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題組內容

Problem 24.(10%) Please answer the following questions briefly

(C) What is the meaning of "Regression to the Mean"? (3%)

其他申論題

(A) Please demonstrate that the regression line will pass the centroid of all observation cases, i.e., , where α̂ and β̂ are the estimated values of α and β respectively by using least squares method., and (X̄, Ȳ) is the centroid of all observation cases. (7%)

(B) Will the situation in ( A ) happen if the constant term α does not exist any more? This is,the simple regression model is formulated as Yᵢ = βXᵢ + εᵢ i = 1,2,....., n. (3%)

(A) What is the meaning of "Degree of Freedom"? (4%)

(B) What is the Nonparametric Statistical Analysis? (3%)

(a) f(x) = for x = 0, 1, 2, 3, 4, 5

(b) f(x) = for x = 0, 1, 2, 3

(c) f(x) = for x = 3, 4, 5, 6

(d) f(x) = for x = 1, 2, 3, 4, 5

(a) Find the value of c that makes f(x, y) a probability density function.

(b) Find the marginal densities f₁(x) and f₂(y)

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