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Simple Linear Regression
Published in Marcello Pagano, Kimberlee Gauvreau, Heather Mattie, Principles of Biostatistics, 2022
Marcello Pagano, Kimberlee Gauvreau, Heather Mattie
The coefficient of determination can be interpreted as the proportion of the variability among the observed values of y that is explained by the linear regression of y on x. This interpretation derives from the relationship between σy, the standard deviation of the outcomes of the response variable Y, and , the standard deviation of y for a specified value of the explanatory variable X, that was presented in Section 17.1:
Choosing among Competing Specifications
Published in Douglas D. Gunzler, Adam T. Perzynski, Adam C. Carle, Structural Equation Modeling for Health and Medicine, 2021
Douglas D. Gunzler, Adam T. Perzynski, Adam C. Carle
In traditional linear regression analysis, the R2 value, the coefficient of determination, is interpreted as the amount of variation in the response that can be explained by the regressors in the model. R2 and adjusted R2 are used in traditional linear regression analysis as goodness of fit measures. These measures are also especially useful when comparing nested models, though in theory, apply to non-nested models as well. In the SEM setting, within a multi-equation model, each equation has a different R2 or adjusted R2. Therefore, examining R2 for magnitude can be both context and equation specific, depending on the set of explanatory variables with respect to that outcome.5 Thus, typically, other indices as described in Chapter 4 are preferred for use as more global measures of goodness of fit. In the context of model re-specification, a researcher can compare the R2 values for a particular outcome across competing models and then evaluate for the model with the highest value.
Linear regression
Published in Ewen Harrison, Pius Riinu, R for Health Data Science, 2020
R-squared is another measure of how close the data are to the fitted line. It is also known as the coefficient of determination and represents the proportion of the dependent variable which is explained by the explanatory variable(s). So 0.0 indicates that none of the variability in the dependent is explained by the explanatory (no relationship between data points and fitted line) and 1.0 indicates that the model explains all of the variability in the dependent (fitted line follows data points exactly).
Application of supervised machine learning algorithms for the evaluation of utricular function on patients with Meniere’s disease: utilizing subjective visual vertical and ocular-vestibular-evoked myogenic potentials
Published in Acta Oto-Laryngologica, 2023
Phillip G. Bragg, Benjamin M. Norton, Michelle R. Petrak, Allyson D. Weiss, Lindsay M. Kandl, Megan L. Corrigan, Cammy L. Bahner, Akihiro J. Matsuoka
Statistical analysis was performed using independent two-group Student’s t-test and one-way ANOVA (with Tukey-Kramer’s post hoc test to identify significant differences between means while controlling the family-wise error rate). Equal population variance was not assumed in one-way ANOVA in order to perform a more stringent statistical analysis given the number of subjects. Pearson’s linear correlation coefficient of determination (r2) was also calculated. The linear regression line was computed using the method of least-squares. The Shapiro–Wilk test was performed to confirm that the data set followed a normal distribution. We set a null hypothesis in that the data are not significantly different from a normal distribution. All these statistical analyses were performed using Python 3.10.5 (Python Software Foundation, Wilmington, Delaware, USA). The following libraries were used for the statistical analysis: Scipy, Numpy, Matplotlib, and Seaborn. Results are reported as means ± one standard deviation unless otherwise noted. A significant p-value is indicative of a significant difference where the probability is less than (p < 0.05*, p < 0.01**).
Contributions of safety critical success factors and safety program elements to overall project success
Published in International Journal of Occupational Safety and Ergonomics, 2023
Mohanad Kamil Buniya, Idris Othman, Riza Yosia Sunindijo, Ali Amer Karakhan, Ahmed Farouk Kineber, Serdar Durdyev
The model’s prediction capability can be assessed from the structural model using PLS-SEM. Hence, once the reliability and validity are established, the evaluation criteria for PLS-SEM results are the coefficients of determination (R2 value). The coefficient of determination is a measure of the proportion of an endogenous construct’s variance as explained by its predictor constructs [124]. The R2 value indicates the number of variance-independent variables clarified by the independent variables. Thus, a larger R2 value raises the predictive capability of the structural model. In this research, the Smart-PLS algorithm was used to compute the R2 value, as presented in Table 8. The result of the analysis reveals the R2 value as 0.690. Accordingly, the adjusted R2 value for project success as the main dependent variable in this model was found to be 0.687. This means that the safety program implementation has the ability to contribute 69.0% to the success of a project. In addition, the results presented in Table 8 also show that safety management CSFs can contribute to safety program implementation with 43.6%.
The impact of teacher’s presence on learning basic surgical tasks with virtual reality headset among medical students
Published in Medical Education Online, 2022
Sofianna Ojala, Joonas Sirola, Timo Nykopp, Heikki Kröger, Henrik Nuutinen
When the teacher was present, the students felt, on average, that they were learning something new with a rating of 7.8 ± 1.8, and when the teacher was not present with a rating of 5.3 ± 2.6; there was a statistically significant difference (p = 0.003) (Table 1). Students felt that VR added value to teaching with a rating of 7.8 ± 1.7 with the teacher present and 5.5 ± 3.0 when the teacher was not present (p = 0.045) (Table 1). The usefulness of the exercise was perceived as good when teacher was present with a rating of 8.3 ± 1.4, but when teacher was not present at the exercise the usefulness was perceived as worse with a rating of 5.3 ± 2.4 (p = 0.001) (Table 1). Usability of the exercise was perceived as the same whether the teacher was present or not with a rating of 6.0–7.3 ± 1.7 (p = 0.060) (Table 1). We also analyzed the effect of presence of the teacher on learning related outcomes (usefulness and usability of the exercise, learned something new, VR added value to teaching) using multivariable analysis of variance (Table 1). The model was adjusted for the covariates listed in Table 1, Basic information. All of the outcome variables were statistically significant. The coefficient of determination (R [2]) was 0.56 for usefulness of the exercise, 0.29 for usability of the exercise, 0.45 for learned something new and 0.36 for VR added value to teaching. Previous use of VR was the only significant covariate for usefulness of the exercise. None of the other covariates showed statistical significance.