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How do you find the conditional variance?
Conditional Variance: Similar to the conditional expectation, we can define the conditional variance of X, Var(X|Y=y), which is the variance of X in the conditional space where we know Y=y. If we let μX|Y(y)=E[X|Y=y], then Var(X|Y=y)=E[(X−μX|Y(y))2|Y=y]=∑xi∈RX(xi−μX|Y(y))2PX|Y(xi)=E[X2|Y=y]−μX|Y(y)2.
What is conditional variance in statistics?
In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function.
Which is the best definition of conditional variance?
Jump to navigation Jump to search. In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables.
How to do a linear regression with constant variance?
Linear regression model with constant variance: E (Y|X = x) = µ Y|X=x = a+bx (population regression line) var(Y|X = x) = σ2 Y|X=x = σ 2 The population regression line connects the conditional means of the response variable for fixed values of the explanatory variable. This population regression line tells how the mean response of Y varies with X.
Which is the best interpretation of the definition of variance?
Thus, one interpretation of variance is that it gives the smallest possible expected squared prediction error. If we have the knowledge of another random variable ( X) that we can use to predict Y, we can potentially use this knowledge to reduce the expected squared error.
When do you use conditioning on a random variable?
Conditioning on discrete random variables. When X takes on countable many values with positive probability, i.e., it is a discrete random variable, we can introduce , the conditional variance of Y given that X=x for any x from S as follows: where recall that is the conditional expectation of Z given that X=x,…