Exam 14: Logistic Regression

Myopia (i.e. ,nearsightedness)is a result of environmental and genetic factors.In Singapore,the percent of military personnel having myopia increased dramatically over a 20-year period.Based on this fact,researchers wondered if the effect of the environment might be stronger and the genetic effect much less pronounced than previously thought.To study this issue,data from a random sample of 429 men,ages nineteen to twenty-five,in the Singapore military were obtained.Among other things,the men in the study were classified as to whether or not they had myopia and whether at least one of their parents had myopia.The results are presented in the table below. Let x be the indicator variable We wish to fit a logistic regression model, ,where p is the binomial probability that a man in the Singapore military has myopia and log is the natural logarithm. Based on the data in the table,what is the estimate b₁ of ₁?

In a recent study,over 33,000 women were asked,"Did you have a mammogram within the last 2 years?" Despite the benefits of screening,about 30% of respondents indicated that they had not had a recent mammogram.The dependent/outcome variable was the proportion of women who reported a recent mammogram.In addition,the following information was collected on each individual: age (40-49,50-64,65-74,75-84),race/ethnicity (Latina,Non-Latina African American,Non-Latina Asian/Pacific Islander,Non-Latina White,and Non-Latina other race/ethnicity),marital status (married or living with partner vs.not currently married),history of breast cancer (yes vs.no),self-rated health (excellent,very good,good,fair,poor),currently with health insurance (yes vs.no),and having a usual source of care (yes vs.no).All variables were treated as categorical (e.g. ,coded as 1 or 0 for each category).A multiple logistic regression model was fitted to the data to predict the probability a woman had a recent mammogram.Software output from SAS is shown below. What is the sample proportion of women who did have a mammogram within the last 2 years?

Do women and men treat female and male children differently? An observational study was conducted near the primate exhibit at the Sacramento Zoo on weekends in 1988.The data are from 37 groups of three-one adult female,one adult male,and one toddler-in which the toddler was being carried.Recorded in the table below are the gender of the adult who was carrying the toddler and the gender of the toddler: What are the odds that an adult carrying a girl was female?

A study was undertaken to assess the quality of cheese as determined by a panel of taste testers.The tasters rated samples of cheese as being acceptable or not acceptable.Those same samples of cheese were analyzed with respect to several variables,one of which was the untransformed concentration of lactic acid,designated as Lactic.A logistic regression was fitted relating the log odds that the cheese was acceptable to the explanatory variable Lactic.The following partial computer output is provided. What is the approximate 90% confidence interval estimate for the true slope of the logistic regression model?

Suppose the odds of there being a major traffic jam on the highway on your way to campus is 5 to 1.What is the probability that there is a traffic jam?

Myopia (i.e. ,nearsightedness)is a result of environmental and genetic factors.In Singapore,the percent of military personnel having myopia increased dramatically over a 20-year period.Based on this fact,researchers wondered if the effect of the environment might be stronger and the genetic effect much less pronounced than previously thought.To study this issue,data from a random sample of 429 men,ages nineteen to twenty-five,in the Singapore military were obtained.Among other things,the men in the study were classified as to whether or not they had myopia and whether at least one of their parents had myopia.The results are presented in the table below. What are the odds that a man with myopia has at least one parent with myopia?

A variable that takes on the values of only 1 and 0 is often called a(n)_________ variable.

Do women and men treat female and male children differently? An observational study was conducted near the primate exhibit at the Sacramento Zoo on weekends in 1988.The data are from 37 groups of three-one adult female,one adult male,and one toddler-in which the toddler was being carried.Recorded in the table below are the gender of the adult who was carrying the toddler and the gender of the toddler: Let x be the indicator variable We wish to fit a logistic regression model, ,where p is the binomial probability that the toddler being carried is a girl and log is the natural logarithm.The following (partial)SPSS output is available. Variables in the Equation What is a 95% confidence interval for the odds ratio?

What is the alternative hypothesis being tested when analyzing data using multiple logistic regression with three explanatory variables?

