# I Statistics proof: y = k x holds for a data set

#### avicenna

Simple linear regression statistics:

If I have a linear relation (or wish to prove such a relation): y = k x where k = constant. I have a set of n experimental data points ...(y0, x0), (y1, x1)... measured with some error estimates.

Is there some way to present how well the n data points shows that the relation: y = kx is proven. What I have in mind is that the regression line will give an error intercept of the Y-axis, say e. Say e = 1.0 x 10^-5. What is the "confidence" for this error estimate.

I want to show error e to be very small say <1.0 10^-7. If I the measurement errors of (yi,xi) ... are very small, how will it help to show y=kx to be "very good" where y=k(1+e)x where e is very small.

#### BvU

Homework Helper

I learned about $\chi^2$ as a measure of goodness of fit. But that was long ago...

 by the way, a visual inspection of the resluts (with error bars) is also a very good idea. Make sure all systematic errors are omitted when drawing the error baars

#### avicenna

I learned about $\chi^2$ as a measure of goodness of fit. But that was long ago...

 by the way, a visual inspection of the resluts (with error bars) is also a very good idea. Make sure all systematic errors are omitted when drawing the error baars
Thanks. I think I now have some idea of what I really wanted. It is not simple straightforward as I thought.

Homework Helper

BvU

### Want to reply to this thread?

"Statistics proof: y = k x holds for a data set"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving