Which of the following statements hold true for the sampling distribution of and, under the least squares assumptions? (Check all that apply.)A. Bo and are unbiased estimators of Bo and B₁, respectively.B. The sampling distribution of B and B₁ is well approximated by the bivariate normal distribution if the sample is sufficiently large.DC Bo1B₁are biased estimators of Bo and B₁, respectively.D. The sampling distribution of B and B, is always well approximated by the bivariate normal distribution.andSuppose a researcher conducts an experiment with a sample size of n = 50.In this case, the normal approximations to the distributions of the OLS estimators of the researcher's regression parametersbe reliable.may notwill notwill

The statements that hold true for the sampling distribution of and under the least squares…

Answered: Which of the following statements hold…

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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Suppose X1,., Xn, for n > 1, are sampled independently from a distribution with mean u and variance o?. Consider the following four estimators for X1+ Xn 2 X1 2 п(п + 1) i=1 a. Calculate the bias of each of these estimators. b. Calculate the standard error for each estimator. c. Which estimator would you choose to use? (Give a reason for your choice).
A random sample is drawn from a population with mean U= 72 and standard deviation o = 6.0. [You may find it useful to reference the z table.) a. Is the sampling distribution of the sample mean with n= 17 andn= 45 normally distributed? O Yes, both the sample means will have a normal distribution. O No, both the sample means will not have a normal distribution. O No, only the sample mean with n=17 will have a normal distribution. O No, only the sample mean with n= 45 will have a normal distribution, b. Calculate the probability that the sample mean falls between 72 and 75 for n= 45. (Round intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) Probability 1 of 8 Next > ere to search (? A R G B
A random sample X1,X2,...,Xn is drawn from the normal distribution. i. Suppose μ is a known parameter. Find the maximum likelihood estimator for σ. ii. Find the bias and variance of the obtained estimator
The graph portrays the decision criterion for a hypothesis test for a population mean. The null hypothesis is H:u=µ. The curve is the normal curve for the test statistic under the assumption that the null hypothesis is true. Use the graph to solve the problem. A graphical display of the decision criterion follows. do 0.9 Do not reject H Reject H, 0.8- 0.7- 0.6- 05- 04 0.3- 0.2- 0.1- !0.014 -059 0.59 L18 137 236 295 3.54 2.197 Determine the rejection region. O0.014 02.197 O All z-scores that lie to the right of 2.197 OAll 2-scores that lie to the left of 2.197
In which of the following scenarios can we assume that the sampling distribution is approximately normal? I. The population distribution for a mean is approximately normal, but the sample size is 5. II. The population distribution for a mean is not normal, but the sample size is 25. III. The population distribution for a mean is not normal, but the sample size is 50. IV. The sample size for a proportion is large enough that np and n(1-p) are both 15. V. The sample size for a proportion is large enough that np and n(1-p) are both 20. a. III, IV, V b. I, III, IV, V c. I, II, III, V d. I, III, V e. I, II, III, IV, V
1. Fit a Gaussian distribution N(x,o?) to the following data. This means that we want to model and represent the given data, in a probabilistic way, using a Gaussian distribution. Then, sketch the distribution. X = [0,0,0.1,0.5,0.9,0.2 ,0.1] Hint: Find the sample mean and sample variance of the data.
R3
2. Given below is a bivariate distribution for the random variables x and y, where x is the number of car sales in a year for Car Dealership 1 and y is the number of car sales in a year for Car Dealership 2. The covariance of x and y is . f(x,y) .2 50 80 .5 30 50 .3 40 60 64 87 96 102

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