Example 6.7 (Parameter estimation under unbiased estimator method) Prove that maximum likelihood estimators of Bo and B1 are the same as those obtained from ordinary least squares (OLS)?
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Q: 66. Find the geometric mean of the following distribution : Values Frequency 352 48 220 10 230 8 160...
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Q: Example 36. dx
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A: question: Okay there is a path diagram that shows the way the world is. (There are no other varia...
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1In the simple linear regression model , the Gauss Markov ( classical ) assumptions guarantee that the OLS estimator of the unknown parameters is BLUE. Among those assumptions , in order to have consistency of the OLS estimator we need ( this is a question on the necessary condition ): Question 4Select one: a. we need that the errors are not correlated with each others and that they have zero mean b. we need that the errors are homoscedastic ( all have the same variance) c. we need that the residuals are not correlated with the explanatory variables and that the residuals have zero mean d. we need that the errors have zero mean and that they are not correlated with the regressors ( no endogeneity) e. we need that the errors are homoscedastic ( all have the same variance) and not correlated with each others ( no serial correlation)In Galton’s height data (Figure 7.1, in Section 7.1), the least-squares line for predictingforearm length (y) from height (x) is y = −0.2967 + 0.2738x.a) Predict the forearm length of a man whose height is 70 in.b) How tall must a man be so that we would predict his forearm length to be 19 in.?c) All the men in a certain group have heights greater than the height computed in part(b). Can you conclude that all their forearms will be at least 19 in. long? Explain.
- 1- The number of items produced in a factory during a week is known to be a randomvariable with mean 50● Using Markov's inequality, what can you say about the probability that this week'sproduction exceeds 75?● If the variance of one week's production is equal to 25, then using Chebyshev'sinequality, what can be said about the probability that this week's production isbetween 40 and 60?What are the difficulties in estimating the following model? Use as much detail as possible in answering this question while considering the Gauss-Markov assumptions and OLS estimator. Economic productivity = β0 + β1Unemployment + β2Innovation + θiControls + ei Where unemployment is the average unemployment rate of a country and innovation is an index of R&D performance.If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y = X1 + X2 +···+ Xn is a sufficient estimator of the parameter θ.
- 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)?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.A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample?A. n = 23B. n = 22C. n = 21D. n = 20E. cannot be determined from the information given
