sample is explained by the regression model? Which variables are significant predictors of LifeSatisfaction? How is each significant predictor related to LifeSatisfaction? What is the multiple regression equation for theModel?Back in main roomSPSS Output Correlation between Life Satisfaction & Reappraisal is significant(and positive): r = .214, p = .001 Correlation between Life Satisfaction & Suppression is significant(and negative): r = -.138, p = .035 Correlation between Reappraisal & Suppression is not significant:r = .086, p = .192 Model 2 significantly improveson Model 1 (F change, p = .014) Variance explained by Model 2= .07 or 7% Model 2 Variance explained isstatistically significant:F (2 ,231) = 8.746, p < .001 Reappraisal is a significantpositive predictor of LifeSatisfaction: β = .227, p < .001 Suppression is a significantnegative predictor of LifeSatisfaction: β = -.158, p = .014 Regression equation: Life Satisfaction = 19.976 + (.278 x Reappraisal) – (.199 x Suppression)Scatterplots: Graphs => Legacy dialogs => Scatter/Dot => Simple Put outcome variable (Life Satisfaction) on Y-axis andthe predictor variable on X-axisReport 2 Due Friday 26th April Worth 30% of final course mark Word limit = 2000 words (excluding references& appendices)References (on MyAberdeen) Gross, J.J. (2013). Emotion regulation: Taking stock andmoving forward. Emotion 13, 359-365. Gross, J.J. & John, O.P. (2003). Individual differences intwo emotion regulation processes: Implications for affect,relationships, and well-being. Journal of Personality &Social Psychology 85, 348-362. Margolis, S., Schwitzgebel, S., Ozer, D.J. & Lyubomirsky,S. (2019). A new measure of life satisfaction: TheRiverside Life Satisfaction Scale. Journal of PersonalityAssessment 101, 621-630.General structure for reports Title: Describe the topic of the study. Abstract: A short (about 150 words) summary of thewhole report, including the purpose of the experiment,hypothesis, method, findings & conclusions (it is best towrite the abstract last, after you have completed therest of the report). Introduction: What is emotion regulation? Why is itimportant? What have previous studies shown? What isthe purpose of this study? Hypotheses? (About 600words.) Method: How the study was carried out (about 400 words), withsubsection headings for –• Participants: Who, how many, their age & gender (see slide # 17).• Design: Is the study design experimental or correlational? What are thevariables of interest in the study?• Materials: Describe all materials necessary for conducting study (e.g.scales used for measuring variables – see slide #18).• Procedure: Describe what participants and researchers did to collect thedata. Results (about 150 words):• Report correlations between variables & refer to these in the text.• Summarize results of linear regression (value for R2 & results ofANOVA test of significance) and explain what it tells you. Is hypothesissupported or not?• Plot relationships between predictor and outcome variables onscatterplots & refer to these in the text, describing what they show.Discussion: (up to 600 words)• Discuss results in relation to hypothesis & and relate back to materialin Introduction. How do results compare to previous literaturementioned in Introduction?• Any potential issues or weaknesses in how study was conducted (e.g.were the measures that were used appropriate)? If so, how might youimprove on the methods employed here? NOTE: if you do mention aweakness, follow your point through (e.g., what was the weakness, whywas it a weakness, and how might this have impacted on the results?).• What are the implications of the findings? What do they tell usabout the topic being studied? Do they have any practical applications?• Any suggestions for future studies to follow up on the findings? Conclusion: Briefly state (no more than about 50 words) themain conclusions to be drawn from the study. References: Only list a reference if you have cited it in thereport, use correct APA format. Appendices: Any additional material you want to include (e.g.SPSS output tables, copies of questionnaires).There are lots of report writing resourceson MyAberdeen in the Report WritingGuides folder – any questions should beposted in FAQs Tutorials discussion boardQuestions? Observational and survey methods Prep-work for the observational part See worksheet for week 8 for full instructions In this activity, you are going to spend 15 minutesobserving people. Take notes so that you areprepared to report on what you have observed.Next week


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