CORRELATION and SIMPLE REGRESSION for QUANTITATIVE VARIABLES - Introduction
CORRECTION:
1) At time 19:56 we write Derivatives Y' and Y''. It is correct to say that in the optimization process, we have to find the derivatives Yc' and Yc" (an analogy to the method of Minimizing and/or Maximizing a Function of a Variable F(x) = z... that is, for the Model Simple Regression with Just Two Random Variables X and Y.
It is important to point out that Our Variables in the Optimization process are the θi, that is, a function f(θ1, θ2, θ3) if, for example f(θ1, θ2, θ3) = θ1X²+θ2X+θ2. The same happens in the Multiple Regression Model that is MORE than Two Variables X, Y Z and etc... we will have the same Variables the θi and even so we will have to determine the Partial Derivatives in relation to the θi in the optimization process, that is, find the Hessian Matrix to characterize the Critical Points of the function f=Yc.)
2) At 23:08 we briefly said that the Natural Logarithm of Zero is One. The correct one is Natural Logarithm of One is Zero (Ln 1 = 0).
3) We say that the Ɵi are the parameters of the Functions that best fit the pairs of points plotted in the Scatter Diagram, for example, Yc = Ɵ1 + Ɵ2 equation of a line the Ɵ1 and Ɵ2 need to be found through the Least Squares Criterion . It is important to emphasize that the term “Parameter” refers to the Population, for example, the Mean µ and the corresponding Statistic is X ̅ (Mean) is from the Sample... What is intended in this different context is to Estimate these Parameters (Statistical Inference ). Thus, in the absence of another term for the Ɵi, we will call them parameters.
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