Thank you for clarifying the problem.
With N observation pairs I believe I can write b=\frac{N \sum x_i y_i - \sum x_i \sum y_i}{N \sum x_i^2 - (\sum x_i)^2}.
I suppose the propagation of error formula \sigma_f^2=\sum (\frac{\partial f}{\partial x_i} \sigma_{x_i} )^2 is then applied to a...
Finding the Uncertainty of the Slope Parameter of a Linear Regression
Suppose I have measurements x_i \pm \sigma_{xi} and y_i \pm \sigma_{yi} where \sigma is the uncertainty in the measurement. If I use a linear regression to estimate the value of b in y=a+bx, I'm struggling to find a...
I agree with Poley; mathematics is the place to start. Otherwise he might just be memorizing facts without actually understanding the science.
I have attached a link to a mathematics book that I often recommend to motivated high school students. Your son is much younger, but if he is already...
As a material is heated, it increases in temperature until it enters a phase transition. During the transition, added heat does not increase the temperature. As this heat is being added, what is the substance? Is it a mixture of liquid and gas perhaps? If so, what are the proportions?
In...
Thank you for your reply. I was in New York recently and greatly enjoyed all of the urban opportunities, but I do think that I would eventually yearn for more natural surroundings. I will visit Ithaca soon, and I expect a similarly dichotomous perception. In the end, I think that each option has...
I am finishing my final year of high school and would like to obtain an undergraduate education in physics or engineering. I was just accepted into Columbia University, the University of Chicago (which does not offer engineering), and Cornell University and plan to attend one of them. If anyone...