Whenever there is a change in X, such change must translate to a change in Y. When using regression analysis, we want to predict the value of Y, provided we have the value of X.īut to have a regression, Y must depend on X in some way. Y is the variable we are trying to predict and is called the dependent variable. The easiest regression model is the simple linear regression: Y is a function of the X variables, and the regression model is a linear approximation of this function. There is a dependent variable, labeled Y, being predicted, and independent variables, labeled x1, x2, and so forth.
In the same way, the amount of time you spend reading our tutorials is affected by your motivation to learn additional statistical methods. “The amount of money you spend depends on the amount of money you earn.” Therefore, it is easy to see why regressions are a must for data science. Moreover, the fundamentals of regression analysis are used in machine learning. And it becomes extremely powerful when combined with techniques like factor analysis. There are also many academic papers based on it. It is applied whenever we have a causal relationship between variables.Ī large portion of the predictive modeling that occurs in practice is carried out through regression analysis. There is no meaningful interpretation for the correlation coefficient as there is for the \(R^2\) value.Regression analysis is one of the most widely used methods for prediction. Know what various correlation coefficient values mean.Know how to calculate the correlation coefficient r from the \(R^2\) value.
Understand the cautions necessary in using the \(R^2\) value as a way of assessing the strength of the linear association.Know how to interpret the \(R^2\) value.That is, they can be 0 even if there is a perfect nonlinear association.
Know that the coefficient of determination (\(R^2\)) and the correlation coefficient (r) are measures of linear association.Interpret the intercept \(b_\) from Minitab's fitted line plot and regression analysis output.Understand the concept of the least squares criterion.Distinguish between a deterministic relationship and a statistical relationship.Upon completion of this lesson, you should be able to: