Q1.Consider the following cross-sectional population regression model relating thedependent variable Y, and regressor X, :Y, = Bo + BIXI + u, wherei = 1,..,n, and X, = Y, + Z..Assume that Cov(Z,u) 0.(a) Explain why X, is an endogenous regressor.(b) Show that Z, is a relevant instrument for X;.%3D

Given Yi=β0+β1Xi+ui Find Part a,b

Answered: Q1. Consider the following…

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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2. Consider the simple linear regression Yi = Bo + B1r, +E, (a) Derive the weighted least squares estimators for 30 and B1. (b) Express the weighted least squares estimator for B1 in terms of the centered variables y; - G and z; – Fu, where ỹu, and E, are the weighted means.
For observed data y=(y1,…,yn)y=(y1,…,yn) with n=21n=21, the above linear regression model was fitted in R, with the following output: >n = 21 >xi = seq(0, n-1,1)/(n-1) >p1 =2*xi-1 >p2 =6*xi^2- 6*xi+1-1/(n-1) > summary(lm(y ~ p1+p2)) Call: lm(formula = y ~ p1 + p2) Residuals: Min 1Q Median 3Q Max -0.5258 -0.2153 0.0813 0.1770 0.4669 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.004238 0.063450 -0.067 0.947 p1 1.181260 0.104784 11.273 1.37e-09 *** p2 -0.953388 0.129422 -7.366 7.77e-07 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.2908 on 18 degrees of freedom Multiple R-squared: 0.9097, Adjusted R-squared: 0.8997 F-statistic: 90.68 on 2 and 18 DF, p-value: 3.989e-10 Write this linear regression model in the vector form and answer the following questions, using the above R output where necessary.
1. Data was collected on 82 vehicles of different models to study the relationship between the weight of a vehicle (wt) and the miles per gallon (mpg) of the vehicle. The output from a regression analysis of the data is attached to the end of the sheet. a)Use the estimated linear regression model for predicting miles per gallon from weight to predict the miles per gallon for a vehicle with a weight of 40. b)Given that the mean weight of vehicles in the sample was 30.9, and that the corrected sum of squares (Sxx ) for weight was 5369., compute an interval estimate of the miles per gallon for an individual vehicle with a weight of 40. c) Here is a listing for a subset of the vehicle data: mpg wt 40.9 22.5 38.4 25.0 33.2 30.0 31.4 30.0 23.6 40.0 19.5 45.0 For this subset of the data, list the Y and X matrices that would be used in the matrix-based approach to regression for predicting miles per gallon from weight. Assume that the simple linear regression model yi = B0 +…
Assume that the econometric model is as follows Yt = β1 + β2X2t + β3X3t + β4X4t + β5X5t + ut You decide to investigate the relationship of the above econometric model using the null hypothesis of H0: β3 + β4 = 1 and β5 = 1. Derive the restricted regression that can be estimated from the above model The regressions are carried out on a sample of 96 quarterly observations, and the residual sums of squares (RSS) for the restricted and unrestricted regressions are 102.87 and 91.41, respectively. Perform the test. What is your conclusion?
7. Consider the simple linear regression given by Y; = B1 + B2X; + u; But instead of assuming E(ux) = 0, suppose one assume E(ux) = 3 Obtain OLS estimator B1, B2.
Find the least-squares regression line û bo + b₁ through the points (-2, 2), (3, 6), (4, 14), (7, 19), (10, 24), and then use it to find point estimates y corresponding to a = 1 and x = 6. For x = 1,9 For x = 6, y = Note:
propose a model that fulfill all five assumptions of the disturbance terms in classical linear regression
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.
2. Find the normal equations to the curve 2* = ax + bx + c %3D 2 = ax+ bx + c
Consider the linear model y=B,+B,x,+B,x,+B,x+P+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 31 44i The LM statistic 3i +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 0.17 O 0.175714 O 0.177203
a sample of 4 students was taken and information about daily pocket money in tl (Y) and spending in tl (x) was collected
b) Suppose you are given the following information for an OLS regression: Σχι X; Y = 830102,T = 22,x=416.5, y = 86.65, x = 3919654, RSS = 130.6 i) Calculate the ordinary least square regression line. Calculate SE (a) and SE (B) Perform the hypothesis test such that Ho: a = -60 versus H₁: α = -60 Perform the hypothesis test such that Ho: P = 0.4 versus H₁: B = 0.4 In both cases use a significance of 5%. ii) iii) iv)

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