Linear Regression

Question 1

if each experimental measurement obeys
Yi = β0 + β1 xi + εi
what are the conditions?

Answer 1

linear relationship between yi and xi values
experimental errors in x values negligible
experimental errors (represented by εi) in y values have a normal distribution with zero mean and constant variance

Question 2

what is the best fit line for a sample?

Answer 2

y = b0 + b1 x
where b0 and b1 is the MEASURED intercept and gradient
these are estimates obtained from the sample for β0 and β1

Question 3

what is the coefficient of determination? how is it found?

Answer 3

r^2 where r is the correlation coefficient (in DB)
it is a measure of linear correlation, always between 0-1