9. Which of the following is true about the difference between bivariate regression and multiple regression analysis?

Select one:

a. Multiple regression analysis involves multiple predictor variables that predict a single outcome (criterion) variable, whereas bivariate regression analysis involves a single predictor variable that predicts a single outcome (criterion) variable.

b. Multiple regression analysis involves multiple predictor variables that predict multiple outcome (criterion) variables, whereas bivariate regression analysis involves a single predictor variable that predicts multiple outcome (criterion) variables.

c. Multiple regression analysis involves a single predictor variable that predicts a single outcome (criterion) variable, whereas bivariate regression analysis involves multiple predictor variables that predict a single outcome (criterion) variable.

d. Multiple regression analysis involves a single predictor variable that predicts multiple outcome (criterion) variables, whereas bivariate regression analysis involves multiple predictor variables that predict a single outcome (criterion) variable.

1. (a) Explain what is meant by the transition probability matrix of a homogeneous Markov chain. [5 marks] (b) Explain what is meant by the stationary distribution of a Markov chain? [5 marks] (c) A Markov chain has transition probability matrix, A, with entries ay, and stationary distribution . Write down an expression for the entries of the reverse Markov chain. [5 marks (d) Consider the following transition probability matrix of a homogo- neous Markov chain, with three states i,j and & (the TPM is in that order). If the stationary vector of the chain is (1/9, 2/9, 2/3), determine whether the Markov chain is reversible. 1 Ik 1- /0.2 0.2 0.6 0.1 0.6 0.3 K 0.1 0.1 0.8 [5 marks] (e) Let X1, X2, X, be a sequence of random variables resulting from the above Markov chain. If X = i and Xy = j what is the probability that X2 = k? [5 marks]Q.4 [12 marks] Give examples for Markov chains with the following properties. (a) The Markov chain has a state which is both transient and essential. [3 marks] (b) The Markov chain has a state which is null recurrent and aperiodic. [3 marks (c) The Markov chain has a stationary but not a limiting distribution? [3 marks] (d) The Markov chain has a stationary distribution which is not unique. 3 marks]15 15 Short-term decision making differs from long-term decision making because: Short-term decision making assumes that variable costs are fixed. Short-term decision making assumes selling prices are fixed. Short-term decision making assumes capacity is fixed. Short-term decision making assumes the accounting data is fixed. 12 7 16