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i am given data for analysis following data:relationship between height and weight,question is :is relationship between them linear?like $y$=$a$+$b$*$x$+$e$ where e is error,or quadratic?or cubic?data is following(y denoted height, x-weight)

y   x
170 65
167 55
189 85
175 70
166 55
174 55
169 69
170 58
184 74
161 56
170 75
182 68
167 51
187 85
178 62
173 60
172 68
178 55
175 65
176 70

i have calculated a and b and get following result

y=139.6155237+0.5308912572*x

i dont know how to calculate e?or what me result means?please help me how to find e and how to check correctness of my work

EDITED:
i have edited my work,i am sure it is correct,what  now should i do?
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  • $\begingroup$ Is this only part of your data? $\endgroup$
    – Julius
    Commented Apr 10, 2012 at 16:29
  • $\begingroup$ not but others are like gender,age and BMI $\endgroup$ Commented Apr 10, 2012 at 16:33
  • $\begingroup$ Yes, coefficients are correct now. What is your task? To estimate the model and find residuals? $\endgroup$
    – Julius
    Commented Apr 10, 2012 at 17:31
  • $\begingroup$ yes exactly,i have put x variable but have not got exact y value,so is it not linear yes? $\endgroup$ Commented Apr 10, 2012 at 17:32
  • $\begingroup$ That is fine, your model can't be perfect. The difference that you get is residual (-4.12 first data point, -1.81 second etc.). Again, try to plot your data. It is hard to tell whether the relationship is linear, there are too few observations, but linear model, in my opinion, is the best choice here. $\endgroup$
    – Julius
    Commented Apr 10, 2012 at 17:38

1 Answer 1

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First you fit the data with your expectation model: $y=a+bx$

Then you compute pertuberations of data points around the model curve (line). Analysis of this will give you variance in data points (the error). The least squares approach expects the errors are distributed normally, so that the errors should be samples drawn from gaussian distribution.

Your (least squares) estimator have two properties: precision and accuracy. I think the precision is what you want to compute. Accuracy is about bias, and this is harder to grasp (e.g. all weights are slighly bigger because of uncalibrated measurement device).

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