Advanced Research Methods
STA4806/ACT2.3/0/2013
Department of Statistics
STA4806: Advanced Research Method in Statistics
Activity 2.3, 2013 Typical Model Questions and Solutions for Assignment 3
Despatch date: 15 July 2013
Open Rubric
2 Model Questions QUESTION 1 The following question is adapted from Dugard P., Todman J. and S. Harry, Data sets for Approaching multivariate analysis: a practical approach introduction. One hundred and ten patients diagnosed as having the eating disorder, bulimia, are recruited to a study designed to evaluate potential predictors of SUCCESS of a ten week course of treatment using cognitive behavioural therapy (CBT). The dependent variable is a success score based on responses to patient and GP post-treatment questionnaires. The potential predictors includes scores on three variables regarded as providing good approximations to interval scales: SELFTEST SEVERITY Score on a self esteem inventory Severity of the eating disorder based on family and patient interviews and questionnaires DEPRESSION Score on a depression inventory (a) (i) Consider the correlation matrix given in Exhibit 1.1. Which of the three independent variables would you think might be the possible predictors and why? (ii) Give the statistics which indicate that the regression model containing all three independent variables gives a significant fit and explain why. (iii) Looking at the section "Coefficients", comment on the t-values of the variables. (iv) What can you deduce from the "tolerance values"? Compare your answer with the conclusion that can be drawn from the values of the "condition numbers." (v) Are there signs of multicollinearity in the data? Justify. (vi) Is the variance of the dependent variable constant over the values of the independent variables? Is the model a good fit? Justify. (b) Use the stepwise regression analysis given in Exhibit 1.2 to answer the following questions: (i) Write down the final model of the multivariate regression analysis. (ii) Evaluate the
Department of Statistics
STA4806: Advanced Research Method in Statistics
Activity 2.3, 2013 Typical Model Questions and Solutions for Assignment 3
Despatch date: 15 July 2013
Open Rubric
2 Model Questions QUESTION 1 The following question is adapted from Dugard P., Todman J. and S. Harry, Data sets for Approaching multivariate analysis: a practical approach introduction. One hundred and ten patients diagnosed as having the eating disorder, bulimia, are recruited to a study designed to evaluate potential predictors of SUCCESS of a ten week course of treatment using cognitive behavioural therapy (CBT). The dependent variable is a success score based on responses to patient and GP post-treatment questionnaires. The potential predictors includes scores on three variables regarded as providing good approximations to interval scales: SELFTEST SEVERITY Score on a self esteem inventory Severity of the eating disorder based on family and patient interviews and questionnaires DEPRESSION Score on a depression inventory (a) (i) Consider the correlation matrix given in Exhibit 1.1. Which of the three independent variables would you think might be the possible predictors and why? (ii) Give the statistics which indicate that the regression model containing all three independent variables gives a significant fit and explain why. (iii) Looking at the section "Coefficients", comment on the t-values of the variables. (iv) What can you deduce from the "tolerance values"? Compare your answer with the conclusion that can be drawn from the values of the "condition numbers." (v) Are there signs of multicollinearity in the data? Justify. (vi) Is the variance of the dependent variable constant over the values of the independent variables? Is the model a good fit? Justify. (b) Use the stepwise regression analysis given in Exhibit 1.2 to answer the following questions: (i) Write down the final model of the multivariate regression analysis. (ii) Evaluate the