The Simple linear regressions Are specific cases that apply only if the data follows a logic Y = AX + B. But in many cases, we can have nonlinear relationships that mathematically describe.
In this type of case, it is necessary, depending on the type of relationship, to linearize the data X and/or Y.
1. Visually identify the type of relationship
First step if we think the regression is nonlinear, visually identify the type of relationship a priori. For this, we build the cloud of points, then we search among one of the 3 models below the one that best fits our situation:
2. Linearize the data
In this case we transform the data Y. We calculate ln (y) and trace the cloud of Point ln (y) according to X. If our choice is right, the dots form a right.
In this case only the data of X is transformed. We compute ln (x) and trace the cloud of Point Ln (x) according to Y. If our choice is good the dots form a straight.
In this case the X and Y data are transformed. We compute ln (x) and ln (y) and then trace the cloud of Point Ln (x) according to ln (y). If our choice is good the dots form a straight.
3. Calculate the linear regression line
Since our data is now linear, we calculate the right of Linear regression Associated Y = A * X + B.
4. Deduce the correlation formula
Having modified the initial data, we will have to do the reverse approach to find the model corresponding to our real situation:
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