Let Y Z3+ e denote the standard form of the multivariate regressionmodel where Y is a matrix of n observations on m dependent variables, Zis the nx (r + 1) design matrix, 3 is the matrix of regression coefficientsand denotes the error matrix. Let Σ denote the m x m covariancematrix of any row of € and assume the rows are independent. The leastsquare estimate for 3 is 3 (Z'Z)-¹Z'Y. The projection matrix isH = Z(Z'Z)-¹Z'. Let the ith column of 3 be denoted by 3, and thei, jth element of Σ by oij. Define the sample covariance matrix of theresiduals byProveΣ=1n-p-1(c) E(ê) = 0(d) cov(ei, k) = Oik (I-H)

Given the standard form of multivariate regression model as Y=Zβ+ε β^=Z'Z-1Z'Y H=ZZ'Z-1Z'

Answered: Let Y = Z3+ € denote the standard form…

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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The following table gives the experience (in years) and the number of computers sold during the previous three months by seven salespersons.Experience ( years)4129610167Computer sold {unit)194228313935211) Determine both dependent and independent variables, and explain the expected relationship between them.2) Calculate the correlation coefficient and the determinant coefficient. Explain what they mean.3) Estimates the simple regression model and comment on the estimated coefficients.4) Predict the number of computers sold during the past three months by salespersons with eleven years of experience.
Can you answer the questions in 3b, 3c, and 3d? Thank you
The regression linear model between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to" 1.364x+1.955 1.364x+3.125 1.955x+1.364 1.25x+2 2x+1.25 correct option?
Consider the one-variable regression model Yi = β0 + β1Xi + ui and suppose that it satisfies the least squares assumptions .The regressor Xi is missing, but data on a related variable, Zi, are available, and the value of Xi is estimated usingX ̃i = E(Xi | Zi). Let wi = X ̃ i - Xi.a. Show that X ̃i is the minimum mean square error estimator of Xi using Zi. That is, let X^i = g(Zi) be some other guess of Xi based on Zi, and show that E[(X^i - Xi)2] ≥ E[(X ̃i - Xi)2].b. Show that E(wi | X ̃i) = 0.c. Suppose that E(ui | Zi) = 0 and that X ̃i is used as the regressor in place of Xi. Show that β^1 is consistent. Is β^0 consistent?
Suppose you want to test whether X2 and X3 can jointly explain Y in the following regression model: Y = Bo + B1X1 + B,X2 + B3X3 + u You obtain data for 85 observations and conduct a joint test of significance at 1% level. Your restricted model is given by, OY = Bo + B3X3 +u OY = Bo + B1X1 + B3 X3 + u OY = Bo + B1X1 + u OY = Bo + u
Each of 25 teenage girls with one brother was asked to provide her own height (y), in inches, and the height (x), in inches, of her brother. The scatterplot below displays the results. Only 22 of the 25 pairs are distinguishable because some of the (x,y) pairs were the same. The equation of the least-squares regression line is ŷ = 35.1 + 0.427x.*Girls are on the y-axis and brothers are on the x-axis* a.) Draw the least-squares regression line on the scatterplot above. b.) One brother’s height was x = 67 inches and his sister’s height was y = 61 inches. Circle the point on the scatterplot above that represents this pair and draw the segment on the scatterplot that corresponds to the residual for it. Give a numerical for the residual. c.) Suppose the point x = 84 , y = 71 is added to the data set. Would the slope of the least squares regression line increase, decrease, or remain about the same?Explain. Would the correlation increase, decrease, or remain about the same? Explain.
(Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y . Suppose that X1 and X2 are uncorrelated. You estimate β1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias? Explain.
Derive the least squares estimators (LSEs) of the parameters in the simple linear regression model.
Consider the linear model y=B,+B,x,+B,x,,+B,x+B,+u, You estimate the model y =B,+B,x,+B,x, observations and obtain the OLS residuals . You then estimate the auxiliary regression +u based on 123 31 3" 3i 41 The LM statistic +1 4/ you obtain to test the null hypothesis that H:B,=B,=0 is 20.91. What is the R2 of the auxiliary regression? It is not possible to say O 0.17 O 0.175714 0.177203
Suppose the PRF of two-variable regression is represented in the equation (1) Y₁ =b₁ + b₁X₁ + u₁, u~i.i.d N(0,0²) (1) We use Ordinary Least Square (OLS) method to estimate the coefficients in (1), The OLS estimated SRF is represented in the equation (2) Y₁ =B₁ + B₁X₁ + e, (2) In which , and B, are OLS estimates of b, and b, respectively. (2) Prove Σe, = 0 (3) Prove Sex = 0
11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2. a) Complete the ANOVA table. b) Find the t-stat of the co-efficient of X c) Find the co-efficient of X.
(Find the least-squares regression line y = bo + bịx through the points (-2, 1), (0, 9), (4, 15), (7, 20), (10, 26), and then use it to find point estimates ŷ corresponding to x = 2 and x = 10. %3D %3D

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