Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...
Suppose you fit the multiple regression model y = β0 + β1x1 + β2x2 + ϵ to n = 30 data points and obtain the following result: y ̂=3.4-4.6x_1+2.7x_2+0.93x_3 The estimated standard errors of β ̂_2 and β ̂_3 are 1.86 and .29, respectively. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Ha: β2 ≠0. Use α = .05. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Ha: β3 ≠0. Use α...
b. Suppose ~ Γ(α, β), with α > 0, β > 0 and let Y-eu. Find the probability density function of Y Find EY and var(Y)
Zambia is import-dependent country shows import model is given as Y= β"0"+ β"1" X"1"+β"2" X"2"+ μ where Y is total imports, X1 is GNP and X2 is price Index of imports. For the past twelve months, data has been collected and compiled as in the table below Obs 1 2 3 4 5 6 7 8 9 10 11 12 Y 57 43 73 37 64 48 56 50 39 43 69 60 X1 220 215 250 241 305 258...
5. Given knots a-to <ti<..< tn b, and data points (tiy), for i-0,..., n, prove the clamped cubic spline S satisfying S,(a) , S,(b)-β satisfies C2[a,b] interpolating the data points and satisfying g'(a)-α, g'(b)-β. for all g 5. Given knots a-to
Given the nxn matrices A,B,C of real numbers, which satisfy the Condition: A+B+C+λΑΒ=0 Α+Β+C+λBC=0 A+B+C+λCA=0 for some λ≠0 ∈ R (α) Prove that I+λΑ,Ι+λΒ,Ι+λC are invertible and AB=BC=CA. (b) Prove that A=B=C
Suppose X and Y are independent and Prove the following a) U=X+Y~gamma(α + β,γ) b) V=X/(X + Y ) ∼ beta(α,β) c) U, V independent d) ~gamma(1/2, 1/2) when W~N(0,1) X ~ gammala, y) and Y ~ gamma(6, 7) We were unable to transcribe this image
Prove that the sample mean (y bar) is the minimizer of L(0, B0)
Given that A.B=0 and A+B=1, prove that (10) (A+C).(A’+B).(B+C) =B.C