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SMART FIELD HOMEWORK FOR CHP 7

# SMART FIELD HOMEWORK FOR CHP 7 - Task 1 A fashion student...

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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 modeling agencies to rate the attractiveness of each model as a percentage with 100% being perfectly attractive(beauty). The data are in the file Supermodel.sav. Unfortunately, this fashion student bought some substandard statistics text and so doesn’t know how to analyze her data. Can you help her out by conducting a multiple regression to see which variables predict a model’s salary? How valid is the regression model? Descriptive Statistics Mean Std. Deviation N Salary per Day (? 11.3385 16.02644 231 Attractiveness (%) 75.9447 6.77303 231 Number of Years as a Model 4.5854 1.57865 231 Age (Years) 18.0679 2.42190 231 Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Durbin-Watson R Square Change F Change df1 df2 Sig. F Change 1 .429 a .184 .173 14.57213 .184 17.066 3 227 .000 2.057 a. Predictors: (Constant), beauty, years, age b. Dependent Variable: salary ANOVA a Model Sum of Squares df Mean Square F Sig. 1 Regression 10871.964 3 3623.988 17.066 .000 b Residual 48202.790 227 212.347 Total 59074.754 230 a. Dependent Variable: salary b. Predictors: (Constant), beauty, years, age Adjusted states the shrinkage from the unadjusted value(0.184) pointing the model could not occur well.

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We could use: Adjusted R 2 =1-[(231-1/231-3-1)(231-2/231-3-2)(231+1/231)](1-0.184)=0.159 This is meaning these results are indicative that the model may not cross generalize well. The population used was 231 models and three predictors were observed which is suitable in observing medium to large effects. The 18.4% of the variance in salary per day, it is a suitable fit of the all data F (3227)=17.07,p<0.0001). The R 2 The tolerance is below 0.2 which also indicates a serious problem in the collinearity of the model. This indicates that the age and years are almost identical meaning they measure almost the same thing. The reasoning for this is because as you age skin becomes wrinkled therefore making it harder to impress others in photo shoots due to large amounts of applied makeup. This is an indicator that the assumption may be unreliable for this model. Model Unstan dardize d Coeffici ents Standar dized Coeffici ents t Sig. 95.0% Confide nce Interval for B Correlat ions Collinearity Statistics B Std. Error Beta Lower Bound Upper Bound Zero- order Partial Part Toleran ce VIF 1 (Consta nt) -60.890 16.497 -3.691 .000 -93.396 -28.384 age 6.234 1.411 .942 4.418 .000 3.454 9.015 .397 .281 .265 .079 12.653 years -5.561 2.122 -.548 -2.621 .009 -9.743 -1.380 .337 -.171 -.157 .082 12.157 beauty -.196 .152 -.083 -1.289 .199 -.497 .104 .068 -.085 -.077 .867 1.153 a. Dependent Variable: salary Collinearity Diagnostics a Model
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SMART FIELD HOMEWORK FOR CHP 7 - Task 1 A fashion student...

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