Statistical measures Bivariate regression and correlation

Statistical measures Bivariate regression and correlation

1. Regression

   • Regression analysis is made up of a set of statistical techniques that serve as a basis for making inferences about the possible relationships between quantities in an investigation or study.
     • Simple linear regression: In this linear regression model, the simple term implies that there is only one regressor variable, X, in the model.
     • Simple linear regression assumptions: It is considered of vital importance that the reader knows the assumptions on which the simple linear regression model is supported so that it can be implemented properly. -The response variable Y is a random variable whose values are observed by selecting the values of the variable predictor X -The predictor variable X is not considered a random variable. history, is a variable that takes fixed values. -The observed values of the response variable are not statistics. cally dependent. -Random errors follow a normal distribution with zero mean and standard deviation σ2 -The regression model is linear in the parameters.
     • Coefficient of determination R2: 74% of the variability of y can be attributed to a linear relationship with x

2. Correlation

   • In correlation analysis, numerical measurements are used to quantify the intensity of the linear association between two or more variables.
     • Covariance: The sample covariance between two real random variables x and y.
     • Linear correlation coefficient: The Pearson correlation coefficient between two real random variables X and Y of finite second moments.
     • Coef. Pearson linear correlation r: The Pearson linear correlation coefficient of two variables, r, tell us if the points have a tendency to line up (excluding horizontal and vertical lines).

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