A Hierarchical Regression Analysis Psychology Essay

A Hierarchical retroflection Analysis Psychology EssayThis study was conducted to determine what the predictors of Body Mass advocator atomic number 18. There were 2 research questions of this study. First research question was How well the type of cocoa and frequence of burnt umber consumption predict body plug king, afterwards overbearing for gender corporal activity? Second research question was How well do fat percentage and cacao tree percentage in coffee tree explain body mass index, after controlling the results of the for the first time research question? In order to reveal the predictors hierarchical backsliding psychoanalysis was used. In this study BMI was outcome variable gender, type of drinking hot chocolate, fat evaluate in chocolate, cocoa order in chocolate, frequency of chocolate consumption and frequency of material activity in a week were predictor variables. The study was conducted with 600 university students.MethodParticipants and the Varia blesThe ideal of the study was consisted of 600 Middle East Technical University students 46.3% (n=278) were male and 53.7% (n=322) were female. restroom sampling method was used to determine the participants. The most crowded places of the university, such as library, market area, dormitory area, were selected as data collection areas.Requisite sample size for multiple regression could be calculated with the formula of number of predictors * 8 + 50. harmonize to formula required sample size is 106 (7*8+50). enchantment thither are 600 students, sample size is quite enough to conduct multiple regression.The questionnaire used in this study was consisted of seven items which are presented in add-in 1. Moreover, at that place is an id number for each participant. Totally, at that place were six continuous and two categorical variables on data file. fudge 1List of variables and brief descriptions in the data fileVariable NameDescription of the variableIdIdentity number of each p articipantBMIBody Mass Index gender sexual practice (1 Male 2 Female)TypeType of chocolate ( 1 take out 2 Berry 3 Peanut) lusciousFat rate (%) in chocolateCacaoCacao rate (%)in chocolateFrequencyFrequency of chocolate consumption (number of chocolates eaten in the last week)ActivityFrequency of somatogenic activity in a week info Analysis PlanIn this study hierarchical regression allow for be held to find out how much the predictors bathroom explain the drug-addicted variable, BMI. In hierarchical regression different frameworks are tested sequentially. In contrast to stepwise regression, researcher decides the sequence of the predictors that included the model. collar different models will be used to determine how much these independent variables predict the dependent variable. In the first model gender and frequency of physical activity in a week will be included into analysis. In the second model, gender and frequency of physical activity in a week will be controlled type o f chocolate and frequency of chocolate consumption will be included into analysis. In the third model, gender, 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, categorical data should be recoded. There are three different ways to do this dummy coding, effects coding and contrast coding. In this study, dummy coding will be used to recode categorical data. In dummy coding, iodin 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 othe r(a) categorical variable, type of chocolate, should be recoded. Milk chocolate will be selected as reference variable and, two other variables will be coded as milkvsberry and milkvspeanut.Likewise all other multivariate statistical methods, Multiple Regression has various confidences and, all these assumptions should be check out before conducting the analysis. First assumption of multiple regression is normality. Unlike other multivariate analysis, regression analysis checks whether the hallucination distributes normally or not. Secondly, multicollinearity, which is high level of inter coefficient of coefficient of correlation among predictor variables, should be checked. Thirdly, assumption of homoscedasticity should be checked. Homoscedasticity assumes that the random variable of the error term is constant across each esteem of the predictor. This means that there should not be seen a pattern on scatter plot. Fourth assumption is independence, that the error term is indepe ndent of the predictors in the model and of the take to bes of the error term for other cases. The fifth assumption of multiple regression is linearity. Lastly, outliers should be check whether they affect the results or not. partial(p) plots, supplement statistics, Cooks D, DF important and Mahalonobis withdrawnness could be used to determine outliers.ResultsDescriptive Statistics evade 2 shows the descriptive statistics of the study. defer 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 week2.62.74600milk chocolate vs berry chocolate.25.44600milk chocolate vs peanut chocolate.27.45600frequency of chocolate consumption4.66.73600fat rate (%) in chocolate51.709.69600cacao rate (%) in chocolate51.959.96600Table 3 shows the correlations between the variables. If the table is examine it is seen that the best predictor of BMI is fat rate in chocolate. There is a positive and high correlation between 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(prenominal) than .90 between the independent variables.Table 3Correlation 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. solve 1 shows the histogram of regression standardized residuals. The histogram shows that there is a normal distribution 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 whoremonger be said that first assumption of multiple regression, normality, is not violated.Figure 1 Histogram of Regression Standardized ResidualFigure 2 P-P Plot of Regression Standardized ResidualThe second assumption of multiple regression to be checked is multicollinearity. Multicollinearity could be checked with correlation matrix, VIF or tolerance prizes. There should not be any 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 col linearity statistics of all three models. VIF values more than four 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 fashion modelCollinearity 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 homo scedasticity. Any pattern should not be seen on the scatter 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 ObservationsData should be checked whether there are outliers or not. Outliers could cause misleading results. There are different ways of checking outliers in multiple regression such as fond(p) plots, leverage statistics, Cooks D, DFBeta and Mahalonobis distance. Each method uses a different calculation method so, multiple methods should be used and then make a decision whether a data is outlier or not.At first, partial 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 controlling outliers should be used. A decision could be made even after all methods were conducted.Figure 5 Partial Plot 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 chocolate 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 TestCase publicationValueCentered Leverage ValueHighest1448.042384.043141.034324.035592.03Lowest1196.002103.003535.054clx.0558.05After controlling leverage values, Cooks distance could be controlled. In Cooks Distance, 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 be outliers. On the other hand, according to Cook and Weisberg (1982) values greater than 1 could be admitted as outlier. So, it can be assumed that there is no outlier. Figure 10 Boxplot of Cooks distanceAfter controlling Cooks Distance, 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 Mahalano bis 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. tierce different models were examined to get a line which predictor explains has how much variance. Table 7 shows the summary of three models. Among three models, the first model is not statistically significant 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% o f total 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 total 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 total variance explained significantly, F (2, 592) = 189.154, p Table 7Regression Analysis Model SummaryModelRR2Change StatisticsDurbin-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 (Const ant), 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 total 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 second 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 indexDiscussionTwo different research questions were tested 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 controlling 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 predicts 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.W hen 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.