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Multiple Linear Regression
Published in Marcello Pagano, Kimberlee Gauvreau, Heather Mattie, Principles of Biostatistics, 2022
Marcello Pagano, Kimberlee Gauvreau, Heather Mattie
In the preceding chapter, we see how simple linear regression can be used to explore the nature of the relationship between two continuous random variables. In particular, it allows us to predict the value of a response or outcome that corresponds to a given value of an explanatory variable. If knowing the value of a single explanatory variable improves our ability to predict the response, however, we might suspect that additional explanatory variables could be used to our advantage. To investigate the more complicated relationship among a number of different variables, we use a natural extension of simple linear regression known as multiple linear regression, or multivariable linear regression.
Linear regression
Published in Ewen Harrison, Pius Riinu, R for Health Data Science, 2020
The last important concept to mention here is confounding. Confounding is a situation in which the association between an explanatory variable (exposure) and outcome (dependent variable) is distorted by the presence of another explanatory variable.
Statistics for Genomics
Published in Altuna Akalin, Computational Genomics with R, 2020
Often, we would like to test the null hypothesis if a coefficient is equal to zero or not. For simple regression, this could mean if there is a relationship between the explanatory variable and the response variable. We would calculate the t-score as follows , and compare it to the t-distribution with to get the p-value.
Joint regression modeling of location and scale parameters of the skew t distribution with application in soil chemistry data
Published in Journal of Applied Statistics, 2022
F. Prataviera, A. M. Batista, P. L. Libardi, G. M. Cordeiro, E. M. M. Ortega
In many practical applications, the response variables are affected by explanatory variables. In the presence of explanatory variables with linear effects, parametric models are widely used and tend to give more precise estimates of the quantities of interest when give good fits. Several regressions have been proposed in the literature by considering the class of location models. For example, [30] extended the beta regression by considering a systematic component for the precision parameter, [22] developed a heteroscedastic nonlinear regression under scale mixtures of SN distributions, [27] introduced the log-beta generalized half-normal geometric regression for censored data, [10] presented the log-generalized Weibull-log-logistic regression for predicting longevity of the mediterranean fruit fly, and [26] introduced a new class of heteroscedastic log-exponentiated Weibull regressions.
Population-Based Projection of Vision-Related Disability in Australia 2020 – 2060: Prevalence, Causes, Associated Factors and Demand for Orientation and Mobility Services
Published in Ophthalmic Epidemiology, 2021
Kuo-yi Jade Chang, Kris Rogers, Thomas Lung, Sophy Shih, Jessie Huang-Lung, Lisa Keay
Logistic regression analyses were performed to examine the associations between various explanatory variables (socio-demographic factors and long-term health conditions) and the dichotomized outcome variables (vision-related disability, self-reported cataracts, macular degeneration, and glaucoma). The major explanatory variable (study factor) selected was age, which was kept as a covariate in all regression models. Other explanatory variables (potential confounders) were selected because they were either a) the demographic factors associated with vision health reported by the previous studies (e.g., sex,12–15 marital status,16,17 education,15,16 employment,17 income15 etc.), b) the main causes of sight loss reported by the participants in 2015 SDAC (e.g., head injuries, stroke, diabetes), and c) the most common long-term health conditions identified in the 2015 SDAC results (e.g., hypertension, back pain, dementia etc.).
Effects of work arrangements on the sleep regimen of creative research and development employees
Published in International Journal of Occupational Safety and Ergonomics, 2020
Aaro Hazak, Erve Sõõru, Heili Hein, Kadri Männasoo
The questionnaire included a total of 90 questions addressing various aspects of the organization of work, work results, sleepiness, sleep patterns, tiredness, health as well as socio-demographic information. A 5-point Likert-type scale is used to gain a response to the question ‘To what extent do you feel that your work is limiting or has limited your sleep regimen?’ (sleeplim) and this is used as the dependent variable in the models presented in this article. Explanatory variables have been selected based on our research hypotheses and extant literature. One of these is the score on the reduced morningness–eveningness questionnaire (rMEQ) by Adan and Almirall [22]. Ordered categories of employee-reported sleeping hours have been incorporated as a further explanatory variable. Other independent variables reflect different aspects of work arrangements and job satisfaction. Age, gender, number of family members and education are the main control variables for individual socio-demographic characteristics in the models. The health factor represents the respondent’s general health condition based on a set of survey questions. Refer to Table 1 for a detailed overview of the model variables and description of the subjects, and to Figure 1 for histograms of some key model variables.