Question 1

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

Accepted Answer

The z-statistic in logistic regression tells the researcher whether the b coefficient for a specific independent variable (X) is significantly different from zero or not. This helps the researcher to determine whether the variable is a significant predictor of the dependent variable (Y) or not. A result with a high z-statistic value indicates a significant relationship between the independent variable and the dependent variable.

Question 2

Which of the following variables best exemplify multinomial logistic regression?

Accepted Answer

Multinomial logistic regression is used when there are three or more nominal outcomes. In this case, only option B, sport played, has three or more possible outcomes and is thus the best choice for multinomial logistic regression. Gender, aerobic capacity, and muscular endurance are all binary or continuous variables and would not be appropriate for multinomial logistic regression.

Question 3

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

Accepted Answer

Logistic regression is used to predict a binary outcome based on one or more predictor variables. In this case, the binary outcome is whether an individual should enter an elite rowing or weightlifting training programme, and the predictor variables are stature, aerobic capacity, muscular strength, and previous sports played. This is an appropriate example of logistic regression because the outcome is binary and the predictor variables are relevant to the outcome. The other options either do not involve a binary outcome or do not have appropriate predictor variables.

Question 4

Examine the performance analysis data below. Which variables may cause problems with the analysis by inflating the standard error? (You may select more than one option.)

Accepted Answer

B AND C

Question 5

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

Accepted Answer

'Polychotomous' is a commonly used term to describe a variable with three or more categories or outcomes, which is synonymous with 'multinomial'. B, C, and D are not related terms for this concept.

Question 6

What type of distribution does deviance follow?

Accepted Answer

Deviance follows a chi-square distribution, as it is calculated by finding the difference between the log-likelihoods of a model and the saturated model, and the resulting statistic follows a chi-square distribution.

Question 7

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)?

Accepted Answer

When evaluating the predictive ability of an independent variable (X) and outcome variable (Y), we use correlation coefficients (such as Pearson's r or Spearman's rho) which range from -1 to +1. This indicates the strength and direction of the relationship between the two variables. Therefore, the correct range for the correlation coefficient is -1 to +1, which is best represented by option C: 0 to 1. Option A and B include ranges that are too wide and not specific to correlation coefficients. Option D is incorrect as negative correlations can occur and be meaningful, thus the range should include negative values.

Question 8

Which of the following statements best describes stepwise regression?

Accepted Answer

Stepwise regression involves predictors being entered into the equation based on statistical analysis, such as selecting variables with the highest correlation or lowest p-value, rather than solely based on underpinning theory.

Question 9

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

Accepted Answer

Logistic regression modelling overcomes the issue of violating linearity by expressing the equation in logarithmic terms, which transforms a non-linear relationship to a linear relationship. This allows the logistic regression model to handle non-linear relationships between the independent and dependent variables.

Question 10

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?

Accepted Answer

Complete separation can lead to large standard errors and unreliable estimates in logistic regression models, making it a negative finding.

Question 11

Which of the following variables best exemplify binary logistic regression?

Accepted Answer

Gender is a binary variable as it has only two categories, male and female. Binary logistic regression is used when there are only two possible outcomes or categories for the dependent variable.

Question 12

Which of the following assumptions should be examined to ensure that bias is minimized? (You may select more than one option.)

Accepted Answer

Linearity between predictors and the logit ensures the model is correctly specified, reducing bias. Independence of errors helps in reducing overdispersion, which can lead to biased estimates.

Question 13

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

Accepted Answer

Logistic regression is used when the outcome variable is a categorical dichotomy variable (e.g. yes/no, success/failure), and the predictor variables can be categorical or continuous.

Question 14

Which of the following is a categorical variable?

Accepted Answer

A categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values, or categories. In this case, the outcome of a match is clearly a categorical variable since it can only be one of three categories: win, draw or lose.

The other options are not categorical variables as they represent numerical values that can take on a continuous range of values. For example, player motivation can range from 1 to 10, and shots on target and complete passes are counts of events that can take on any non-negative integer value.

Question 15

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?

Accepted Answer

A partial correlation value of -.83 indicates a strong negative relationship, meaning as the predictor value increases, the likelihood of the outcome variable decreases.

Question 16

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?

Accepted Answer

A probability value of .1 means there is only a 10% chance that the X variable(s) will correctly predict Y. This is not a high likelihood and is therefore considered very unlikely.

Question 17

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?

Accepted Answer

Deviance is expressed as -2 times the natural logarithm of the ratio of the likelihood of the null model to the likelihood of the fitted model. Therefore, the correct expression for deviance is Deviance = -2 × log-likelihood.

Question 18

By what alternative name is the z-statistic known?

Accepted Answer

The z-statistic is also known as the Wald statistic, named after the statistician Abraham Wald who developed it.

Question 19

What is meant by the term 'parsimony'?

Accepted Answer

Parsimony refers to the principle of preferring simpler explanations over complex ones when multiple explanations can account for a phenomenon. This principle is based on the idea that simpler explanations are more likely to be correct and that complex explanations that involve multiple assumptions are less likely to be accurate.

Question 20

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

Accepted Answer

Logistic regression is a non-linear model that is used to predict the probability of an event occurring.

Quiz 20: Categorical Outcomes: Logistic Regression