4. What is unbiasedness? Let X1, X2,..., X, be a random sample from b(1,p). Then show that T = m(m-1) n(n-1) is an unbiased estimator of 7(p) = p², where m =ΣX.

Suppose that you are given a decision situation with three possible states of nature: s1, s2, and s3. The prior probabilities are P(s1) = 0.2, P(s2) = 0.5, and P(s3) = 0.3. With sample information I, P(I|s1) = 0.1, P(I|s2) = 0.05, and P(I|s3) = 0.2. Compute the revised (or posterior) probabilities: P(s1|I), P(s2|I), and P(s3|I).

Consider a Poisson distribution with . Write the appropriate Poisson probability mass function. Compute f(2). Compute f(1). Compute .

Consider the generalised linear regression model: y = Xẞ + e, with E[e] = 0 and E[ee] = 022. Let the model be estimated using both OLS and GLS, and let the OLS estimator of ẞ be denoted as BOLS and its GLS estimator as BGLS. Which of the following statements are incorrect about the OLS and GLS estimators? (a) BOLS is BLUE (b) BGLS is BLUE (c) The variance of BOLS cannot be less than that of BGLS (d) BGLS is more efficient that BOLS

An F test Extrapolation is used to test the hypothesis that the values of the regression parameters Bo, B₁, B2, ... Bq are all zero. The least squares method A t test

If there is positive correlation between two sets of numbers, then _______. Group of answer choices r = 0 r < 0 r > 0 SSE=1 MSE = 1

The regression analysis is normally depicted as "y = Ax+ B." What does "A" indicate in the equation? A) It is the expected change in the independent variable for a one-unit change in the dependent variable OB) It is the significance level for the test OC) It is the expected change in the dependent variable for a one-unit change in the independent variable OD) The confidence interval

Consider the following set of dependent and independent variables. Complete parts a through c below. y 9 11 D 15 15 21 24 28 32 X1 2 6 6 8 6 11 15 20 X2 16 10 14 11 3 8 7 4 a. Using technology, construct a regression model using both independent variables. y= (15.3952) + (1.0092) x₁ + (-0.5869)x2 (Round to four decimal places as needed.) b. Test the significance of each independent variable using α = 0.05. Test the significance of x₁. Identify the null and alternative hypotheses. Ho B₁ = H₁ B₁ 0 0 (Type integers or decimals.) Calculate the appropriate test statistic. The test statistic is 4.20 (Round to two decimal places as needed.) Determine the appropriate critical value(s) for α = 0.05. The critical value(s) is (are) ☐ (Round to two decimal places as needed. Use a comma to separate answers as needed.)

(i) (a) Find the value L(32) of the Lagrange polynomial at 32 and the relative error in the approximation of f(32) by L(32). (b) Show your work by filling in the standard table for the method showing the process of evaluation of the Lagrange polynomial at the given point: Ik Uk La(z) VkLk(2) (c) Accordingly. L(32)= and the relative error in question is given by RE(f(32) L(32)) = (ii) Find the value L(38) of the Lagrange polynomial at 38 and the relative error in the approximation of f(38) by L(38). Proceed then as in the previous part by filling in the standard table Ik Uk LA(z) UkLk(2) and by providing the required values: L(38) RE(f(38) L(38))=

Consider the following set of dependent and independent variables. Complete parts a through c below. y 10 11 15 15 21 24 27 32 X1 2 6 6 8 6 11 17 21 X2 17 9 13 10 3 8 6 4 a. Using technology, construct a regression model using both independent variables. = + + (Round to four decimal places as needed.)