ith leverage value (hat-value) = (H)ii= hii, ith diagnal entry of hat matrix• The h¡¡ is considered to be large ifhii > 2 * h = 2 *k + 1 = # of parameters,k + 1nn = # of sample,where Ehii = k+1h = average of diagonal entry. 2. Using the linear model ofy = Bo + B12 +€,a researcher calculated the hat-matrix H and the residual e using 6 observations.H = X(X'X)-¹X' =[0.2516 0.1101 0.3931 0.0534 0.1101 0.08180.1101 0.2044 0.0157 0.2421 0.2044 0.22330.3931 0.1572 0.7704 -0.1352 0.0157 -0.05970.0535 0.2421 -0.1352 0.3176 0.2421 0.22330.1101 0.2044 0.0157 0.2421 0.2044 0.223270.2233 0.25160.0818 0.2232 -0.0597 0.2799(c)ut σ. That is,(b) Identify observations with large leverage value.identify usta vatiCONS1 12e =-0.02]0.12-0.560.88-0.01-0.07

The leverage values are given as the diagonal elements of hat matrix H, as:hii = {0.2516, 0.2044,…

Answered: 2. Using the linear model of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 7 18 9 26 23 Compute b0 and b1 (to 1 decimal).b1 b0 Complete the estimated regression equation (to 1 decimal).^y = + x Use the estimated regression equation to predict the value of y when x = 6 (to 1 decimal).^y =
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
Suppose I estimate the following regression models with BP test p-values: == Y₁ =α0+α1Xi+ei Y₁ = ßo + B₁Xi + ß2X ² + vi pval = 0.76 p val = 0.056 pval = 0.00013 Y₁ = 00 + 01Xi + 02X² +03X3 + Zi At the 5% level, which functional form(s) seem(s) appropriate to describe the relationship between Yi and Xi. (a) Form (1) only (b) Form (3) only (c) Form (1) and (2) only (d) Form (1) and (3) only (e) Form (1), (2) and (3) (1)
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e

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