[Regression Analysis] How do you solve this? 5. Suppose that we are fitting the straight line Y; = Bo+B₁; +€, but the variance of theY's now depend on the level of x; that is,V(Y₁|x₁) = ², V(Y₂|x2) = ², ···, V(Yn]£n):=0²Wnwhere the w, are known constants, often called weights. Find the maximum likelihoodestimates for 30 and 3₁. Assume that E(₂) = 0 and that Y's are Normally distributed.Show all your work and circle your final answers.

The straight line is fitted.The variance of the 's relies on the level of .weights's are normally…

Answered: 5. Suppose that we are fitting the…

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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The demand for a commodity is given by Q = β0 + β1P + u, whereQ denotes quantity, P denotes price, and u denotes factors other thanprice that determine demand. Supply for the commodity is given byQ = ϒ0 + ϒ1P + v, where v denotes factors other than price that determinesupply. Suppose that u and v both have a mean of zero, have variancesσ2u and σ2v, and are mutually uncorrelated.a. Solve the two simultaneous equations to show how Q and P dependon u and v.b. Derive the means of P and Q.c. Derive the variance of P, the variance of Q, and the covariancebetween Q and P.d. A random sample of observations of (Qi, Pi) is collected, and Qi isregressed on Pi. (That is, Qi is the regressand, and Pi is the regressor.)Suppose that the sample is very large. i. Use your answers to (b) and (c) to derive values of the regressioncoefficients. ii. A researcher uses the slope of this regression as an estimate of theslope of the demand function (β1). Is the estimated slope too largeor too small?
1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?
If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.
2- An expert estimates that the distribution parameter for durability times of parts produced with machine A in the factory is different from the distribution parameter for durability times of parts produced with machine B. Durability times of 4 parts produced from machine A and 4 parts produced from machine B are given below. Find the Mann-Whitney U value by using these data. a) 18 B) 6 NS) 16 D) 20 TO) 12
4) Here are data on the lengths of male and female roaches (in mm). Your job is to find out if there is adifference between male and female roaches (this should be two sided - why?).males 15.4 13.9 12.7 9.6 6.6 10.7 9.9 13.3 16.2 9.0 11.4 16.6 12.2females 16.7 16.3 12.8 16.9 15.1 12.8 18.7 18.3 8.6 13.6 15.3 16.2 13.4It's up to you to figure out what the best procedure is, what kind of hypotheses to use, which α to use,what test to use, and so on. Make sure you follow all the appropriate steps. You should probably use Ras you’ll get done much quicker. Remember to very clearly state your results in writing. Never turn in just an R printout .Hint: how do you decide which test to use? What kind of distributions do the data have?
A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…
In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.
Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4
Let X1, X2, ... , Xn be a random sample, normally distributed with mean μ and variance σ2If σ2 is unknown, find a minimum value for n to guarantee, with probability 0.90, that a 0.95 CI for μ will have length no more than σ/4 explain.
When a least squares line is fit to the 12 observations in the labor cost data, we obtain SSE =656, 214.3589. Calculate s2 and s (isnt n-k-1)?
Suppose X, Y, Z are iid observations from a Poisson distribution with parameter λ, which is unknown. Consider the 3 estimators T1 = X + Y − Z, T2 = 2X + Y + Z 4 , T3 = 3X + Y + Z 5 . (a) Which among the above estimators are unbiased? (b) Among the class of unbiased estimators, which has the minimum variance?
A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?

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