Week 7 Self-Assessment, Solutions

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Logistic regression is flexible enough to allow you to predict a binomial outcome (survived: yes/no) with both categorical and continuous variables. Test whether chivalry existed on the Titanic as it sank. Set up your analyses using survived as the dependent variable, age as a covariate, and sex as a factor. Build the model in three blocks. Block 1 includes age, Block 2 sex, Block 3 sex*age (their interaction). Under Model Fit, make sure that AIC is checked as well as the overall model test. Under Model coefficients, make sure Likelihood ratio tests, odds ratio, and confidence intervals are all checked. Under estimated marginal means, you can make different plots. Set up three "Terms." Term1 Age, Term 2 Sex, Term 3 Age then Sex. Note. The following questions focus a lot on prediction. This means that the results are used to predict the odds and probability that a specific person would survive. The use of regression for prediction is one of its key applications and forms the basis of machine learning and predictive modeling. You have set up three different nested models. Based on the overall model Chi-squared tests, which models are significant? All of them are significant. Nested models are compared to see if the more sophisticated model is significantly better than the

simpler model. The model with the interaction in it significantly better that the model with just the two main effects. True There are multiple ways of assessing which model is best. The AIC is a common measure used to compare models. The smaller this measure is, the better the model. Which model has the smallest AIC? Model 3 Based on Model 2, females are more likely to survive the wreck than men.

True, when the reference level is set to Male, you can see that the LOGIT estimate is greater than zero (2.466 Based on Model 2, what is the odds ratio for a female surviving the wreck as compared to a man? Answer as X.XX The odds ratio is 11.77. Make sure Male is teh reference level Question 6 Assume your prof was on the Titanic. Let's try to predict whether he would survive! He is a 47 year old male, who could afford a second class ticket. Use Model 1, which only contains the age. Blank 1 What is the estimate (also known as the log-odds) of his survival? Answer as X.XXXX

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LOGIT  log-odds = Intercept + 47 x AgeParam LOGIT  0.05672  47 x (-0.01096 LOGIT = 0.05672  0.51512 LOGIT  0.57184 Blank 2 What is the odds ratio of his survival, as compared to a newborn (the intercept value)? This is the e^Answer in blank 1. Answer as X.XXXX odds = Blank 3 What is the probability that a 47 year old person (we have not used sex in the model yet) will survive? Answer as X.XXXX Prob = odds/1+odds) You can confirm the answer in blank 3 by looking at the estimated marginal means plot. Question 7 Assume your prof was on the Titanic. Let's try to predict whether he would survive! He is a 47 year old male, who could afford a second class ticket. Use Model 3. Blank 1 What is the estimate (also known as the log-odds) of his survival? Note, you have to enter something for sex. Whether you enter a zero or a one depends on what the reference level is. One way makes this calculation MUCH easier than the other. Answer as X.XXXX LOGIT  intercept + Sex + Age x AgeParam + (Sex x Age) x InteractionParameter Set Sex reference to male; therefore, when we want to make estimates about males we enetr 0 wherever sex goes in the model. LOGIT  0.72395  0.02142  47 LOGIT  1.73069 Blank 2 What is the odds ratio of his survival, as compared to a newborn (the intercept value)? This is the e^Answer in blank 1. Answer as X.XXXX odds = Blank 3 What is the probability that a 47 year old male will survive? Answer as X.XXXX Prob = odd/1+odds) = 0.15050 You can confirm the answer in blank 3 by looking at the estimated marginal means plot. Question 8

What if your prof was female? Let's try to predict whether she would survive! She is a 47 year old female, who could afford a second class ticket. Use Model 3. Blank 1 What is the estimate (also known as the log-odds) of her survival? Note, you have to enter something for sex. You can use the same parameters from the question about a 47 yo male. Or, you can make your life easier and change the reference level. Whether you enter a zero or a one depends on what the reference level is. One way makes this calculation MUCH easier than the other. Answer as X.XXXX You could change the reference level to female and do this problem exactly like the question above. I will not and do it the hard way. LOGIT  intercept + Sex + Age x AgeParam + (Sex x Age) x InteractionParameter LOGIT  0.72395  1.31775  0.02142  47  0.04112  1  47 LOGIT  1.5197 Blank 2 What is the odds ratio of her survival, as compared to a newborn (the intercept value)? This is the e^Answer in blank 1. Answer as X.XXXX odds = Blank 3 What is the probability that a 47 year old female will survive? Answer as X.XXXX Prob = odd/1+odds) = 4.57085/5.57085 Prob = 0.82049 You can confirm the answer in blank 3 by looking at the estimated marginal means plot. Question 9 As the ship sank, it was every person for themselves when trying to get onto the life boats. No, there was some chivalry because the probability of males surviving was MUCH lower than females.

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