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 Analysis checklist: Linear regression

### Can the relationship between X and Y be graphed as a straight line?

In many experiments the relationship between X and Y is curved, making linear regression inappropriate. It rarely helps to transform the data to force the relationship to be linear. Better, use nonlinear curve fitting.

### Is the scatter of data around the line Gaussian (at least approximately)?

Linear regression analysis assumes that the scatter of data around the best-fit line is Gaussian.

### Is the variability the same everywhere?

Linear regression assumes that scatter of points around the best-fit line has the same standard deviation all along the curve. The assumption is violated if the points with high or low X values tend to be further from the best-fit line. The assumption that the standard deviation is the same everywhere is termed homoscedasticity. (If the scatter goes up as Y goes up, you need to perform a weighted regression. Prism can't do this via the linear regression analysis. Instead, use nonlinear regression but choose to fit to a straight-line model.

### Do you know the X values precisely?

The linear regression model assumes that X values are exactly correct, and that experimental error or biological variability only affects the Y values. This is rarely the case, but it is sufficient to assume that any imprecision in measuring X is very small compared to the variability in Y.

### Are the data points independent?

Whether one point is above or below the line is a matter of chance, and does not influence whether another point is above or below the line.

### Are the X and Y values intertwined?

If the value of X is used to calculate Y (or the value of Y is used to calculate X) then linear regression calculations are invalid. One example is a Scatchard plot, where the Y value (bound/free) is calculated from the X value. Another example would be a graph of midterm exam scores (X) vs. total course grades(Y). Since the midterm exam score is a component of the total course grade, linear regression is not valid for these data.