Reference no: EM132857110

Suppose we have a coin that has a θ probability of Heads. We don't know the parameter θ, but we assume its prior distribution is θ ∼ Uniform{0.25,0.5,0.75} (this is a discrete uniform distribution, placing equal probability on each value in the finite list). The data we observe is X, the outcome of a single flip of the coin, with X = 1 for Heads and X = 0 for Tails.

(a) Write down a hierarchical model for the data X.

(b) Compute P(X = 1).

(c) What is the posterior distribution of the parameter θ (i.e., the conditional distribution of θ | X)?

(d) Suppose we observe X = 1. Now we will flip the same coin again, to obtain a new outcome Y .

Conditional on what we've observed so far, what is the probability that Y = 1?

1. Evaluate the tolerance statistics. Is multicollinearity a problem?

2. What variables create the model to predict Ingdp? What statistic support your response?

3. Is the model significant in predicting Ingdp? Explain.

4. What percentage of variance in Ingdp is explained by the model?

5. Write the regression equation.

6. What are the result statements?