Explanation
Regression is the process of using several inputs to produce one or more outputs. For example The input might be the income, education and current debt of a customer The output might be the probability, expressed as a percent that the customer will default on a loan. Contrast this to classification where the output is not a number, but a class.

Explanation
R square can be made high, it means when we add more variables R-square will increase. And R-square will never decreases if you add more independent variables. Higher R square value can have lower the residuals.

Explanation
Given two random variables X and Y whose joint distribution is known, the marginal distribution of X is simply the probability distribution of X averaging over information about Y.
It is the probability distribution of X when the value of Y is not known. This is typically calculated by summing or integrating the joint probability distribution over Y. ' For discrete random variables, the marginal probability mass function can be written as Pr(X = x). This is Text Description automatically generated with low confidence

where Pr(X = x,Y = y) is the joint distribution of X and Y, while Pr(X = x|Y = y) is the conditional distribution of X given Y In this case, the variable Y has been marginalized out.
Bivariate marginal and joint probabilities for discrete random variables are often displayed as two-way tables.
Similarly for continuous random variables, the marginal probability density function can be written as pX(x). This is Diagram Description automatically generated with medium confidence

where pX.Y(x.y) gives the joint distribution of X and Y while pX|Y(x|y) gives the conditional distribution for X given Y Again: the variable Y has been marginalized out.
Note that a marginal probability can always be written as an expected value:
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Intuitively, the marginal probability of X is computed by examining the conditional probability of X given a particular value of Y, and then averaging this conditional probability over the distribution of all values of Y This follows from the definition of expected value, i.e. in general A picture containing diagram Description automatically generated