Myopia (i.e. ,nearsightedness)is a result of environmental and genetic factors.In Singapore,the percent of military personnel having myopia increased dramatically over a 20-year period.Based on this fact,researchers wondered if the effect of the environment might be stronger and the genetic effect much less pronounced than previously thought.To study this issue,data from a random sample of 429 men,ages nineteen to twenty-five,in the Singapore military were obtained.Among other things,the men in the study were classified as to whether or not they had myopia and whether at least one of their parents had myopia.The results are presented in the table below. What are the odds that a man with at least one parent with myopia also has myopia? (Note: Use three significant digits for the calculation. )

In a recent study,over 33,000 women were asked,"Did you have a mammogram within the last 2 years?" Despite the benefits of screening,about 30% of respondents indicated that they had not had a recent mammogram.The dependent/outcome variable was the proportion of women who reported a recent mammogram.In addition,the following information was collected on each individual: age (40-49,50-64,65-74,75-84),race/ethnicity (Latina,Non-Latina African American,Non-Latina Asian/Pacific Islander,Non-Latina White,and Non-Latina other race/ethnicity),marital status (married or living with partner vs.not currently married),history of breast cancer (yes vs.no),self-rated health (excellent,very good,good,fair,poor),currently with health insurance (yes vs.no),and having a usual source of care (yes vs.no).All variables were treated as categorical (e.g. ,coded as 1 or 0 for each category).A multiple logistic regression model was fitted to the data to predict the probability a woman had a recent mammogram.Software output from SAS is shown below. What is the equation for the estimated odds that a fifty-year-old,single,black woman who has no history of breast cancer and is in good health had a recent mammogram?

Babies who are born prematurely are susceptible to the development of a lung condition known as bronchopulmonary dysplasia (BPD).A sample of babies who weighed less than 1750 grams at birth,and who required intubation during the first few hours of life,was followed to determine the probability that the child develops BPD later in life.To model the probability that a child develops BPD as a function of the baby's birth weight x,a logistic regression was fitted.The fitted equation was found to be = 4.0343 - 0.0042x. From this equation,what would be the estimated probability that a child who weighed 1100 grams at birth develops BPD?

Do women and men treat female and male children differently? An observational study was conducted near the primate exhibit at the Sacramento Zoo on weekends in 1988.The data are from 37 groups of three-one adult female,one adult male,and one toddler-in which the toddler was being carried.Recorded in the table below are the gender of the adult who was carrying the toddler and the gender of the toddler: What are the odds that a female adult was carrying a girl?

Suppose the proportion of students in a simple random sample who own a tablet computer is .80 and the proportion of students that do not own a tablet is .20.What are the odds that a student owns a tablet?

In logistic regression,what statistic is used for statistical inference when you have one explanatory variable?

In a recent study,over 33,000 women were asked,"Did you have a mammogram within the last 2 years?" Despite the benefits of screening,about 30% of respondents indicated that they had not had a recent mammogram.The dependent/outcome variable was the proportion of women who reported a recent mammogram.In addition,the following information was collected on each individual: age (40-49,50-64,65-74,75-84),race/ethnicity (Latina,Non-Latina African American,Non-Latina Asian/Pacific Islander,Non-Latina White,and Non-Latina other race/ethnicity),marital status (married or living with partner vs.not currently married),history of breast cancer (yes vs.no),self-rated health (excellent,very good,good,fair,poor),currently with health insurance (yes vs.no),and having a usual source of care (yes vs.no).All variables were treated as categorical (e.g. ,coded as 1 or 0 for each category).A multiple logistic regression model was fitted to the data to predict the probability a woman had a recent mammogram.Software output from SAS is shown below. What are the odds that a woman did have a mammogram within the last 2 years?

In logistic regression with one explanatory variable,what is the value of the X² test statistic when the P-value is .05?

Using logistic regression,you are going to test the null hypothesis against the alternative hypothesis .Suppose b₁ = .8 and the standard error is .2.What is the value of the chi-square test statistic?

In a recent study,over 33,000 women were asked,"Did you have a mammogram within the last 2 years?" Despite the benefits of screening,about 30% of respondents indicated that they had not had a recent mammogram.The dependent/outcome variable was the proportion of women who reported a recent mammogram.In addition,the following information was collected on each individual: age (40-49,50-64,65-74,75-84),race/ethnicity (Latina,Non-Latina African American,Non-Latina Asian/Pacific Islander,Non-Latina White,and Non-Latina other race/ethnicity),marital status (married or living with partner vs.not currently married),history of breast cancer (yes vs.no),self-rated health (excellent,very good,good,fair,poor),currently with health insurance (yes vs.no),and having a usual source of care (yes vs.no).All variables were treated as categorical (e.g. ,coded as 1 or 0 for each category).A multiple logistic regression model was fitted to the data to predict the probability a woman had a recent mammogram.Software output from SAS is shown below. What is the equation for the estimated odds that a forty-year-old,married,Latina woman who has a history of breast cancer and is in excellent health had a recent mammogram?

Suppose the odds of being "unfriended" on Facebook by one of your friends is 2 to 3.What is the probability of being unfriended?