20.a) Define the term 'unit root' and explain why it is important to test for unit root in time seriesdata before attempting to build an empirical model.b) A researcher wants to test for the presence of unit root in time-series data and decidesto use the Dickey-Fuller (DF) test. He estimates a regression of the formAyt = μ+ yt-1 + Utand obtains the estimate = -0.75 with standard error = 0.24i) Given the data, and a critical value of -2.88, perform the DF test. What are the nulland alternative hypotheses for this test? What is the main conclusion from this test?ii) Another researcher suggests that there may be a problem with this methodologysince it assumes that the disturbances are white noise. Suggest a possible sourceof difficulty and how the researcher might in practice get around it.

This question consists of two parts. In the first part, the concept of a unit root in time series…

Answered: a) Define the term 'unit root' and…

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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An article considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1900 + 1.3x, and that the standard deviation of the random deviation ϵ is 350 psi. (a) What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2000? (Round your answer to four decimal places.) (b) What is the probability that the observed value of 28-day strength will exceed 5000 psi when the value of accelerated strength is 2600? (Round your answer to four decimal places.) (c) Consider making two independent observations on 28-day strength, the first for an accelerated strength of 2000 and the second for x = 2600. What is the probability that the second observation will exceed the first by more than 1000 psi? (Round your answer to four decimal places.) (d) Let Y1 and Y2 denote observations on 28-day strength…
After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS;) on a cow's body led to a different level of milk production (MP;). The researchers estimate the OLS regression: where WS, is a binary variable of the form: WS₁ = MP = 5.36 +0.26 x WS₁, (2.23) (0.06) 1, if the th cow has white spots 0, if the th cow doesn't have white spots The 95% confidence interval for the coefficient ₁ is (₁). (Round your answers to four decimal places.) Based on this interval, we will the hypothesis P₁ = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? O A. The coefficient is the sum of the conditional expectation of the presence of white spots on a cow with respect to the average milk production. OB. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white…
N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
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?
ruan Use wage1.txt data set for this question. Consider the following regression: logtwage)-Bo-Beduc-3.exper+u. Suppose we want to test whether the return of an additional year in school will pay more than spending an additional year in the labor market Which of the following is the correct set of hypotheses for this test? Ho: 1-2 HA: 1-20 31 Ho: 1-2 HA: 1-8 270 Ho: 1-220HA: 1-³ 20 Ho: 1-2 HA: 1-820 0.91
"given a simple regression with slope b=3, s (sub y)=8, and s (sub x)= 2, and n=30. Find the standard error of the estimate."
4. A simple linear regression is fit to a dataset. Unfortunately, the corresponding ANOVA table is not complete because some quantities in the table are missing due to unknown digital errors. Calculate the missing values, denoted by "?", in the ANOVA table based on the other available values. Is this regression model significant (α = 0.05)? Source Regression Residual Total df ? ? 21 SS ? ? ? MS = SS/df ? 1.13 F-Ratio 430.65 p-value ?
We are interested in estimating the following model log(wage) = Bo + Bieduc + Bzexper + u where • wage=hourly wage, in US dollars; • educ=number of years of education; • exper=number of years of work experience. The variable ctuit is the change in college tuition facing students from age 17 to age 18 and is used as an IV for educ. We run the first stage regression for educ and get the following output: Source s df MS Number of obs 1,230 F (2, 1227) 550.19 Model 3220.84426 2 1610.42213 Prob > F 0.0000 Residual 3591.43541 1,227 2.92700523 0.4728 R-squared Adj R-squared 0.4719 Total 6812.27967 1,229 5.54294522 Root MSE 1.7108 educ Coef. Std. Err. t P>|t| [95% Conf. Interval] ctuit -.1859575 .0608175 -3.06 0.002 -.3052752 -.0666398 exper -.521161 .0157156 -33.16 0.000 -.5519933 -.4903286 _cons 18.63905 .1757961 106.03 0.000 18.29415 18.98394 Is the assumption of instrument relevance satisfied? Why yes, or why not?
You estimate a regression equation Y = a + b1X1 + b2X2 + b3X3 on a data set of 300 observations and obtain the following results: R-squared = 0.83 standard error of regression = 45.O F-statistic = 93.4 (p-value = .0007) Coefficient Estimates t-statistic for Estimate p-value in(_) a = 100.0 b1 = 25.0 12.53 (p < .001) 0.82 (p - 0.61) 4.73 (p < .01) 14.63 (p < .001) The null hypothesis that b1 = b2 = b3 = 0. b2 = 15.0 b3 = 10.0 is strongly rejected using 5% critical value cannot be rejected using 5% critical value is in the range of no clear determination using 5% critical value
Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…
Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: β1 = 0 and the alternative hypothesis Ha: β1 ≠ 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?
Explain the various concepts & tools of regression with time series data?

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