Question 1

By what alternative name is the z-statistic known?
A) Wald statistic
B) Murphy's statistic
C) Katch statistic
D) Wilmore statistic

Accepted Answer

The z-statistic is also known as the Wald statistic.

Question 2

Logistic regression uses the log-likelihood statistic to evaluate the fit of a model, based on the predicted and observed values, and is closely related to the deviance, but how is deviance expressed?
A) Deviance = -2 × log-likelihood
B) Deviance = -2 / log-likelihood
C) Deviance = log-likelihood / (-2)
D) Deviance = log-likelihood / ((-2) × (-2))

Accepted Answer

Deviance is expressed as -2 times the log-likelihood statistic.

Question 3

Why were the answers provided in Q20 selected?
A) The variable(s) have a value of 0 in them.
B) The variable(s) have a value of 5 or less in them.
C) The variables are continuous as opposed to categorical.
D) The variables are categorical as opposed to continuous.

Accepted Answer

The answers provided in Q20 were selected because they follow the criteria of having a value of 5 or less in them, indicating a low level of satisfaction.

Question 4

Based on the data presented above, three of the variables (undisclosed) were deemed sufficient to predict the outcome of a match. A chi-square value of 6.74 was obtained. How would you interpret this value?
A) Significant at the .01 level
B) Significant at the .05 level
C) Significant at the .10 level
D) Not statistically significant

Accepted Answer

A chi-square value of 6.74 with degrees of freedom equal to 2 and a significance level of .05 corresponds to a p-value of approximately .03. This means that there is less than a 5% chance of obtaining a chi-square value of 6.74 or higher by chance alone, which is considered statistically significant at the .05 level.

Question 5

Which of the following is another name for 'multinomial'?
A) Polychotomous
B) Bichotomous
C) Serialchotomous
D) Linearchotomous

Accepted Answer

Multinomial is another word for polychotomous, which means having multiple categories or response options. Bichotomous refers to having only two categories or response options. Serialchotomous and linearchotomous are not commonly used terms in statistics.

Question 6

Suppose you were investigating the influence of player decisions (e.g. where to distribute a pass) during a game of basketball on the outcome of the match. The partial correlation value between the predictor and outcome variable is known as the R-statistic in logistic regression and ranges from -1 to +1. If a value of -.83 was obtained, what would you conclude about the influence player decisions have on the outcome of the game?
A) As the predictor value increases, the likelihood of the outcome variable decreases.
B) As the predictor value increases, the likelihood of the outcome variable increases.
C) The difference between the predictor and outcome variables is due to chance.
D) All of the above are correct depending on the conditions.

Accepted Answer

The answer of Suppose you were investigating the influence of...

Question 7

In linear and multiple regression, Y is predicted from one or more independent (X) variables. In logistic regression, it is the probability of the X variables predicting Y that is used. What is the likelihood that the X variable(s) will predict Y if a probability value of .1 is produced?
A) Very unlikely
B) Very likely
C) Likely
D) A prefect prediction

Accepted Answer

A probability value of .1 indicates a low likelihood of the X variable(s) predicting Y, making it very unlikely.

Question 8

As with the t-statistic in linear regression, the z-statistic is used in logistic regression, but what does the value tell the researcher?
A) Whether the b coefficient for variable X (i.e. gradient) is significantly different from 0 or not
B) Whether the b coefficient for variable X (i.e. gradient) is significantly different from 1 or not
C) Whether the b coefficient for variable Y (i.e. gradient) is significantly different from 0 or not
D) Whether the b coefficient for variable Y (i.e. gradient) is significantly different from 1 or not

Accepted Answer

The z-statistic in logistic regression tells the researcher whether the b coefficient for the independent variable (X) is significantly different from 0 or not. This indicates whether or not the independent variable has a significant impact on the outcome variable (Y) in the logistic regression model.

Question 9

Which of the following variables best exemplify multinomial logistic regression?
A) Gender
B) Sport played
C) Aerobic capacity
D) Muscular endurance

Accepted Answer

Multinomial logistic regression is used when there are three or more categories in the outcome variable. In this case, the only variable that fits the criteria is option B - Sport played, as it has multiple categories such as basketball, soccer, etc.

Question 10

What type of distribution does deviance follow?
A) Chi-square distribution
B) t-distribution
C) F-distribution
D) z-distribution

Accepted Answer

Deviance follows a chi-square distribution. This is because deviance is calculated as the difference between the log-likelihood of the model and the log-likelihood of a saturated model, which can be represented as a sum of squares. The distribution of this sum of squares is the chi-square distribution.

Question 11

A group of researchers were interested in predicting the outcome of football matches. They found that time in possession of the ball, shots on target from within the area and corners won perfectly predicted the result. This is known as complete separation. Is this a positive or a negative finding and why?
A) Positive - increased accuracy
B) Positive - reduction in Type I error
C) Negative - creates large standard errors
D) Negative - increased Type II error

Accepted Answer

The answer of A group of researchers were interested in...

Question 12

Which of the following statements best describes stepwise regression?
A) Predictors are entered into an equation based on statistical analysis as opposed to underpinning theory.
B) Predictors are entered into an equation based on underpinning theory as opposed to statistical analysis.
C) Predictors are entered into an equation based on underpinning theory and statistical analysis.
D) Predictors are entered into an equation based on random allocation.

Accepted Answer

Stepwise regression involves selecting predictors based on statistical analysis rather than theoretical underpinnings. The procedure typically involves starting with a full model that includes all potential predictors, and then iteratively removing or adding predictors based on their p-values or other statistical criteria. Therefore, the predictors that end up in the final equation may not be those that are most theoretically relevant or meaningful, but rather those that have the strongest statistical association with the outcome.

