Question 1

In which of the following situations can binary logistic regression be used?
A) Kate wants to examine if gender (0=male, 1=female) can predict the aggression level of teenagers. She uses the number of self-reported aggressive behaviors in the previous month as the measure of aggression level.
B) Amy wants to use aggression level to predict whether a student will finish high school (0=no, 1=yes). The aggression level is measured by the occurrence of self-reported aggressive behaviors in the previous month.
C) Pete wants to predict the starting salary of teachers based on their highest level of education (Associate, Bachelor, Master, Ph. D or professional).
D) Mike wants to use parents' level of education to predict the highest level of education achieved by their children. He codes the level of education into six categories: some school, high school graduate, some college, two-year college, four-year college, and postgraduate.

Accepted Answer

Binary logistic regression is used when the dependent variable is binary (0 or 1, yes or no, etc.). In option B, Amy is predicting a binary outcome (whether a student will finish high school or not) based on aggression level, making it a suitable situation for binary logistic regression.

Question 2

Which one of the following can be used as an appropriate independent variable for binary logistic regression?
A) dichotomous variable
B) multinomial variable
C) continuous variable
D) none of the above
E) all of the above

Accepted Answer

E

Question 3

Which one of the following statements is true about OLS regression and logistic regression?
A) OLS regression uses continuous variables as independent variables, whereas logistic regression uses categorical variables as independent variables.
B) OLS regression assumes that the conditional distribution of the dependent variable is normal, whereas logistic regression makes no such assumption.
C) In OLS regression the predicted value (Y') is continuous, whereas in logistic regression the predicted probability is either 0 or 1.
D) In OLS regression there are always residuals in the model, whereas in logistic regression there are no residuals or errors.

Accepted Answer

OLS regression indeed assumes that the conditional distribution of the dependent variable, given the independent variables, is normal. This is a key assumption for the validity of OLS parameter estimates. On the other hand, logistic regression does not make this assumption. Instead, it models the probability that a dependent variable is in a particular category (for binary logistic regression, this is typically a 0 or 1 outcome) using the logistic function, without assuming a normal distribution of the dependent variable.

Question 4

Which of the following would be appropriate outcomes to examine with binary logistic regression?
A) Types of college degree (associate's degree, bachelor's degree)
B) Levels of education (high school, college, postgraduate)
C) Marital status (single, common-law married, married, divorced, separated, widowed)
D) Grades in a test (A, B, C, D, E)
E) All of the above

Accepted Answer

The answer of Which of the following would be appropriate...

Question 5

Based on a logistic regression model, the odds of Sandy passing a test is 4. Based on the odds, what is the probability that Sandy will pass the test?
A) 0.8
B) 0.4
C) 0.25
D) 0.2
E) cannot be determined.

Accepted Answer

The probability of an event given its odds is calculated as odds / (1 + odds). For odds of 4, the probability is 4 / (1 + 4) = 4 / 5 = 0.8.

Question 6

Based on a logistic regression model, Cindy did some calculation and predicted that the probability of her passing a test is 0.5. What are the odds that Sue will pass the test?
A) 1/2
B) 1
C) 2
D) 5
E) cannot be determined.

Accepted Answer

The odds of an event are calculated as the probability of the event occurring divided by the probability of the event not occurring. If the probability of passing the test is 0.5, then the probability of not passing is also 0.5. Therefore, the odds are 0.5 / 0.5 = 1.

Question 7

Which of the following statements about the relationship between Odds(Y=1) and Logit(Y) is false?
A) When the odds increase, the logit of Y increases.
B) When the odds are larger than 1, the logit of Y has positive value.
C) When the odds are smaller than 1, the logit of Y has negative value.
D) When the odds are 1, the logit of Y may either be positive or negative.

Accepted Answer

The logit function, defined as the logarithm of the odds, will be zero when the odds are 1. This is because log(1) = 0, making statement D false.

Question 8

In the logistic regression model, which of the following is assumed to have a linear relationship with the independent variables?
A) the dichotomous variable Y
B) Odds(Y =1)
C) logit(Y), i.e., the log odds ratio
D) error term

Accepted Answer

In logistic regression, the logit function (log odds) is assumed to have a linear relationship with the independent variables.

Question 9

A study was conducted to investigate variables associated with dropping out of high school. The following logistic regression model was obtained:
Logit(YS1U1B1iS1U1B0) = 3.5 - 1.3XS1U1B11S1U1B0 + 2.3XS1U1B12S1U1B0.
Y: 1= dropped out of high school; 0= did not drop out of high school;
XS1U1B11S1U1B0: cumulative high school GPA obtained;
XS1U1B12S1U1B0: 1 = retained in at least one grade; 0 = never retained in any grade.
-What is being predicted in this model?
A) The mean difference in cumulative GPA between students who dropped out of high school and those who finished high school.
B) The percentage of students who will drop out before graduating high school.
C) The odds that a student will drop out of high school.
D) The odds that a student had been retained in at least one grade if he dropped out of high school.

