A Hierarchical Regression Analysis Psychology Essay

A Hierarchical lapsing compend Psychology EssayThis necessitate was conducted to rig what the predictors of Body Mass Index are. There were two research researchs of this take in. counterbalance research header was How well the fictitious character of java and oftenness of deep b actors linen outgo predict body the great unwashed index, after tyrannical for sexuality physical action at law? Second research question was How well do toothsome percentage and cacao percentage in coffee bean justify body mass index, after unequivocal the results of the first base research question? In order to reveal the predictors hierarchical reversion analysis was utilize. In this ruminate BMI was forthcome variable sexual urge, type of coffee, fat direct in coffee pluck, cocoa deem in drinking cocoa, exacting frequence of coffee tree consumption and oftenness of physical military action in a workweek were predictor variables. The ask was conducted with 600 university students.MethodParticipants and the varyingsThe sample of the study was consisted of 600 Middle East Technical University students 46.3% (n=278) were potent and 53.7% (n=322) were female. Convenience sampling method was use to determine the participants. The most crowd places of the university, such as library, market area, dormitory area, were selected as selective information line of battle areas.Requisite sample size for three-fold regress could be deliberate with the formula of fig of predictors * 8 + 50. According to formula required sample size is 106 (7*8+50). While in that respect are 600 students, sample size is quite enough to conduct multiple regress.The questionnaire used in this study was consisted of seven items which are presented in tabulate 1. Moreover, on that point is an id number for for to apiece maven one participant. Tot every(prenominal)y, there were six continuous and two savourless variables on data appoint.Table 1List of vari ables and brief descriptions in the data fileVariable NameDescription of the variableIdIdentity number of each participantBMIBody Mass Indexgrammatical sexual practiceGender (1 male 2 Female)TypeType of umber ( 1 Milk 2 Berry 3 Peanut)FatFat rate (%) in coffee berrycacao treeCacao rate (%)in coffeeFrequencyFrequency of chocolate consumption (number of chocolates eaten in the last week)ActivityFrequency of physical activity in a week entropy Analysis PlanIn this study hierarchical turnaround exit be held to find out how much the predictors tummy relieve the dependent variable, BMI. In hierarchical statistical degeneration different ensamples are turn uped sequentially. In contrast to stepwise regression, research worker decides the sequence of the predictors that included the get. tierce different shams get out be used to determine how much these self-directed variables predict the dependent variable. In the first model sexuality and frequency of physical activity i n a week will be included into analysis. In the aid model, sexual practice and frequency of physical activity in a week will be controlled type of chocolate and frequency of chocolate consumption will be included into analysis. In the third model, sex, frequency of physical activity in a week, type of chocolate and frequency of chocolate consumption will be controlled, fat percentage and cacao percentage in chocolate will be included into analysis.To conduct the regression analysis, flat data should be recoded. There are three different ship buttocksal to do this make coding, effects coding and contrast coding. In this study, dummy coding will be used to recode categorical data. In dummy coding, one categorical variable recode into different variables that the number of new variables are one less than the number of categories. Nevertheless, a categorical variable should have at least three levels to be recoded. A categorical variable with two levels such as gender neednt to be recoded. In this study there were two categorical data gender and type of chocolate. As it mentioned before, gender neednt to be recoded. The other categorical variable, type of chocolate, should be recoded. Milk chocolate will be selected as persona variable and, two other variables will be coded as drawvsberry and take outvs unimportant. besides all other multivariate statistical methods, Multiple Regression has mingled presumptuousnesss and, all these presumptions should be examine before conducting the analysis. primary assumption of multiple regression is normality. strange other multivariate analysis, regression analysis