The Null Hypothesis That The Overall Slope Is Zero

616 Words2 Pages

The given reports the P value testing the null hypothesis that the overall slope is zero,

the best fit value of the slope is 0.00. The P value answers the question: If the true slope is zero, what is the chance that the slope will be further from zero than the observed slope due only to random sampling. Since the observed slope is zero, there is almost a 100% chance of obtaining a slope that is further than zero than observed! So the P value is greater than 0.99, as high as a P value can be. Some people are confused and think the P value should be small purely because the points for a pattern. Not so. The P value, from conventional linear regression fitting both slope and intercept, will be small only when the points form a linear pattern that is not horizontal. …show more content…

To make the line go through the origin and also go near the points, the best-fit line has a slope is far from zero. Since the line is far from horizontal, the P value is tiny. Given the constraint that the line must go through the origin (X=0, Y=0; lower-left of graph), the data are quite convincing that best fit line is far from horizontal, so it makes sense that the P value is tiny.

Constraining a line to go through the origin (or some other point) can be very useful in some situations. Usually this option is used to fit calibration curves used for interpolation, in which case the P value is not useful. If you force the line through the origin, be very wary when interpreting the P value. It is rarely useful, and easy to misinterpret.

The given reports the P value testing the null hypothesis that the overall slope is

Open Document