Consider a regression study involing a dependent variable y, and quantitative independent variable , and a categorical independent variable with three possible levels (level 1, level 2, and level 3).
a. How many dummy variables are required to represent the categorical variable?
b. Write a multiple regression equation relating and the categorical variable to y.
Consider a regression study involing a dependent variable y, and quantitative independent variable , and a categorical independent variable with three possible levels (level 1, level 2, and level 3).
a. How many dummy variables are required to represent the categorical variable?
b. Write a multiple regression equation relating and the categorical variable to y.
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You are given a fair die, i.e. the outcomes of any throw are contained in the sample space Let the event A be that an even number is thrown and the event B that a multiple of three is thrown. Now consider the two random variables X and Y. X takes on a value of 1 if the event A has occurred and the value 0 if A has not occurred. The random variable Y takes on the value of 1 if the event B has occurred and the value zero if B has not occurred.
(a) Derive the joint pdf of X and Y. Provide this in the form of a table
Y=0 Y=1
X=0 | ||
X=1 |
b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?