Accepted Answer

The logistic regression model predicts the log odds of a binary outcome, in this case, the odds that a student will drop out of high school based on their cumulative GPA and whether they have been retained in a grade.

Question 10

A study was conducted to investigate variables associated with dropping out of high school. The following logistic regression model was obtained:
Logit(YS1U1B1iS1U1B0) = 3.5 - 1.3XS1U1B11S1U1B0 + 2.3XS1U1B12S1U1B0.
Y: 1= dropped out of high school; 0= did not drop out of high school;
XS1U1B11S1U1B0: cumulative high school GPA obtained;
XS1U1B12S1U1B0: 1 = retained in at least one grade; 0 = never retained in any grade.
-Based on logistic regression, if a student has been retained in at least one grade, the chance that he/she will drop out of high school
A) increases.
B) decreases.
C) stays the same.
D) is uncertain.

Accepted Answer

The coefficient for being retained in at least one grade (2.3) is positive, indicating that if a student has been retained, the chance of dropping out of high school increases.

Question 11

A study was conducted to investigate variables associated with dropping out of high school. The following logistic regression model was obtained:
Logit(YS1U1B1iS1U1B0) = 3.5 - 1.3XS1U1B11S1U1B0 + 2.3XS1U1B12S1U1B0.
Y: 1= dropped out of high school; 0= did not drop out of high school;
XS1U1B11S1U1B0: cumulative high school GPA obtained;
XS1U1B12S1U1B0: 1 = retained in at least one grade; 0 = never retained in any grade.
-If Mindy has a high school GPA of 3, and has never repeated a grade, which of the following predictions can be derived from the model?
A) Mindy has more than 50% probability of dropping out of high school.
B) Mindy has less than 50% probability of dropping out of high school.
C) Mindy has exactly 50% probability of dropping out of high school.
D) Mindy will drop out of high school.
E) Mindy will not drop out of high school.

Accepted Answer

Given Mindy's GPA of 3 and never having repeated a grade, the logistic regression equation becomes Logit(P) = 3.5 - 1.3(3) + 2.3(0) = 3.5 - 3.9 = -0.4. Since the logit is negative, it implies P < 0.5, indicating Mindy has less than a 50% probability of dropping out.

Question 12

In logistic regression, which of the following statements about probability, odds, and log odds is true?
A) Probability, odds, and log odds can all be computed from the regression line.
B) Probability, odds, and log odds all have the same range of possible values.
C) Probability, odds, and log odds are all assumed to have a linear relationship with the independent variables.
D) Probability, odds, and log odds are all measured on the same scale.

Accepted Answer

In logistic regression, the probability of the dependent variable being a certain value (usually 1) is modeled using the logistic function. The odds are the ratio of the probability of the event occurring to the probability of the event not occurring, and log odds (or the logit function) is the natural logarithm of the odds. These can all be derived from the regression coefficients (the regression line in a conceptual sense), but they do not share the same range of values, are not assumed to have a linear relationship with the independent variables (the relationship is logistic), and are not measured on the same scale.

Question 13

Aaron is studying smoking behavior and has coded "smoker" as "1" and "non-smoker" as "0." Which of the following is a correct interpretation if the odds ratio is equal to 1?
A) The probability of being a smoker is equal to that of being a non-smoker.
B) The probability of being a smoker is substantially greater than that of being a non-smoker.
C) The probability of being a smoker is substantially smaller than that of being a non-smoker.
D) Cannot be determined from the information provided.

Accepted Answer

An odds ratio of 1 indicates that the event (in this case, being a smoker) is equally likely in both groups being compared, meaning the probability of being a smoker is equal to that of being a non-smoker.

Question 14

For a logistic regression model, if −2LL = 0, it indicates that
A) the model has perfect fit but the model cannot be estimated.
B) the model is a poor fit to the data.
C) the value of the log likelihood function is 0.
D) a computational error has been made.

Accepted Answer

When −2LL (negative two times the log likelihood) equals 0, it indicates that the model has a perfect fit to the data. This is because the log likelihood reaches its maximum value (which is 0 in the ideal case for −2LL) when the model predictions perfectly match the observed data. However, achieving a perfect fit is extremely rare in practice and might indicate overfitting or an error in model specification.