checks whether the phantasm distributes normally or non. Secondly, multicollinearity, which is high level of intercorrelation among predictor variables, should be checked. Thirdly, assumption of homoscedasticity should be checked. Homoscedasticity assumes that the partition of the error term is constant across each foster of the predictor. This me ans that there should not be seen a conformation on turn out bandage. Fourth assumption is independence, that the error term is supreme of the predictors in the model and of the set of the error term for other cases. The fifth part assumption of multiple regression is linearity. Lastly, outliers should be check whether they affect the results or not. overtone plots, leverage statistics, Cooks D, DF important and Mahalonobis out maintain could be used to determine outliers. coresdescriptive StatisticsTable 2 awards the descriptive statistics of the study. Table 2 shows that there is no missing data mean of dependent variable, BMI, is 24.65 and the standard deviation is 4.48.Table 2Descriptive StatisticsMeanStd. DeviationNbody mass index24.654.48600Gender1.54.50600physical activity in a week2.62.74600 take out chocolate vs berry chocolate.25.44600milk chocolate vs peanut chocolate.27.45600frequency of chocolate consumption4.66.73600fat rate (%) in chocolate51.709.69600cacao ra te (%) in chocolate51.959.96600Table 3 shows the correlations amongst the variables. If the table is examine it is seen that the high hat predictor of BMI is fat rate in chocolate. There is a positive and high correlation in the midst of the BMI and fat rate in chocolate. On the other hand, there is no correlation between BMI and gender, physical activity in a week, milk chocolate vs berry chocolate. Moreover, there is no correlation higher than .90 between the main(a) variables.Table 3 correlativity Matrix12345678Pearson Correlationbody mass index (1)1.00Gender (2)-.031.00physical activity in a week (3).04-.131.00milk chocolate vs berry chocolate (4)-.03.03-.111.00milk chocolate vs peanut chocolate (5).23-.02.12-.361.00frequency of chocolate (6) consumption.31.12.15-.05.191.00fat rate (%) in chocolate (7).64-.12.08.02.21.301.00cacao rate (%) in chocolate (8).52.08.03-.04.22.28.511.00AssumptionsThe first assumption of multiple regression to be checked is normality. Unlike other analysis, normality of residuals is checked whether errors normally distributed or not. Normality of residuals could be checked via two different ways histogram and P-P plot. Figure 1 shows the histogram of regression standardized residuals. The histogram shows that there is a normal diffusion of residuals. The frequency distribution of residuals is close to normal distribution line. Moreover, figure 2 shows the P-P plot of regression standardized residuals and it shows that distribution of errors is normal. It can be said that first assumption of multiple regression, normality, is not violated.Figure 1 Histogram of Regression Standardized equalizerFigure 2 P-P speckle of Regression Standardized ResidualThe punt assumption of multiple regression to be checked is multicollinearity. Multicollinearity could be checked with correlation ground substance, VIF or allowance measures. There should not be whatever correlation that is higher than .90 between two independent variables. When the correlation matrix (Table 3) is examined there is no correlation higher than .90 between two independent variables. Table 4 shows the collinearity statistics of all three models. VIF values more than tetrad or tolerance values higher than .20 are indicators of multicollinearity. Table 4 shows that there is no VIF value higher than four or tolerance value higher than .20. So, assumption of multicollinearity is not violated.Table 4Collinearity Statistics simulateCollinearity StatisticsToleranceVIF1(Constant)Gender.981.02physical activity in a week.981.022(Constant)Gender.961.04physical activity in a week.941.06milk chocolate vs berry chocolate.871.15milk chocolate vs peanut chocolate.841.19frequency of chocolate consumption.931.083(Constant)Gender.921.08physical activity in a week.941.06milk chocolate vs berry chocolate.861.17milk chocolate vs peanut chocolate.801.24frequency of chocolate consumption.841.19fat rate (%) in chocolate.671.49cacao rate (%) in chocolate.701.43The third assumption of multiple regression to be checked is homoscedasticity. Scatter plot of predicted value and residual is used to control homoscedasticity. Any pattern should not be seen on the fool away plot. Figure 4 shows that there is no pattern on the scatter plot