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

In summary, simple linear regression statistics involves proving a linear relation between two variables, y and x, by using a set of experimental data points with error estimates. The regression line can provide an error intercept of the Y-axis, which can be used to determine the confidence for the error estimate. The smaller the error, the better the fit for the linear relation. Other measures, such as ##\chi^2## and visual inspection, can also be used to assess the goodness of fit. Additional resources, such as Kirchner's work and the ReliaWiki website, can provide further insight into analyzing and interpreting regression results.
  • #1
avicenna
84
8
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.
 
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  • #2
Google is your friend.

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

[edit] 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
 
  • #3
BvU said:
Google is your friend.

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

[edit] 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.
 

1. What is the significance of the equation y = kx in statistics?

The equation y = kx is significant in statistics because it represents a linear relationship between two variables, where y is the dependent variable and x is the independent variable. The constant k, also known as the slope, represents the rate of change between the two variables.

2. How is the equation y = kx used to analyze data?

The equation y = kx is used to analyze data by fitting a line to a scatter plot of the data points. The slope of the line, k, can then be calculated to determine the relationship between the two variables. This can help identify patterns and make predictions about the data.

3. What does it mean if the equation y = kx holds for a data set?

If the equation y = kx holds for a data set, it means that there is a strong linear relationship between the two variables being analyzed. This indicates that the data points follow a specific pattern and can be described by a straight line.

4. Can the equation y = kx be used to make predictions about the data?

Yes, the equation y = kx can be used to make predictions about the data. By calculating the slope, k, and plugging in values for x, we can determine the corresponding values for y and make predictions about future data points that may fall on the same linear trend.

5. What are some potential limitations of using the equation y = kx in statistics?

One potential limitation of using the equation y = kx in statistics is that it assumes a linear relationship between the two variables being analyzed. If the relationship is actually non-linear, the equation may not accurately represent the data. Additionally, the equation may not be applicable to all types of data and may not be useful in certain scenarios.

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