Question 15

Herbert is studying the risk factors associated with heart diseases. He identified three risk factors (age, sex, and cholesterol level), and built two different models. Model 1: Logit(Y_i) = -7 + 2.5X₁ - X₂. -2LL = 3 Model 2: Logit(Y_i) = -8.5 + 1.5X₃ -2LL = 8 Y: 1= diagnosed with major heart disease; 0 = no major heart disease; X₁: age in years (above 40); X₂: sex, where 0 is male and 1 is female; X₃: cholesterol level (in mmol/L) Herbert conducted a log likelihood difference test (p = .025) and concluded that Model 1 fit the data significantly better than Model 2. Evaluate his analysis. A) The analysis is not valid. The two models cannot be compared using the log likelihood difference test because they are not nested models. B) The interpretation of the test results is erroneous. The fact that the null hypothesis is rejected indicates that Model 2 fit the data better than Model 1. C) The interpretation of the test results is erroneous. The fact that null hypothesis is rejected indicates that Model 1 and Model 2 do not differ substantially in fit. D) There is nothing wrong with the analysis.

Accepted Answer

The two models cannot be directly compared using a log likelihood difference test because they are not nested models. Nested models are those where one model is a special case of the other, typically by setting some parameters to zero. Since Model 1 and Model 2 include different predictors (age, sex vs. cholesterol level), they do not satisfy this criterion.

Question 16

If the logistic regression model is a good fit to the data, which of the following test(s) will likely have significant results?
A) log likelihood difference test
B) Hosmer-Lemeshow goodness-of-fit test
C) both a and b
D) neither a nor b

Accepted Answer

The log likelihood difference test is used to compare the fit of two nested models, and a significant result indicates that the more complex model fits the data better.

Question 17

In logistic regression, the multiple R² pseudovariance explained values A) measure the proportion of variance explained in the dichotomous outcome variable. B) measure the effect size for the model. C) will increase as more variables are added to the model. D) are generally small for models with good fit.

Accepted Answer

In logistic regression, the multiple R² pseudovariance explained values measure the effect size for the model, indicating how well the model explains the variability in the outcome.

Question 18

Aaron is studying smoking behavior and has coded "smoker" as "1" and "non-smoker" as "0." The predictor is the number of family members who smoke. Which of the following is a correct interpretation of an odds ratio of +2?
A) For every additional family member who smokes, the odds of being a smoker increase by 100%.
B) For every additional family member who smokes, the odds of being a smoker decrease by 100%.
C) For every one-unit increase in being a smoker, the odds of having a family member who smoke increase by 100%.
D) For every one-unit increase in being a smoker, the odds of having a family member who smoke decrease by 100%.

Accepted Answer

An odds ratio of +2 means that for every additional family member who smokes, the odds of being a smoker double, or increase by 100%. This is because an odds ratio represents the factor by which the odds increase (in this case, by 2) for each unit increase in the predictor variable.

Question 19

In the smoking study, Aaron has obtained the following classification table. 
-What is the false positive rate?
A) 20%
B) 28%
C) 48%
D) 52%

Accepted Answer

The answer of In the smoking study, Aaron has obtained...

Question 20

In the smoking study, Aaron has obtained the following classification table. 
-What is the false negative rate?
A) 20%
B) 28%
C) 48%
D) 52%

Accepted Answer

The answer of In the smoking study, Aaron has obtained...

Quiz 19: Logistic Regression

In which of the following situations can binary logistic regression be used?

Which one of the following can be used as an appropriate independent variable for binary logistic regression?

Which one of the following statements is true about OLS regression and logistic regression?

Which of the following would be appropriate outcomes to examine with binary logistic regression?

Based on a logistic regression model, the odds of Sandy passing a test is 4. Based on the odds, what is the probability that Sandy will pass the test?

Based on a logistic regression model, Cindy did some calculation and predicted that the probability of her passing a test is 0.5. What are the odds that Sue will pass the test?

Which of the following statements about the relationship between Odds(Y=1) and Logit(Y) is false?

In the logistic regression model, which of the following is assumed to have a linear relationship with the independent variables?

In logistic regression, which of the following statements about probability, odds, and log odds is true?

Aaron is studying smoking behavior and has coded "smoker" as "1" and "non-smoker" as "0." Which of the following is a correct interpretation if the odds ratio is equal to 1?

For a logistic regression model, if −2LL = 0, it indicates that

If the logistic regression model is a good fit to the data, which of the following test(s) will likely have significant results?

In logistic regression, the multiple R2 pseudovariance explained values

Aaron is studying smoking behavior and has coded "smoker" as "1" and "non-smoker" as "0." The predictor is the number of family members who smoke. Which of the following is a correct interpretation of an odds ratio of +2?

In the smoking study, Aaron has obtained the following classification table. -What is the false positive rate?

In the smoking study, Aaron has obtained the following classification table. -What is the false negative rate?

In logistic regression, the multiple R² pseudovariance explained values