Consider the regression modely = a + ßx+u,where x is an endogenous variable.a) Write x₁ = x + ê; and show that = x.b) Suppose there are k valid instruments: Z1, Z2, ..., Zk.Let x₁= πo+f1zil + π2Zi2+...+îkzik. Show that the 2SLS estimator is equivalentto an IV estimator using as an instrument:Σ₁₁(&i- Ñ)(vi- V) _ Σ₁(Ri—Ñ)(Yi-Y)Ei=1(xi-x)² 21(®i- Đ)(xi-x)=[Hint: OLS first order conditions imply №₁ ê¡Â¡ = 0 and Σ¼_₁ ê¡= 0.]c) Suppose there is only one instrument z and ✰; = fo+ fizi. Show that the 2SLSestimator is numerically identical to the IV estimator:=Σ₁ (Îi—Ñ)(vi-V) – Σ₁(²₁-7)(vi-V)Σ=1(ât− x)2 Σ₁ (Z₁-7)(xi-x)*n[Hint: Use the result in (b) and plug in â; and ☎ = ñîo+â¦Z.]

Answered: Image /qna-images/answer/f3298933-9260-4d47-9456-2f6a63589a48.jpg

Answered: Consider the regression model y = 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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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.
7) Consider the following Matlab outputs for linear regression. Write the suggested regression equation, comment of the results and the quality of the model (interpret the Matlab output): mdl = Linear regression model: y -1 +x1 Estimated Coefficients: Estimate SE tStat pValue (Intercept) х1 6.9506 2.2358 3.1088 0.0020599 -0.043871 0.077609 -0.56528 0.57231 Number of observations: 300, Error degrees of freedom: 298 Root Mean Squared Error: 19.7 R-squared: 0.00107, Adjusted R-Squared -0.00228 F-statistic vs. constant model: 0.32, p-value = 0.572
A medical researcher conducted an observational study to understand the recovery rate for patients infected with the COVID-19 in Malaysia. The researcher contacted thirteen COVID-19 survivors and interviewed them regarding their recovery experience. Two of the questions asked are the recovery period (in days) and the number of days that have passed since receiving the second dose of COVID-19 vaccine prior to infection. The recorded data is summarized as (at the image files). i) Identify the dependent variable in the study. ii) Calculate the correlation coefficient and interpret its value. iii) Estimate the regression model parameters and write the estimated linear regression model. iv) Based on your answer in iii), predict the recovery period if a person is infected with COVID-19 after 200 days of receiving second dose of COVID-19 vaccine. v) Table 1 represents the incomplete ANOVA table of the study. Find the values of P, Q, R and S. vi) Test the linearity between the two variables…
ANSWER THE FOLLOWING QUESTION.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.54 cm, y = 81.35 kg, r=0.186, P-value = 0.064, and y = - 109 + 1.12x. Find the best predicted value of ŷ (weight) given an adult male who is 180 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 180 cm tall is (Round to two decimal places as needed.) kg.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.61 cm, y = 81.52 kg, r=0.271, P-value=0.006, and y = -103 +1.18x. Find the best predicted value of ŷ (weight) given an adult male who is 155 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
find the least squares regression line equation from the given data.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 193 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.59 cm, y = 81.52 kg, r= 0.416, P-value = 0.000, and y = - 102 + 1.13x. Find the best predicted value of y (weight) given an adult male who is 147 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 147 cm tall is kg. (Round to two decimal places as needed.)
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 189 cm and weights of 37 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.50 cm, y =81.41 kg, r=0.232, P-value = 0.020, and y = - 109 + 1.17x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is kg. (Round to two decimal places as needed.)
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.
2

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