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![Suppose that in the linear model Y₁ Bo + B₁X₂ + U₁, the error u
is correlated with the regressor X; and that observations (Y₁, X₂) are
independent and identically distributed and that the fourth moments
of Y; and X; are finite. Is the OLS estimator 3₁ biased? Is it consistent?
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- Suppose that @, and ô, are unbiased estimators of the parameter 0 and that V@,) = 15 and V(@2) = 4. What is the relative efficiency of the two estimators?please answer ASAPSuppose the conditional mean function is Y = Bo + BiX + B2X² + B3X3 + U %3D where E[U]X]3D0. By mistake, a researcher omitted X^2 and X^3 terms in the regression and ran regression of Y on X and an intercept only. It turns out that covariance between X and B2X2 + B3X° is nonzero. Is the OLS estimator researcher computed consistent for beta 1? Yes, since the omitted variables are just functions of X. Yes, since the covariance between X and B2X2 + B3X is nonzero No, since the covariance between X and B2X4 + B3X° is nonzero No, since the omitted variables are negligibly small.
- 10. which of ins follouig tali mut io not true for logistic Regression ? a) If tanget do binary 5) îf target is contiuuous but covalialis are binary me une losistic regressiou. . ) If +arget io binaty ana coveriales whe alko brinary me ze lo gistie rejressidu . me use lojis tic degresionSuppose that we have two independent data sets from the same process. One was collected in the past and another was collected recently. The observations are: {(r;; Yi), i = 1, n1} and {(r;, Yi), i = n1 + 1, .. , n1 + n2}. The two models are postulated to be 2. Yi ao + a1x; + Ei, i = 1, . . , n1, %3D = Bo + B1x; + Ei; i = n1 +1,,n, where n = nị + n2. a) Express these separate models as a single model in matrix form. b) Find A and c for testing Ho : a1 =A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=3,Y=4).
- A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=4) Determine E(X) Determine VY|X=2).A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=4,Y=3). Determine fxy(X=3,Y=4). Determine fxy(X=4,Y=4).A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. A) Assuming this is regarded as a pilot study, how many children are needed in each group (assuming equal numbers in each group) to have a 95% chance of detecting a significant difference using a two-sided test with α = .05? B) Answer the question in Problem A if the investigators use a one-sided rather than a two-sided test. Suppose 40 children, both of whose parents smoke, and 50 children, neither of whose parents smoke, are recruited for the study. C) How much power would…
- A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5−9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L. A) What are the appropriate null and alternative hypotheses to compare the means of the two groups? B) What is the appropriate test procedure for the hypotheses in Problem A? C) Carry out the test in Problem B using the criticalvalue method. D) Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke.2. Suppose you are to fit a linear model which is forced to have an intercept equal to 5, of the form given by: Y₁ = 5 + B₁X₁ + &; for i = 1,2,.., n where & has mean 0 and variance o² for any value of X. a) Derive the least squares estimator, ₁ of the slope ₁. b) Find E(₁) and o² (B₁). c) Derive the maximum likelihood estimator, ₁ of the slope ₁. Is it the same as the least squares estimator? d) What is the estimator of the variance of the random error term? e) Prove whether or not it is still true that Σ₁ e₁ = 0.Q5) If the following data set obey linear regression equation, i.e. y=a+bx 3 4 5 9 11 42 38 31 28 29 a) the predicted value of y if x := 12.5 is 24.368 O 24.379 O 24.452 O 24.542 O none of all above O ४ y
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