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f) Perform a test Ho Bclass = 0 vs H₁: Belass <0. g) Define the "null deviance" and "residual deviance" in the output. h) Perform a test about the significance of the overall model. Exercise 2 The titanic dataset is a collection of data about 714 passengers, and the goal is to predict the survival (Survival: 1 if the passenger survived, 0 if they did not) based on some personal characteristics. In particular, here we consider the ticket class (Class: 1 = first, 0 = second or third; dummy), the gender (Gender: man = 1, woman = 0; dummy), and the age (Age, in years). Fitting a logistic regression model in R produces the following summary: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.5003 0.2462 6.09 0.0000 Class 2.0103 0.2479 8.11 0.0000 Gender -2.5473 0.2017 ?? 0.0000 Age -0.0299 0.0074 -4.06 ?? Null deviance: 964.52 Residual deviance: 675.14 a) Write the corresponding theoretical model and the expression of the estimated model. b) Write the likelihood and log-likelihood function. c) Complete the missing values in the table. For Pr(>|z|) of Age, write an approximate value. What variables are statistically significant? d) Provide an estimate of the odds for a woman aged 30 with a ticket of first class (denote this individual as "A"). How do you expect this value to change if you consider a person with the same characteristics but aged 31 (denote this individual as "B")? e) Provide the interpretation of the coefficient associated with the Class variable. Given the estimate of this coefficient, what is the effect of this covariate on the survival probability?

f) Perform a test Ho Bclass = 0 vs H₁: Belass <0. g) Define the "null deviance" and "residual deviance" in the output. h) Perform a test about the significance of the overall model. Exercise 2 The titanic dataset is a collection of data about 714 passengers, and the goal is to predict the survival (Survival: 1 if the passenger survived, 0 if they did not) based on some personal characteristics. In particular, here we consider the ticket class (Class: 1 = first, 0 = second or third; dummy), the gender (Gender: man = 1, woman = 0; dummy), and the age (Age, in years). Fitting a logistic regression model in R produces the following summary: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.5003 0.2462 6.09 0.0000 Class 2.0103 0.2479 8.11 0.0000 Gender -2.5473 0.2017 ?? 0.0000 Age -0.0299 0.0074 -4.06 ?? Null deviance: 964.52 Residual deviance: 675.14 a) Write the corresponding theoretical model and the expression of the estimated model. b) Write the likelihood and log-likelihood function. c) Complete the missing values in the table. For Pr(>|z|) of Age, write an approximate value. What variables are statistically significant? d) Provide an estimate of the odds for a woman aged 30 with a ticket of first class (denote this individual as "A"). How do you expect this value to change if you consider a person with the same characteristics but aged 31 (denote this individual as "B")? e) Provide the interpretation of the coefficient associated with the Class variable. Given the estimate of this coefficient, what is the effect of this covariate on the survival probability?

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 14CR
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For context, the images attached below are from a February 2024 past paper in statistical modeling

f) Perform a test Ho Bclass = 0 vs H₁: Belass <0. g) Define the "null deviance" and "residual deviance" in the output. h) Perform a test about the significance of the overall model.
Transcribed Image Text:f) Perform a test Ho Bclass = 0 vs H₁: Belass <0. g) Define the "null deviance" and "residual deviance" in the output. h) Perform a test about the significance of the overall model.
Exercise 2 The titanic dataset is a collection of data about 714 passengers, and the goal is to predict the survival (Survival: 1 if the passenger survived, 0 if they did not) based on some personal characteristics. In particular, here we consider the ticket class (Class: 1 = first, 0 = second or third; dummy), the gender (Gender: man = 1, woman = 0; dummy), and the age (Age, in years). Fitting a logistic regression model in R produces the following summary: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.5003 0.2462 6.09 0.0000 Class 2.0103 0.2479 8.11 0.0000 Gender -2.5473 0.2017 ?? 0.0000 Age -0.0299 0.0074 -4.06 ?? Null deviance: 964.52 Residual deviance: 675.14 a) Write the corresponding theoretical model and the expression of the estimated model. b) Write the likelihood and log-likelihood function. c) Complete the missing values in the table. For Pr(>|z|) of Age, write an approximate value. What variables are statistically significant? d) Provide an estimate of the odds for a woman aged 30 with a ticket of first class (denote this individual as "A"). How do you expect this value to change if you consider a person with the same characteristics but aged 31 (denote this individual as "B")? e) Provide the interpretation of the coefficient associated with the Class variable. Given the estimate of this coefficient, what is the effect of this covariate on the survival probability?
Transcribed Image Text:Exercise 2 The titanic dataset is a collection of data about 714 passengers, and the goal is to predict the survival (Survival: 1 if the passenger survived, 0 if they did not) based on some personal characteristics. In particular, here we consider the ticket class (Class: 1 = first, 0 = second or third; dummy), the gender (Gender: man = 1, woman = 0; dummy), and the age (Age, in years). Fitting a logistic regression model in R produces the following summary: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.5003 0.2462 6.09 0.0000 Class 2.0103 0.2479 8.11 0.0000 Gender -2.5473 0.2017 ?? 0.0000 Age -0.0299 0.0074 -4.06 ?? Null deviance: 964.52 Residual deviance: 675.14 a) Write the corresponding theoretical model and the expression of the estimated model. b) Write the likelihood and log-likelihood function. c) Complete the missing values in the table. For Pr(>|z|) of Age, write an approximate value. What variables are statistically significant? d) Provide an estimate of the odds for a woman aged 30 with a ticket of first class (denote this individual as "A"). How do you expect this value to change if you consider a person with the same characteristics but aged 31 (denote this individual as "B")? e) Provide the interpretation of the coefficient associated with the Class variable. Given the estimate of this coefficient, what is the effect of this covariate on the survival probability?
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