Question #52693

Yi = B1 + B2Xi + ui
a) What does ui represent?
b) What is the expected value of the ui's and what is their probability distribution?
c) What does an "unbiased" estimator mean?
d) Why are the coefficients of a Sample Regression Function considered random variables?
e) Write the formula for the Variance of a regression coefficient and comment on how the various components of the equation influences the magnitude of the variance.
can you give me the example?

Expert's answer

Yi = B1 + B2Xi + ui

a) ui represents random variable.

b) The expected value of a random variable is intuitively the long-run average value of repetitions of the experiment it represents.

c) unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value.

d) The coefficients of a Sample Regression Function are considered to be random variables, because their value is subject to variations due to chance.

e) Variance measures how far a set of numbers is spread out. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data points are very spread out around the mean and from each other.

a) ui represents random variable.

b) The expected value of a random variable is intuitively the long-run average value of repetitions of the experiment it represents.

c) unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the calculation equals the true value.

d) The coefficients of a Sample Regression Function are considered to be random variables, because their value is subject to variations due to chance.

e) Variance measures how far a set of numbers is spread out. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data points are very spread out around the mean and from each other.

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