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NAU EPS 625 - Multiple Linear Regression

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Multiple Linear Regression Example (Simultaneous Entry) – KEYMultiple Linear Regression Example (Simultaneous Entry) – KEYA resilience researcher conducted a study with an at-risk preschool population in a continuingeffort to determine why many children growing up in potentially damaging environments comethrough relatively unharmed and well adjusted whereas other children succumb to the stress.This preschool population was deemed to be at risk for educational and developmental delaysdue to a number of risk factors, including low social status, parental psychiatric disorders orcriminality, and overcrowding/large family size. Because past resilience research suggested thatfamily social support, child biological dispositions (temperament), and characteristics of homeenvironment are associated with the likelihood of future adaptive outcomes, the researcherdecided to investigate these variables to determine whether they would be powerful predictors ofresilience in a sample of 30 at-risk preschool children. The children were tested for age-appropriate developmental abilities (verbal, motor, cognitive, self-help, emotional, and social),and an aggregate score for these abilities was used as the dependent measure of resilience.(Higher scores indicate greater overall developmental abilities.) Families were asked to fill out asocial support questionnaire to measure the helpfulness of sources of support to families raising ayoung child. (Higher scores indicate greater support.) Teachers were asked to rate aspects of eachchild’s home environment (such as emotional and verbal responsiveness to parents, learning andlanguage stimulation, availability of play materials, and so on) during regular home visits.(Higher scores indicate a more positive home environment.) Teachers also completed a childtemperament scale. (Higher scores indicate an easy, adaptive, flexible temperament style, andlower scores indicate an intense, difficult, less malleable temperamental style.)NOTE: For this scenario, the child’s developmental ability (DEVELOP) is thedependent variable, Y – and the following three variables are the independentvariables, X’s:- (SUPPORT) – Social Support- (TEMPER) – Temperament- (HOMEENV) – Home EnvironmentUsing the above scenario and the data provided in the SPSS output,answer the following questions (where - = .05):1. First – check for multicollinearity. Conduct the appropriate diagnostic analysis and indicateyour findings.Based on the Variance Inflation FactorAll VIF values were well under 10.0, and as such indicate noconcerns with multicollinearity for this set of data.Social Support’s VIF 2.141Temperament’s VIF 1.356Home Environment’s VIF 2.1742. Regress developmental ability (DEVELOP) on social support (SUPPORT), temperament(TEMPER), and home environment (HOMEENV).a. What proportion of the variance in developmental ability is explained by SUPPORT,TEMPER, and HOMEENV?Approximately 87%  R2 = 0.865b. Does the set of variables significantly predict developmental ability? Indicate how youcame to this conclusion.Yes  (From the ANOVA Table) F(3, 26) = 55.342, p < .001c. Which of these three variables have a significant influence on developmental ability?Indicate how you came to this conclusion.Social Support Yes t = 6.284, p (.000) < α (0.05)Temperament No t = 1.967, p (.060) > α (0.05)Home Environment Yes t = 2.080, p (.048) < α (0.05)d. Which of these three variables have the greatest influence (relative importance) ondevelopmental ability? Indicate how you came to this conclusion.In order of importance (from greatest to least):Social Support β = .663 significant t, p (.000) < α (0.05)Home Environment β = .221 significant t, p(.048) < α (0.05)(Temperament was not significant, and as such is not identified as being significantly influential for this sample)e. Choose any one of the three predictor (independent) variables and explain its beta valueas it relates to the criterion (dependent) variable.Social Support Higher levels of a child’s Social Support (controlling for the effects of Temperament and Home Environment) are associated with higher levels of Developmental Ability to a significant degree (β = .663)MLR – KEYPage 2Home Environment Higher levels of a child’s Home Environment (controlling for the effects of Social Supportand Temperament) are associated with higher levels of Developmental Ability to a significant degree (β = .221)(Temperament would not be discussed here as it was not found to be significant for this sample.)3. Based on the results of this study, would you suggest to future researchers to remove any ofthe predictor (independent) variables that were used in this analysis? If so, which one(s) andwhy, or if not, why not.I would not suggest removing any of the predictor variables from this model (so as to not miss specify the model) because all of the betas (β) were above .05 (i.e., Social Support β = .663, Temperament β = .165, and Home Environment β = .221).4. What is the degree of error for this regression analysis?Standard Error of the Estimate = 5.664MLR – KEYPage 35. Complete Tables 1 and 2 using three (3) decimal places. Don’t forget to put asterisks whereapplicable on Table 2 (showing significance).Table 1Means, Standard Deviations, and Correlations for Regression of Developmental Ability1 2 3 41. Developmental Ability 1.000 .899 .582 .7762. Social Support 1.000 .468 .7163. Temperament 1.000 .4814. Home Environment 1.000Means 39.400 54.230 33.100 24.530Standard Deviations 14.576 21.614 8.285 5.728N = 30Table 2Results of Regression of Developmental AbilityIndependent Variables B - tSocial Support .447 .663 6.284***Temperament .291 .165 1.967Home Environment .563 .221 2.080*Note. R2 = .865, p < .001*p < .05, ***p < .001MLR – KEYPage


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