Answers (Chapter 5) - Discovering Statistics Using SPSS...

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Discovering Statistics Using SPSS: Chapter 5 Dr. Andy Field Page 1 5/22/2003 Chapter 5: Answers Task 1 A fashion student was interested in factors that predicted the salaries of catwalk models. She collected data from 231 models. For each model she asked them their salary per day on days when they were working ( salary ), their age ( age ), how many years they had worked as a model ( years ), and then got a panel of experts from modelling agencies to rate the attractiveness of each model as a percentage with 100% being perfectly attractive ( beauty ). The data are on the CD-ROM in the file Supermodel.sav . Unfortunately, this fashion student bought some substandard statistics text and so doesn’t know how to analyse her data Can you help her out by conducting a multiple regression to see which factor predict a model’s salary? How valid is the regression model? Model Summary b .429 a .184 .173 14.57213 .184 17.066 3 227 .000 2.057 Model 1 R R Square Adjusted R Square Std. Error of the Estimate R Square Change F Change df1 df2 Sig. F Change Change Statistics Durbin-W atson Predictors: (Constant), Attractiveness (%), Number of Years as a Model, Age (Years) a. Dependent Variable: Salary per Day (£) b. ANOVA b 10871.964 3 3623.988 17.066 .000 a 48202.790 227 212.347 59074.754 230 Regression Residual Total Model 1 Sum of Squares df Mean Square F Sig. Predictors: (Constant), Attractiveness (%), Number of Years as a Model, Age (Years) a. Dependent Variable: Salary per Day (£) b. To begin with a sample size of 231, with 3 predictors seems reasonable because this would easily detect medium to large effects (see the diagram in the Chapter). Overall, the model accounts for 18.4% of the variance in salaries and is a significant fit of the data ( F (3, 227) = 17.07, p < .001). The adjusted R 2 (.17) shows some shrinkage from the unadjusted value (.184) indicating that the model may not generalises well. We can also use Stein’s formula: [ ] 159 . 0 841 . 0 1 ) 816 . 0 ( 031 . 1 1 ) 184 . 0 1 ( 231 1 231 2 3 231 2 231 1 3 231 1 231 1 adjusted 2 = = = + = R This also shows that the model may not cross generalise well.
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Discovering Statistics Using SPSS: Chapter 5 Dr. Andy Field Page 2 5/22/2003 Coefficients a -60.890 16.497 -3.691 .000 -93.396 -28.384 6.234 1.411 .942 4.418 .000 3.454 9.015 .079 12.653 -5.561 2.122 -.548 -2.621 .009 -9.743 -1.380 .082 12.157 -.196 .152 -.083 -1.289 .199 -.497 .104 .867 1.153 (Constant) Age (Years) Number of Years as a Model Attractiveness (%) Model 1 B Std. Error Unstandardized Coefficients Beta Standardized Coefficients t Sig. Lower Bound Upper Bound 95% Confidence Interval for B Tolerance VIF Collinearity Statistics Dependent Variable: Salary per Day (£) a.
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