so, there is not homoscedasticity.Figure 4 Scatter plot of predicted value and residualThe fourth assumption of multiple regression to be checked is independence. Independence is affected by the order of the independent variables and can be ignored if the order of independent variables is not important. Order of the independent variables is important in this study so, independence should be checked in this study. Independence is checked with Durbin-Watson value that should be between 1.5 and 2.5. Durbin-Watson value of the model is 1.88 so, independence assumption is not violated.The last assumption of multiple regression is linearity. We assume that linearity is not violated in this study.Influential ObservationsD ata should be checked whether there are outliers or not. Outliers could cause misguide results. There are different ways of checking outliers in multiple regression such as Partial plots, leverage statistics, Cooks D, DF of import and Mahalonobis distance. Each method uses a different calculation method so, multiple methods should be used and consequently make a decision whether a data is outlier or not.At first, partial tone plots of the dependent variable with each of the independent variable is examined (see on figure 5,6,7,8 and 9). Some cases that could be outliers are seen on each partial plot but, this should not be forgotten, making decision over partial plots is a subjective way and other ways of despotic outliers should be used. A decision could be made even after all methods were conducted.Figure 5 Partial diagram of BMI and physical activity in a weekFigure 6 Partial Plot of BMI and milk chocolate vs peanut chocolateFigure 7 Partial Plot of BMI and frequency of choc olate consumptionFigure 8 Partial Plot of BMI and fat rate in chocolateFigure 9 Partial Plot of BMI and cacao rate in chocolateAfter controlling partial plots, leverage value could be controlled to identify the outliers. It is seen that there is no case, leverage value of which is higher than .50. According to leverage test results there is no outlier.Table 5Extreme Values of Leverage sieveCase NumberValueCentered Leverage ValueHighest1448.042384.043141.034324.035592.03Lowest1196.002103.003535.054160.0558.05After controlling leverage values, Cooks distance could be controlled. In Cooks outperform, a value greater than the value, calculated with the formula of mean + 2 * standard deviation, can be admitted as outlier. In this study critical value is .008 (.002+2*(.003)). maximum value of Cooks distance is .03 so, it is expected that there will be outliers. Boxplot of Cooks distance (figure 10) shows that the cases 499, 438, 449, 236, 284, 484, 37, 354, 137, 97, 324 and 165 could b e outliers. On the other hand, according to Cook and Weisberg (1982) values greater than 1 could be admitted as outlier. So, it can be presume that there is no outlier.Figure 10 Boxplot of Cooks distanceAfter controlling Cooks place, DF Beta values of each independent variable could be checked. DF Beta value shows the change in regression coefficient due to deletion of that row with outlier. According to Field (2009) a case can be outlier if absolute value of DF Beta is higher than one. According to Stevens (2002) a case can be outlier if absolute value of DF Beta is higher than two. In this study there is no case that has DF Beta value higher than one (see figure 11). According to DF Beta test values there is no outlier in this study.Figure 11 Boxplots of DF Beta values of Independent VariablesLastly, Mahalanobis Distance could be controlled to identify the outliers. If there is any case that is greater than the value of chi square at =.001 that could be admitted as outlier. The critical value at =.001 with seven predictors is 24.32. Table 6 shows the extreme values for this study and there is no value greater than 24.32. According to Mahalanobis distance test there is no outlier.Table 6Extreme Values of Mahalanobis DistanceCase NumberValueMahalanobis DistanceHighest144823.72238420.90314120.50432419.15559217.99Lowest11962.6221032.6235352.7841602.78582.78If the results of each test is summarizedPartial plots shows that there could be outliers,Leverage values show that there is no outliers,Cooks distance values show that there is no outlier,DF Beta values show that there is no outlier.According to results of the tests, it could be assumed that there is no outlier.Regression ResultsA hierarchical regression analysis was conducted to identify the predictors of BMI. ternion different models were examined to understand which predictor explains has how much