Question 13

How does logistic regression modelling overcome the issue of violating linearity?
A) Equation expressed in logarithmic terms
B) Equation expressed in sigma terms
C) Equation expressed in alpha terms
D) Equation expressed in polynomial terms

Accepted Answer

Logistic regression overcomes the issue of violating linearity by expressing the equation in logarithmic terms, which allows for a non-linear relationship between the independent and dependent variables while still maintaining the sigmoidal shape of the curve.

Question 14

What is meant by the term 'parsimony'?
A) Simpler explanations of a phenomenon are preferred to complex explanations.
B) As more variables are identified, the model becomes more informed.
C) Complex explanations of a phenomenon are more accurate.
D) Simpler explanations have insufficient power.

Accepted Answer

Parsimony refers to the principle that simpler explanations are preferred to complex ones. It is also sometimes referred to as Occam's Razor.

Question 15

Logistic regression is most appropriate on which of the following models?
A) Non-linear model
B) Linear model
C) Serial model
D) Multiple regression model

Accepted Answer

The answer of Logistic regression is most appropriate on which...

Question 16

Which of the following is a categorical variable?
A) Player motivation (Likert scale between 1 and 10)
B) Outcome of a match (win, draw or lose)
C) Shots on target during a football match
D) Complete passes during a football match

Accepted Answer

A categorical variable is a variable that can take on a limited, and usually fixed, number of possible values. In this case, the outcome of a match can only be one of three categories: win, draw or lose. Therefore, it is a categorical variable. Player motivation, shots on target and complete passes all have numerical values, and therefore are not categorical variables.

Question 17

Which of the following is the most appropriate explanation of logistic regression?
A) The use of predictor variables that are categorical or continuous, but the outcome variable is a categorical dichotomy variable.
B) The use of predictor variables that have to be continuous, but the outcome variable is a categorical dichotomy variable.
C) The use of predictor variables that have to be categorical, but the outcome variable is a categorical dichotomy variable.
D) The use of predictor variables that are categorical or continuous, but the outcome variable is a continuous variable.

Accepted Answer

Logistic regression is a statistical method used to analyze the relationship between predictor variables and a categorical outcome variable, such as yes/no or pass/fail. The predictor variables can be either categorical or continuous, but the outcome variable must be a categorical dichotomy variable.

Question 18

Which of the following variables best exemplify binary logistic regression?
A) Gender
B) Sport played
C) Aerobic capacity
D) Muscular endurance

Accepted Answer

Binary logistic regression is used when the dependent variable is dichotomous, meaning it only has two possible outcomes. Gender fits this criteria as it has two possible outcomes: male or female. Sport played, aerobic capacity, and muscular endurance are not dichotomous variables.

Question 19

Which of the following is the most appropriate example of logistic regression?
A) The use of stature, aerobic capacity, muscular strength and previous sports played to predict whether an individual should enter an elite rowing or weightlifting training programme.
B) The use of aerobic capacity to predict marathon race time.
C) The use of aerobic capacity to predict whether an individual should develop muscular strength and endurance.
D) The use of stature, aerobic capacity, muscular strength and previous sports played to predict aerobic capacity.

Accepted Answer

Logistic regression is commonly used for binary classification problems, where the outcome variable is categorical with two possible values. In this case, the outcome variable is whether an individual should enter an elite rowing or weightlifting training program or not, making it a binary classification problem. The predictor variables are stature, aerobic capacity, muscular strength, and previous sports played.

Question 20

What range is used when evaluating the predictive ability of an independent (X) variable (e.g. numbers of passes in field hockey) and the outcome (Y) variable (e.g. outcome of the game - win, draw or lose)?
A) 1 to 100
B) 0 to 100
C) 0 to 1
D) -1 to +1

Accepted Answer

The range used when evaluating the predictive ability of an independent variable and the outcome variable is typically 0 to 1, as it represents the percentage or probability of the outcome being affected by the independent variable. For example, if the independent variable is the number of passes in field hockey, a regression analysis might show that it has a predictive ability of 0.75, meaning that 75% of the outcome (win, draw, or lose) can be attributed to the number of passes. This range is commonly used in statistics and data analysis.

Quiz 20: Categorical Outcomes: Logistic Regression

By what alternative name is the z-statistic known?

Logistic regression uses the log-likelihood statistic to evaluate the fit of a model, based on the predicted and observed values, and is closely related to the deviance, but how is deviance expressed?

Why were the answers provided in Q20 selected?

Based on the data presented above, three of the variables (undisclosed) were deemed sufficient to predict the outcome of a match. A chi-square value of 6.74 was obtained. How would you interpret this value?

Which of the following is another name for 'multinomial'?

In linear and multiple regression, Y is predicted from one or more independent (X) variables. In logistic regression, it is the probability of the X variables predicting Y that is used. What is the likelihood that the X variable(s) will predict Y if a probability value of .1 is produced?

As with the t-statistic in linear regression, the z-statistic is used in logistic regression, but what does the value tell the researcher?

Which of the following variables best exemplify multinomial logistic regression?

What type of distribution does deviance follow?

Which of the following statements best describes stepwise regression?

How does logistic regression modelling overcome the issue of violating linearity?

What is meant by the term 'parsimony'?

Logistic regression is most appropriate on which of the following models?

Which of the following is a categorical variable?

Which of the following is the most appropriate explanation of logistic regression?

Which of the following variables best exemplify binary logistic regression?

Which of the following is the most appropriate example of logistic regression?

What range is used when evaluating the predictive ability of an independent (X) variable (e.g. numbers of passes in field hockey) and the outcome (Y) variable (e.g. outcome of the game - win, draw or lose) ?