Here is some info Binary Logistic Regression Introduction A binary logistic regression was conducted to examine whether Severity_of_Illness had a significant effect on the odds of observing the no category of Medical_Adherence. The reference category for Medical_Adherence was yes. Results The overall model was not significant based on an alpha of .05, 2(3) = 1.77, p = .622, suggesting that Severity_of_Illness did not have a significant effect on the odds of observing the no category of Medical_Adherence. McFadden's R-squared was calculated to examine the model fit, where values greater than .2 are indicative of models with excellent fit (Louviere et al., 2000). The McFadden R-squared value calculated for this model was 0.03. Since the overall model was not significant, the individual predictors were not examined further. Table 1 summarizes the results of the regression model. Table 1 Logistic Regression Results with Severity_of_Illness Predicting Medical_Adherence Variable B SE 2 p OR 95.00% CI (Intercept) -0.69 0.50 1.92 .166 - - Severity_of_Illnessmoderate -0.49 0.76 0.41 .523 0.62 [0.14, 2.73] Severity_of_Illnessmajor -0.29 0.84 0.12 .732 0.75 [0.14, 3.90] Severity_of_Illnessextreme -1.39 1.17 1.40 .237 0.25 [0.03, 2.49] Note. 2(3) = 1.77, p = .622, McFadden R2 = 0.03. References Louviere, J. J., Hensher, D. A., & Swait, J. D. (2000). Stated choice methods: Analysis and Applications. Cambridge University Press. https://doi.org/10.1017/CBO9780511753831 Intellectus Statistics [Online computer software]. (2025). Intellectus Statistics. https://statistics.intellectus360.com Glossaries Binary Logistic Regression Binary logistic regression is used to examine the relationship between one or more independent (predictor) variables and a single dichotomous dependent (outcome) variable. The purpose of this analysis is to use the independent variables to estimate the probability that a case is a member of one group versus the other (e.g., whether a patient has cancer or not). The binary logistic regression creates a linear combination of all the independent variables to predict the log-odds of the dependent variable. In this analysis, the overall significance of the regression model is tested by computing the 2 statistic, which is used with the df to compute the p-value (i.e., significance level). A significant overall model means that the set of independent variables significantly predict the dependent variable. If the overall model is significant, the significance of each independent variable is assessed. An odds ratio (OR) is computed for each independent variable and shows the extent that each independent variable affects the probability that a case is a member of one outcome group versus the other. In order to conduct a binary logistic regression, the dependent variable must be dichotomous (i.e., there are only two possible outcomes), the observations must be independent of each other, and the relationship between the independent variables and the logit-transformed dependent variable must be linear. Fun Fact! In economics, the binary logistic regression model may be referred to as a discrete choice model, meaning it is used to predict the choice between two alternatives. Chi-Square Test Statistic (2): Used with the df to compute the p-value of the overall model and each predictor in the model. Degrees of Freedom (df): Refers to the number of values used to compute a statistic; used with 2 to compute the p-value. Dummy-Code: Performed in order to add a nominal or ordinal independent variable into the regression model; turns the one variable into a series of dichotomous "yes/no" variables, one for each category; one of the categories are left out of the regression as the reference group that all other categories are compared to. McFadden R2: Measures the goodness-of-fit of the model. It tends to be more conservative than R2 values utilized in linear regression models. McFadden R2 values of .2 or greater indicate an excellent model fit. Multicollinearity: A state of very high intercorrelations or inter-associations among a set of variables. Odds Ratio (OR): Gives the factor increase in likelihood of the dependent variable occurring for every one unit increase in the predictor; sometimes labeled in statistical output as Exp(). p-value: The probability of obtaining the observed results if the null hypothesis (no relationship between the independent variable(s) and dependent variable) is true. Reference Category: Category of the dependent variable that the likelihood the other category is compared to. Standard Error (SE): How much the B is expected to vary. Unstandardized Beta (B): The slope of the predictor with the log-odds of the dependent variable. Variance Inflation Factors: A measurement to assess the amount of multicollinearity present in regression analysis. Raw Output Binary Logistic Regression with Medical_Adherence predicted by Severity_of_Illness Included Variables: Medical_Adherence and Severity_of_Illness Sample Size (Complete Cases): N = 55 Coefficients: Variable B SE 2 p OR 95.000% CI (Intercept) -0.693 0.500 1.922 0.166 Severity_of_Illnessmoderate -0.486 0.760 0.409 0.523 0.615 [0.139, 2.727] Severity_of_Illnessmajor -0.288 0.842 0.117 0.732 0.750 [0.144, 3.903] Severity_of_Illnessextreme -1.386 1.173 1.398 0.237 0.250 [0.0251, 2.489] Model Fit Statistics: 2 = 1.765 on 3 df, p = 0.622, McFadden R2 = 0.0283, Cox-Snell R2 = 0.0316, Nagelkerke R2 = 0.0466, Residual Deviance = 60.635, Residual df = 51