Problem 1. [SW 14.6] In Exercise 14.5(b) (which is copied below for your reference), suppose youpredict Y using Y/2 instead of Y. Hint: Notice that in this exercise, Y is an out-of-sample valuewith respect to the sample we have. In other words, Y is not part of the sample, so it does not enterthe formula for Y = 1/2 (Y₁ + Y₂ + ... + Y10).n(g) In a realistic setting, the value of µ is unknown. What advice would you give someone who isdeciding between using Y and Y/2?For reference, here is Exercise 14.5(b). (It is not part of this problem set, but it may be helpfulfor you to do this exercise before attempting 14.6.) Y is a random variable with mean = 2 andvariance o² = 25. Suppose you don't know the value of μ but you have access to a random sampleof size n = 10 from the same population. Let Y denote the sample mean from this random sample.You predict the value of Y using Y.(i) Show that the prediction error can be decomposed as Y -Y = (Y – µ) – (Ỹ – µ), where Y - μis the prediction error of the oracle predictor and fl Y is the error associated with using Yas an estimate of μ.(ii) Show that (Y-μ) has a mean of 0, that (Y− µ) has a mean of 0,and that Y - Y has a mean of 0.(iii) Show that Y - μ and Y - μ are uncorrelated.(iv) Show that the MSPE of Y is MSPE = E (Y − µ)² + E (Ỹ − µ)² =(v) Show that MSPE = 25 (1 + 1) = 27.5.= var (Y) + var (Y).

It is given that the sample size is n=10. The sample mean is Y=1nY1+Y2+...+Y10. The population…

Answered: Problem 1. [SW 14.6] In Exercise…

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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Wage B1 B2 educ + €, where = 1. Wage means daily wage measured in dollars. 2. educ means years of education (schooling) The regression output is given below: reg wage educ Source | SS df MS Number of obs = 100 F(2, 97) = 97.14 Model 10000.00 1 5000.00 Prob > F = 0.0000 Residual | 10000.00 98 100.00 R-squared = 0.5000 Adj R-squared = 0.4900 Total | 20000.00 99 200.00 Root MSE = 10.000 wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] educ | 10.0000 _cons | 10.0000 5.0000 10.0000 2.00 0.050 0.0000 20.0000 1.00 0.317 -20.0000 30.0000
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QUESTION 1 Consider the following ARMA model for {y,}: y,=a,+ j=1 a + - E,+ 1=1 where {e} is the residual. Which of the following assumption(s) on the residuals {E} is needed to enable forecasting with this model in practice? Oa. a. ɛ ̟ is normally distributed. O b.e E, is mean-independent of y,y,-2…….. and e Oc. and e are stochastically independent for all +s O d. All of the above. QUESTION 2 How can the validity of the assumption(s) identified in Question 1 be examined in practice? O d. Use the Breusch-Pagan test, where the null hypothesis is that the distribution is normal. O D.Use the Ljung-Box test, where the null hypothesis is that the first K autocorrelations are zero. O C. Examine the SACF and SPACF of the estimated residuals O d. Both (b) and (c).
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QUESTION 5 Assume that we estimated the following model by OLS: y=B+Bix+u. The sample size of the data is n-62. We calculated that the standard errors for B. and B. are se(B)-1 and se(p.)-2. Also, the estimates for B. and B. are- B-3 and B-5. We want to test: He: B₁ 4.5 H: Bi <4.5. for a 0.05 significance level. What is the (approximate) p-value of the test? [We denote the estimates by bold font] 0³-0.05 Ob-0.07 0 0.03 Od-0.09
Section E: The IQ scores of a sample of 15 boys randomly selected from the population of fifteen year-old boys in Victoria were recorded, and the sample mean and sample standard deviation from this sample were 106 and 4, respectively. The IQ scores of a sample of 12 girls randomly selected from the population of fifteen year-old girls in Victoria were recorded, and the sample mean and sample standard deviation from this sample were 114 and 5, respectively. Let μ₁ denote the mean IQ score for fifteen year-old boys in Victoria and let µ₂ denote the mean IQ score for fifteen year-old girls in Victoria. Researchers want to test, at the 5% level of significance, the null hypothesis - Ho: M1 - µ2 = −1 vs the alternative hypothesis Ha : µ₁ − µ₂ −1. Assume the population standard deviations of the two groups are equal and that the assumptions of a two-independent sample t-test are satisfied. Answer the following questions.
Question 3: a. Write R code to simulate n observations (X,Y) from the model: X~ N(0,5), Y|X- N (2X +3,3). (Hint: use rnorm to generate random variables from the normal distri- bution. b. Simulate 50 datasets for n = 30, and, for each dataset, fit a regression model (Y|X = Bo+ BiX+c). Make a histogram of the 50 estimates of 3₁. What are the sample mean and sample variance of these 50 estimates?
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17. What is the test statistic and its distribution for the hypothesis test stated in the preamble of Section E? X₁ X ₂ − (μ₁ −μ²), I ~ t25 – µ₂) – OT T = √² + $ n1 N₂ – µ2)¸ T X₁ X ₂ − (µμ₁ −μ₂) I ~ t25 - - OT: - s² S² + n1 N₂ Ď HD Tt26 ΟΤ , SD/√n X₁ – X₂ − (µ₁ − µ₂) - OT= T~ t26 " S² S² + n1 N₂ =
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Question 3 of 23 Step 1 of 1 Identify the population, the sample, and any population parameters or sample statistics in the given scenario. 01:28:43 In the 1960s, a poll was taken of 2617 homeowners in the United States. The average price of homes owned by those surveyed was $18,500. Keypad Keyboard Shortcuts Population: none given; Sample: 2617 homeowners polled; Sample Statistic: $18,500 Population: U.S. homeowners; Sample: 2617 homeowners polled; Population Parameter: $18,500 Population: U.S. homeowners; Sample: 2617 homeowners polled; Sample Statistic: $18,500 O Population: U.S. homeowners; Sample: none given; Population Parameter: $18,500
QUESTION 2 A survey by marketing students at KU was conducted to consider how many students attend football games regularly during the season. A random sample of 42 students was collected to estimate the proportion of students who regularly attend football games. The sample proportion was found to be 35%. Thirty-five percent is a O a. point estimate O b. sample parameter C. population parameter O d. point estimator

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