SPSS Data: Optimism and Longevity, Multicollinearity & Significant Analysis (Statistics Project Sample)

Optimism and Longevity
PSY 870: Module 7 Problem Set
[Student’s Name]
[Institution Name]
Optimism and Longevity
Variable Correlations
An evaluation of variable correlations is important in establishing both the magnitude and the nature of the relationship that exists between variables (Coakes, 2012). In the present case, longevity (years lived after diagnosis) is the dependent variable and the predictors include socioeconomic status (SES), Age and Optimism. As such, the correlations between the dependent and the independent variables are as presented in table 1.
Table 1
Summary of correlations between variables (N = 244)
Years Lived after DiagnosisAgeSocioeconomic StatusOptimismYears Lived after Diagnosis1.00Age-.33***1.00Socioeconomic Status.37***-.29***1.00Optimism.57***-.43***.52***1.00Notes: ***p < .001 As shown in table 1, there are highly significant (p’s < .001) correlations between longevity and the predictors. In this case, the higher the age, the lower the longevity, r = -.33, p < .001. On the other hand, a higher socioeconomic status is associated with increased longevity, r = .37, p < .001. Similarly, increased optimism leads to increased longevity, r = .57, p < .001.
Multicollinearity
The variable Age has a weak-negative relationship with socioeconomic status (r = -.29, p < .001) and a moderate-negative relationship with Optimism (r = -.43, p < .001). This presents no potential problem with multicollinearity. However, there is a strong-positive relationship between optimism and socioeconomic status (r = .52, p < .001). This could indicate a possible problem with multicollinearity.
Goodness of Fit
The model has R-Squared = 0.343, with an adjusted R-Squared = 0.334. This indicates that about 33.4% of the variance around the mean in the longevity is explained by the independent variables in the model. Further, the regression model is highly significant (F(3, 240) = 41.68, p < .001).
Significant Analysis
The coefficient for the intercept, b0 = 3.73, is not significant in the model, t (240) = 1.77, p = .078. Similarly, the coefficient for Age, b1 = -0.07, is not significant in the model, t(240) = -1.68, p = .095. The coefficient for socioeconomic status, b2 = 0.24, is not significant in the model, t(240) = 1.44, p = .151. In contrast, the coefficient for Optimism (b3 = 0.18) is highly significant in the model, t(240) = 7.43, p < .001.
Results Section
In predicting the number of years lived after diagnosis of incurable cancer, the regression model is obtained as Years lived after diagnosis = 3.73 – 0.07*(Age) + 0.24 (Socioeconomic Status) + 0.18*(Optimism). This model is highly significant, F (3, 240) = 41.68, p < .001. However, significance analysis shows that Optimism is the highest and most significant contributor in the model to predict longevity. The adjusted coefficient of determination (adjusted R-squared) is .334, which means that about 33.4% of the variance in the number of years lived after diagnosis is accounted for by Age, SES, and Optimism.
Appendix: SPSS Outputs
GET
FILE='C:\Users\JT\Downloads\5996036_ch5bdata.sav'.
DATASET NAME DataSet1 WINDOW=FRONT.
REGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI(95) R ANOVA
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT yrslived
/METHOD=ENTER age ses optimism.
Regression
NotesOutput Created28-MAR-2014 10:14:04CommentsInputDataC:\Users\JT\Downloads\5996036_ch5bdata.savActive DatasetDataSet1FilterWeightSplit FileN of Rows in Working Data File244Missing Value HandlingDefinition of MissingUser-defined missing values are treated as missing.Cases UsedStatistics are based on cases with no missing values for any variable used.SyntaxREGRESSION
/DESCRIPTIVES MEAN STDDEV CORR SIG N
/MISSING LISTWISE
/STATISTICS COEFF OUTS CI(95) R ANOVA
/CRITERIA=PIN(.05) POUT(.10)
/NOORIGIN
/DEPENDENT yrslived
/METHOD=ENTER age ses optimism.ResourcesProcessor Time00:00:00.03Elapsed Time00:00:00.12Memory Required1948 bytesAdditional Memory Required for Residual Plots0 bytes
[DataSet1] C:\Users\JT\Downloads\5996036_ch5bdata.sav
Descriptive StatisticsMeanStd. DeviationNYears Lived after Diagnosis12.744.470244Age29.665.976244Socioeconomic Status4.691.678244Optimism57.3812.405244CorrelationsYears Lived after DiagnosisAgeSocioeconomic StatusOptimismPearson CorrelationYears...