To check that linear regression is an appropriate analysis for these data, ask yourself these questions.

Question

Discussion

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. Either transform the data, or use a program (such as GraphPad Prism) that can perform nonlinear curve fitting.

Is the scatter of data around the line Gaussian (at least approximately)? Linear regression analysis assumes that the scatter 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.

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. See Avoid Scatchard, Lineweaver-Burk and similar transforms 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.

Ask this in the mathematics section.