variableness. Table 7 shows the abridgment of three models. Among three models, the first model is not st atistically meaningful the second and third models are significant.In the first model gender and physical activity in a week were the predictors. This model explains the .2% of be variance, but insignificant F (2, 597) = .67 p .05.In the second model, milk chocolate vs berry chocolate, milk chocolate vs peanut chocolate and frequency of chocolate consumption are the predictors after controlling for the effect of gender and physical activity in a week. This model explains 13% of tot variance explained significantly, F (3, 594) = 28.901 p In the third model, cacao rate (%) in chocolate, fat rate (%) in chocolate are the predictors of BMI after controlling for the effect of gender, physical activity in a week, milk chocolate vs berry chocolate, milk chocolate vs peanut chocolate and frequency of chocolate consumption. This model explains 34% of quantity variance explained significantly, F (2, 592) = 189.154, p Table 7Regression Analysis perplex SummaryModelRR2Change StatisticsDu rbin-WatsonR2Fdf1df2 Sig. F1.05a.00.00.692597.502.36b.13.1328.903594.003.69c.47.34189.152592.001.879a. Predictors (Constant), physical activity in a week, genderb. Predictors (Constant), physical activity in a week, gender, milk chocolate vs berry chocolate, frequency of chocolate consumption, milk chocolate vs peanut chocolatec. Predictors (Constant), physical activity in a week, gender, milk chocolate vs berry chocolate, frequency of chocolate consumption, milk chocolate vs peanut chocolate, cacao rate (%) in chocolate, fat rate (%) in chocolated. Dependent Variable body mass indexTable 8 shows the Coefficients of Hierarchical Regression Analysis that shows the significance and inwardness variance explained by each predictor. In the first model any of the predictors significantly predicts the dependent variable, BMI. It can be said that neither the model, nor the predictors are statistically significant and do not predict the outcome variable, F (2, 597) = .67 p .05.In the secon d model, boilers suit model is significant, F (3, 594) = 28.901 p In the third model, overall model is significant, F (2, 592) = 189.154, p Table 8Coefficients of Hierarchical Regression AnalysisModelUnstandardized CoefficientsStandardized CoefficientstpCorrelationsBStd. ErrorBetaPart1(Constant)24.419.94125.938.000Gender-.232.370-.026-.628.530-.026physical activity in a week.226.251.037.900.369.0372(Constant)17.1651.30913.110.000milk chocolate vs berry chocolate.539.423.0521.273.204.049milk chocolate vs peanut chocolate1.943.420.1934.629.000.177frequency of chocolate consumption1.751.245.2837.135.000.2733(Constant)5.4261.1914.557.000fat rate (%) in chocolate.221.017.47713.033.000.390cacao rate (%) in chocolate.109.016.2426.766.000.203a. Dependent Variable body mass index discussionTwo different research questions were tried to be answered in this study. First research question was How well the type of chocolate and frequency of chocolate consumption predict body mass index, after c ontrolling for gender physical activity?. Second research question was How well do fat percentage and cacao percentage in chocolate explain body mass index, after controlling the results of the first research question?.A hierarchical regression analysis was conducted to answer the research questions. Three models were examined to find the predictors and their contribution to these models. The first model that examines that how well gender and physical activity in a week predict the dependent variable. Result of the first model shows that neither model nor predictors significantly predict the BMI.The second model examined to answer the first research question. This model predicts 13% of total variance explained. Milk chocolate vs berry chocolate does not significantly explain the BMI. Milk chocolate vs peanut chocolate explains 3%, frequency of chocolate consumption explains 7% of total variance explained.The third model examined to answer the second research question. This model pre dicts 47% of total variance explained and 34% of total variance explained uniquely. Fat rate in chocolate explains 15% and cacao rate in chocolate explains 4% of total variance uniquely.When all models were examined it is seen that fat rate in chocolate is the best predictor of BMI by explaining 15% of total variance explained. Frequency of chocolate consumption is the second by explaining 7% of total variance explained. Cacao rate is the third predictor by explaining 4% of total variance explained.