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When the simple regression equation y, = B1 + B2x, +U,, t=1,2,
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When the simple regression equation y, = B1 + B2x, +U,, t=1,2,...,I is written in matrix notation, the OLS estimator is $=(XX)" Xy. Then: Select one: O O O A. XX has dimension Tx T and its inverse can not always be found. B. X'y has dimension 2 x 1 C. X'y has dimension I x 1 D. B^ has dimension 1 x 1 i.e. it is a scalar E. XX has dimension 2 x 2 and its inverse can always be found. O
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The random variable X takes on the value of 1 if the return on a portfolio of bonds has risen and the value of zero if the return on the bond portfolio has fallen. The random variable Y takes on the value of 1 if the return on a portfolio of equities has risen and the value of zero if the return on the equity portfolio has fallen. The joint probability density function of the random variables X and Y is given in the following table: X=0 Probabilities Y=0 Y=1 0.15 X=1 0.31 0.41 0.13 What is the conditional probability that the return on the portfolio of equities fell given that the return on the portfolio of bonds was seen to rise? i.e. Calculate P(Y=0|X=1) Select one: A. 0.2232 B. 0.3100 C. 0.4306 D. 0.6739 E. 0.3312
Expert Solution
the first option A is the correct option.
because X=[x1, x2,........................,xt] hence X'X will be of TXT dimension.
its inverse can only be found when we can find detX is non zero.
because inverese of X'X=adj X/ det X hence det x can only be found when all x variables are linearly independent.
Hence option A is the correct option.
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