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However, before we conduct linear regression, we must first make sure that four assumptions are met:. Linear relationship: There exists a linear relationship between the independent variable, x, and the dependent variable, y. In particular, there is no correlation between consecutive residuals in time series data. If one or more of these assumptions are violated, then the results of our linear regression may be unreliable or even misleading.

Logistic regression analysis is a popular and widely used analysis that is similar to linear regression analysis except that the outcome is dichotomous e. The epidemiology module on Regression Analysis provides a brief explanation of the rationale for logistic regression and how it is an extension of multiple linear regression. In essence see page 5 of that module. In essence, we examine the odds of an outcome occurring or not , and by using the natural log of the odds of the outcome as the dependent variable the relationships can be linearized and treated much like multiple linear regression. Simple logistic regression analysis refers to the regression application with one dichotomous outcome and one independent variable; multiple logistic regression analysis applies when there is a single dichotomous outcome and more than one independent variable. Here again we will present the general concept. Hosmer and Lemeshow provide a very detailed description of logistic regression analysis and its applications.

In statistics , simple linear regression is a linear regression model with a single explanatory variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor. It is common to make the additional stipulation that the ordinary least squares OLS method should be used: the accuracy of each predicted value is measured by its squared residual vertical distance between the point of the data set and the fitted line , and the goal is to make the sum of these squared deviations as small as possible. Other regression methods that can be used in place of ordinary least squares include least absolute deviations minimizing the sum of absolute values of residuals and the Theil—Sen estimator which chooses a line whose slope is the median of the slopes determined by pairs of sample points.

In statistical modeling , regression analysis is a set of statistical processes for estimating the relationships between a dependent variable often called the 'outcome variable' and one or more independent variables often called 'predictors', 'covariates', or 'features'. The most common form of regression analysis is linear regression , in which one finds the line or a more complex linear combination that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line or hyperplane that minimizes the sum of squared differences between the true data and that line or hyperplane.

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Great to have some time to digest and make any edits before submission.

Very simple and easy.